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id="toc-Urban_complex_systems" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Urban_complex_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Urban complex systems</span> </div> </a> <ul id="toc-Urban_complex_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Computational_finance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Computational_finance"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Computational finance</span> </div> </a> <ul id="toc-Computational_finance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Computational_biology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Computational_biology"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Computational biology</span> </div> </a> <ul id="toc-Computational_biology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Complex_systems_theory" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Complex_systems_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Complex systems theory</span> </div> </a> <ul id="toc-Complex_systems_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Computational_science_and_engineering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Computational_science_and_engineering"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Computational science and engineering</span> </div> </a> <ul id="toc-Computational_science_and_engineering-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Methods_and_algorithms" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Methods_and_algorithms"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Methods and algorithms</span> </div> </a> <ul id="toc-Methods_and_algorithms-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Conferences_and_journals" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Conferences_and_journals"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Conferences and journals</span> </div> </a> <ul id="toc-Conferences_and_journals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Education" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Education"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Education</span> </div> </a> <button aria-controls="toc-Education-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Education subsection</span> </button> <ul id="toc-Education-sublist" class="vector-toc-list"> <li id="toc-Subfields" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Subfields"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Subfields</span> </div> </a> <ul id="toc-Subfields-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Additional_sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Additional_sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Additional sources</span> </div> </a> <ul id="toc-Additional_sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div 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mw-first-heading"><span class="mw-page-title-main">Computational science</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%97%E0%A6%A3%E0%A6%A8%E0%A6%BE%E0%A6%AE%E0%A7%82%E0%A6%B2%E0%A6%95_%E0%A6%AC%E0%A6%BF%E0%A6%9C%E0%A7%8D%E0%A6%9E%E0%A6%BE%E0%A6%A8" title="পরিগণনামূলক বিজ্ঞান – Bangla" lang="bn" hreflang="bn" data-title="পরিগণনামূলক বিজ্ঞান" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Ci%C3%A8ncia_computacional" title="Ciència computacional – Catalan" lang="ca" hreflang="ca" data-title="Ciència computacional" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Wissenschaftliches_Rechnen" title="Wissenschaftliches Rechnen – German" lang="de" hreflang="de" data-title="Wissenschaftliches Rechnen" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Arvutusteadus" title="Arvutusteadus – Estonian" lang="et" hreflang="et" data-title="Arvutusteadus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Computaci%C3%B3n_cient%C3%ADfica" title="Computación científica – Spanish" lang="es" hreflang="es" data-title="Computación científica" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%D9%84%D9%85_%D9%85%D8%AD%D8%A7%D8%B3%D8%A8%D9%87" title="علم محاسبه – Persian" lang="fa" hreflang="fa" data-title="علم محاسبه" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Sciences_num%C3%A9riques" title="Sciences numériques – French" lang="fr" hreflang="fr" data-title="Sciences numériques" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B3%84%EC%82%B0%EA%B3%BC%ED%95%99" title="계산과학 – Korean" lang="ko" hreflang="ko" data-title="계산과학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%95%E0%A4%B2%E0%A4%A8_%E0%A4%B5%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%9E%E0%A4%BE%E0%A4%A8" title="परिकलन विज्ञान – Hindi" lang="hi" hreflang="hi" data-title="परिकलन विज्ञान" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Scienza_computazionale" title="Scienza computazionale – Italian" lang="it" hreflang="it" data-title="Scienza computazionale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sains_pengiraan" title="Sains pengiraan – Malay" lang="ms" hreflang="ms" data-title="Sains pengiraan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Cumputa%C3%A7on_cient%C3%ADfica" title="Cumputaçon científica – Mirandese" lang="mwl" hreflang="mwl" data-title="Cumputaçon científica" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-mn badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BE%D1%86%D0%BE%D0%BD_%D0%B1%D0%BE%D0%B4%D0%BE%D1%85_%D1%88%D0%B8%D0%BD%D0%B6%D0%BB%D1%8D%D1%85_%D1%83%D1%85%D0%B0%D0%B0%D0%BD" title="Тооцон бодох шинжлэх ухаан – Mongolian" lang="mn" hreflang="mn" data-title="Тооцон бодох шинжлэх ухаан" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Computationele_wetenschap" title="Computationele wetenschap – Dutch" lang="nl" hreflang="nl" data-title="Computationele wetenschap" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%A8%88%E7%AE%97%E7%A7%91%E5%AD%A6" title="計算科学 – Japanese" lang="ja" hreflang="ja" data-title="計算科学" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Computa%C3%A7%C3%A3o_cient%C3%ADfica" title="Computação científica – Portuguese" lang="pt" hreflang="pt" data-title="Computação científica" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A0%D0%B0%D1%87%D1%83%D0%BD%D0%B0%D1%80%D1%81%D0%BA%D0%B0_%D0%BD%D0%B0%D1%83%D0%BA%D0%B0" title="Рачунарска наука – Serbian" lang="sr" hreflang="sr" data-title="Рачунарска наука" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Laskennallinen_tiede" title="Laskennallinen tiede – Finnish" lang="fi" hreflang="fi" data-title="Laskennallinen tiede" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%B1%E0%AE%BF%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D_%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%AE%E0%AF%88" title="அறிவியல் கணிமை – Tamil" lang="ta" hreflang="ta" data-title="அறிவியல் கணிமை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Bilimsel_hesaplama" title="Bilimsel hesaplama – Turkish" lang="tr" hreflang="tr" data-title="Bilimsel hesaplama" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Khoa_h%E1%BB%8Dc_t%C3%ADnh_to%C3%A1n" title="Khoa học tính toán – Vietnamese" lang="vi" hreflang="vi" data-title="Khoa học tính toán" data-language-autonym="Tiếng Việt" 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In particular, the article does not describe the idea of computational science at a concrete level.<span class="hide-when-compact"> Please help <a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarify the article</a>. There might be a discussion about this on <a href="/wiki/Talk:Computational_science" title="Talk:Computational science">the talk page</a>.</span> <span class="date-container"><i>(<span class="date">December 2021</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p> <b>Computational science</b>, also known as <b>scientific computing</b>, <b>technical computing</b> or <b>scientific computation</b> (<b>SC</b>), is a division of science, and more specifically the <a href="/wiki/Computer_science" title="Computer science">Computer Sciences</a>, which uses advanced <a href="/wiki/Computing" title="Computing">computing</a> capabilities to understand and solve complex physical problems. While this typically extends into <a href="/wiki/Visual_computing" title="Visual computing">visual computation</a>, this field of study typically includes: </p> <ul><li><a href="/wiki/Algorithm" title="Algorithm">Algorithms</a> (<a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical</a> and non-numerical): <a href="/wiki/Mathematical_model" title="Mathematical model">mathematical models</a>, <a href="/wiki/Computational_model" title="Computational model">computational models</a>, and <a href="/wiki/Computer_simulation" title="Computer simulation">computer simulations</a> developed to solve <a href="/wiki/Sciences" class="mw-redirect" title="Sciences">sciences</a> (e.g, <a href="/wiki/Computational_physics" title="Computational physics">physical</a>, <a href="/wiki/Computational_biology" title="Computational biology">biological</a>, and <a href="/wiki/Computational_sociology" title="Computational sociology">social</a>), <a href="/wiki/Engineering" title="Engineering">engineering</a>, and <a href="/wiki/Humanities" title="Humanities">humanities</a> problems</li> <li><a href="/wiki/Computer_hardware" title="Computer hardware">Computer hardware</a> that develops and optimizes the advanced system <a href="/wiki/Computer_hardware" title="Computer hardware">hardware</a>, <a href="/wiki/Firmware" title="Firmware">firmware</a>, <a href="/wiki/Computer_network" title="Computer network">networking</a>, and <a href="/wiki/Data_management" title="Data management">data management</a> components needed to solve computationally demanding problems</li> <li>The computing infrastructure that supports both the science and engineering problem solving and the developmental computer and <a href="/wiki/Information_science" title="Information science">information science</a></li></ul> <p>In practical use, it is typically the application of <a href="/wiki/Computer_simulation" title="Computer simulation">computer simulation</a> and other forms of <a href="/wiki/Computation" title="Computation">computation</a> from <a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical analysis</a> and <a href="/wiki/Theoretical_computer_science" title="Theoretical computer science">theoretical computer science</a> to solve problems in various scientific disciplines. The field is different from theory and laboratory experiments, which are the traditional forms of science and <a href="/wiki/Engineering" title="Engineering">engineering</a>. The scientific computing approach is to gain understanding through the analysis of mathematical models implemented on <a href="/wiki/Computer" title="Computer">computers</a>. Scientists and engineers develop <a href="/wiki/Computer_programs" class="mw-redirect" title="Computer programs">computer programs</a> and <a href="/wiki/Application_software" title="Application software">application software</a> that model systems being studied and run these programs with various sets of input parameters. The essence of computational science is the application of numerical algorithms<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Computational_mathematics" title="Computational mathematics">computational mathematics</a>. In some cases, these models require massive amounts of calculations (usually <a href="/wiki/Floating-point" class="mw-redirect" title="Floating-point">floating-point</a>) and are often executed on <a href="/wiki/Supercomputer" title="Supercomputer">supercomputers</a> or <a href="/wiki/Distributed_computing" title="Distributed computing">distributed computing</a> platforms.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="check whether this is sourced in the body (December 2021)">verification needed</span></a></i>]</sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="The_computational_scientist">The computational scientist</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=1" title="Edit section: The computational scientist"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ways_to_study_a_system.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Ways_to_study_a_system.png/220px-Ways_to_study_a_system.png" decoding="async" width="220" height="127" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Ways_to_study_a_system.png/330px-Ways_to_study_a_system.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Ways_to_study_a_system.png/440px-Ways_to_study_a_system.png 2x" data-file-width="2370" data-file-height="1368" /></a><figcaption>Ways to study a system</figcaption></figure> <p>The term <a href="/wiki/Computational_scientist" title="Computational scientist">computational scientist</a> is used to describe someone skilled in scientific computing. Such a person is usually a scientist, an engineer, or an applied mathematician who applies <a href="/wiki/High-performance_computing" title="High-performance computing">high-performance computing</a> in different ways to advance the state-of-the-art in their respective applied disciplines in physics, chemistry, or engineering. </p><p>Computational science is now commonly considered a third mode of <a href="/wiki/Science" title="Science">science</a> <sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2022)">citation needed</span></a></i>]</sup>, complementing and adding to <a href="/wiki/Experimentation" class="mw-redirect" title="Experimentation">experimentation</a>/<a href="/wiki/Observation" title="Observation">observation</a> and <a href="/wiki/Theory" title="Theory">theory</a> (see image).<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Here, one defines a <a href="/wiki/System" title="System">system</a> as a potential source of data,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> an <a href="/wiki/Experiment" title="Experiment">experiment</a> as a process of extracting data from a system by exerting it through its inputs<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and a <a href="/wiki/Computer_model" class="mw-redirect" title="Computer model">model</a> (<i>M</i>) for a system (<i>S</i>) and an experiment (<i>E</i>) as anything to which <i>E</i> can be applied in order to answer questions about <i>S</i>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> A computational scientist should be capable of: </p> <ul><li>recognizing <b>complex problems</b></li> <li>adequately <b>conceptualizing</b> the system containing these problems</li> <li>designing a framework of algorithms suitable for studying this system: the <b>simulation</b></li> <li>choosing a suitable <b>computing infrastructure</b> (<a href="/wiki/Parallel_computing" title="Parallel computing">parallel computing</a>/<a href="/wiki/Grid_computing" title="Grid computing">grid computing</a>/<a href="/wiki/Supercomputer" title="Supercomputer">supercomputers</a>)</li> <li>hereby, maximizing the <b>computational power</b> of the simulation</li> <li>assessing to what level the output of the simulation resembles the systems: the model is <b>validated</b></li> <li>adjusting the conceptualization of the system accordingly</li> <li>repeat the cycle until a suitable level of validation is obtained: the computational scientist trusts that the simulation generates adequately realistic results for the system under the studied conditions</li></ul> <p>Substantial effort in computational sciences has been devoted to developing algorithms, efficient implementation in programming languages, and validating computational results. A collection of problems and solutions in computational science can be found in Steeb, Hardy, Hardy, and Stoop (2004).<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>Philosophers of science addressed the question to what degree computational science qualifies as science, among them Humphreys<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> and Gelfert.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> They address the general question of epistemology: how does gain insight from such computational science approaches? Tolk<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> uses these insights to show the epistemological constraints of computer-based simulation research. As computational science uses mathematical models representing the underlying theory in executable form, in essence, they apply modeling (theory building) and simulation (implementation and execution). While simulation and computational science are our most sophisticated way to express our knowledge and understanding, they also come with all constraints and limits already known for computational solutions.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Applications_of_computational_science">Applications of computational science</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=2" title="Edit section: Applications of computational science"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Problem domains for computational science/scientific computing include: </p> <div class="mw-heading mw-heading3"><h3 id="Predictive_computational_science">Predictive computational science</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=3" title="Edit section: Predictive computational science"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Predictive computational science is a scientific discipline concerned with the formulation, calibration, numerical solution, and validation of mathematical models designed to predict specific aspects of physical events, given initial and boundary conditions, and a set of characterizing parameters and associated uncertainties.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> In typical cases, the predictive statement is formulated in terms of probabilities. For example, given a mechanical component and a periodic loading condition, "the probability is (say) 90% that the number of cycles at failure (Nf) will be in the interval N1<Nf<N2".<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Urban_complex_systems">Urban complex systems</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=4" title="Edit section: Urban complex systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cities are massively complex systems created by humans, made up of humans, and governed by humans. Trying to predict, understand and somehow shape the development of cities in the future requires complex thinking and computational models and simulations to help mitigate challenges and possible disasters. The focus of research in urban complex systems is, through modeling and simulation, to build a greater understanding of city dynamics and help prepare for the coming <a href="/wiki/Urbanization" title="Urbanization">urbanization</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Computational_finance">Computational finance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=5" title="Edit section: Computational finance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Computational_finance" title="Computational finance">Computational finance</a></div> <p>In <a href="/wiki/Financial_market" title="Financial market">financial markets</a>, huge volumes of interdependent assets are traded by a large number of interacting market participants in different locations and time zones. Their behavior is of unprecedented complexity and the characterization and measurement of the risk inherent to this highly diverse set of instruments is typically based on complicated <a href="/wiki/Mathematical_model" title="Mathematical model">mathematical</a> and <a href="/wiki/Computational_model" title="Computational model">computational models</a>. Solving these models exactly in closed form, even at a single instrument level, is typically not possible, and therefore we have to look for efficient <a href="/wiki/Numerical_algorithm" class="mw-redirect" title="Numerical algorithm">numerical algorithms</a>. This has become even more urgent and complex recently, as the credit crisis<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Avoid_weasel_words" class="mw-redirect" title="Wikipedia:Avoid weasel words"><span title="The material near this tag possibly uses too vague attribution or weasel words. (December 2021)">which?</span></a></i>]</sup> has clearly<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag may use weasel words or too-vague attribution. (December 2021)">according to whom?</span></a></i>]</sup> demonstrated the role of cascading effects<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Avoid_weasel_words" class="mw-redirect" title="Wikipedia:Avoid weasel words"><span title="The material near this tag possibly uses too vague attribution or weasel words. (December 2021)">which?</span></a></i>]</sup> going from single instruments through portfolios of single institutions to even the interconnected trading network. Understanding this requires a multi-scale and holistic approach where interdependent risk factors such as market, credit, and liquidity risk are modeled simultaneously and at different interconnected scales.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Computational_biology">Computational biology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=6" title="Edit section: Computational biology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Computational_biology" title="Computational biology">Computational biology</a></div> <p>Exciting new developments in <a href="/wiki/Biotechnology" title="Biotechnology">biotechnology</a> are now revolutionizing biology and <a href="/wiki/Biomedical_research" class="mw-redirect" title="Biomedical research">biomedical research</a>. Examples of these techniques are <a href="/wiki/DNA_sequencing" title="DNA sequencing">high-throughput sequencing</a>, high-throughput <a href="/wiki/Real-time_polymerase_chain_reaction" title="Real-time polymerase chain reaction">quantitative PCR</a>, intra-cellular imaging, <a href="/wiki/In_situ_hybridization" title="In situ hybridization">in-situ hybridization</a> of gene expression, three-dimensional imaging techniques like <a href="/wiki/Light_sheet_fluorescence_microscopy" title="Light sheet fluorescence microscopy">Light Sheet Fluorescence Microscopy</a>, and <a href="/wiki/Optical_projection_tomography" title="Optical projection tomography">Optical Projection (micro)-Computer Tomography</a>. Given the massive amounts of complicated data that is generated by these techniques, their meaningful interpretation, and even their storage, form major challenges calling for new approaches. Going beyond current bioinformatics approaches, <a href="/wiki/Computational_biology" title="Computational biology">computational biology</a> needs to develop new methods to discover meaningful patterns in these large data sets. Model-based reconstruction of <a href="/wiki/Gene_regulatory_network" title="Gene regulatory network">gene networks</a> can be used to organize the gene expression data in a systematic way and to guide future data collection. A major challenge here is to understand how gene regulation is controlling fundamental biological processes like <a href="/wiki/Biomineralization" title="Biomineralization">biomineralization</a> and <a href="/wiki/Embryogenesis" class="mw-redirect" title="Embryogenesis">embryogenesis</a>. The sub-processes like <a href="/wiki/Gene_regulation" class="mw-redirect" title="Gene regulation">gene regulation</a>, <a href="/wiki/Organic_compound" title="Organic compound">organic molecules</a> interacting with the mineral deposition process, <a href="/wiki/Cell_(biology)" title="Cell (biology)">cellular processes</a>, <a href="/wiki/Physiology" title="Physiology">physiology</a>, and other processes at the tissue and environmental levels are linked. Rather than being directed by a central control mechanism, biomineralization and embryogenesis can be viewed as an emergent behavior resulting from a complex system in which several sub-processes on very different <a href="/wiki/Temporal_scales" title="Temporal scales">temporal</a> and <a href="/wiki/Spatial_scale" title="Spatial scale">spatial scales</a> (ranging from nanometer and nanoseconds to meters and years) are connected into a multi-scale system. One of the few available options<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Avoid_weasel_words" class="mw-redirect" title="Wikipedia:Avoid weasel words"><span title="The material near this tag possibly uses too vague attribution or weasel words. (December 2021)">which?</span></a></i>]</sup> to understand such systems is by developing a <a href="/wiki/Multiscale_modeling" title="Multiscale modeling">multi-scale model</a> of the system.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Complex_systems_theory">Complex systems theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=7" title="Edit section: Complex systems theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Complex_systems" class="mw-redirect" title="Complex systems">Complex systems</a></div> <p>Using <a href="/wiki/Information_theory" title="Information theory">information theory</a>, <a href="/wiki/Non-equilibrium_thermodynamics" title="Non-equilibrium thermodynamics">non-equilibrium dynamics</a>, and explicit simulations, computational systems theory tries to uncover the true nature of <a href="/wiki/Complex_adaptive_system" title="Complex adaptive system">complex adaptive systems</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Computational_science_and_engineering">Computational science and engineering</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=8" title="Edit section: Computational science and engineering"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Computational_engineering" title="Computational engineering">Computational engineering</a></div> <p>Computational science and engineering (CSE) is a relatively new<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers" title="Wikipedia:Manual of Style/Dates and numbers"><span title="This term requires quantification. (December 2021)">quantify</span></a></i>]</sup> discipline that deals with the development and application of computational models and simulations, often coupled with <a href="/wiki/High-performance_computing" title="High-performance computing">high-performance computing</a>, to solve complex physical problems arising in engineering analysis and design (computational engineering) as well as natural phenomena (computational science). CSE has become accepted amongst scientists, engineers and academics as the "third mode of discovery" (next to theory and experimentation).<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> In many fields, computer simulation is integral and therefore essential to business and research. Computer simulation provides the capability to enter fields that are either inaccessible to traditional experimentation or where carrying out traditional empirical inquiries is prohibitively expensive. CSE should neither be confused with pure <a href="/wiki/Computer_science" title="Computer science">computer science</a>, nor with <a href="/wiki/Computer_engineering" title="Computer engineering">computer engineering</a>, although a wide domain in the former is used in CSE (e.g., certain algorithms, data structures, parallel programming, high-performance computing), and some problems in the latter can be modeled and solved with CSE methods (as an application area).<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Methods_and_algorithms">Methods and algorithms</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=9" title="Edit section: Methods and algorithms"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Algorithms and mathematical methods used in computational science are varied. Commonly applied methods include: </p> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Computer_algebra" title="Computer algebra">Computer algebra</a>,<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> including symbolic computation in fields such as statistics, equation solving, algebra, calculus, geometry, linear algebra, tensor analysis (multilinear algebra), optimization</li> <li><a href="/wiki/Numerical_analysis" title="Numerical analysis">Numerical analysis</a>,<sup id="cite_ref-stoer_17-0" class="reference"><a href="#cite_note-stoer-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-conte_18-0" class="reference"><a href="#cite_note-conte-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-green_19-0" class="reference"><a href="#cite_note-green-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-linz_20-0" class="reference"><a href="#cite_note-linz-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> including <a href="/wiki/Computing" title="Computing">Computing</a> derivatives by <a href="/wiki/Finite_difference" title="Finite difference">finite differences</a> <ul><li>Application of <a href="/wiki/Taylor_series" title="Taylor series">Taylor series</a> as convergent and asymptotic series</li> <li><a href="/wiki/Computing" title="Computing">Computing</a> derivatives by <a href="/wiki/Automatic_differentiation" title="Automatic differentiation">Automatic differentiation</a> (AD)</li> <li><a href="/wiki/Finite_element_method" title="Finite element method">Finite element method</a> for solving PDEs<sup id="cite_ref-bs_21-0" class="reference"><a href="#cite_note-bs-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-or_22-0" class="reference"><a href="#cite_note-or-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li>High order difference approximations via <a href="/wiki/Taylor_series" title="Taylor series">Taylor series</a> and <a href="/wiki/Richardson_extrapolation" title="Richardson extrapolation">Richardson extrapolation</a></li> <li><a href="/wiki/Methods_of_integration" class="mw-redirect" title="Methods of integration">Methods of integration</a><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> on a uniform <a href="/wiki/Mesh_(mathematics)" class="mw-redirect" title="Mesh (mathematics)">mesh</a>: <a href="/wiki/Rectangle_rule" class="mw-redirect" title="Rectangle rule">rectangle rule</a> (also called <i>midpoint rule</i>), <a href="/wiki/Trapezoid_rule" class="mw-redirect" title="Trapezoid rule">trapezoid rule</a>, <a href="/wiki/Simpson%27s_rule" title="Simpson's rule">Simpson's rule</a></li> <li><a href="/wiki/Runge%E2%80%93Kutta_methods" title="Runge–Kutta methods">Runge–Kutta methods</a> for solving ordinary differential equations</li> <li><a href="/wiki/Newton%27s_method" title="Newton's method">Newton's method</a><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup></li></ul></li> <li><a href="/wiki/Discrete_Fourier_transform" title="Discrete Fourier transform">Discrete Fourier transform</a></li> <li><a href="/wiki/Monte_Carlo_method" title="Monte Carlo method">Monte Carlo methods</a><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Numerical_linear_algebra" title="Numerical linear algebra">Numerical linear algebra</a>,<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> including decompositions and <a href="/wiki/Eigenvalue_algorithm" title="Eigenvalue algorithm">eigenvalue algorithms</a></li> <li><a href="/wiki/Linear_programming" title="Linear programming">Linear programming</a><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Branch_and_cut" title="Branch and cut">Branch and cut</a></li> <li><a href="/wiki/Branch_and_bound" title="Branch and bound">Branch and bound</a></li> <li><a href="/wiki/Molecular_dynamics" title="Molecular dynamics">Molecular dynamics</a>, <a href="/wiki/Car%E2%80%93Parrinello_molecular_dynamics" title="Car–Parrinello molecular dynamics">Car–Parrinello molecular dynamics</a></li> <li><a href="/wiki/Space_mapping" title="Space mapping">Space mapping</a></li> <li><a href="/wiki/Time_stepping" class="mw-redirect" title="Time stepping">Time stepping</a> methods for dynamical systems</li></ul> </div> <p>Historically and today, Fortran remains popular for most applications of scientific computing.<sup id="cite_ref-ars_32-0" class="reference"><a href="#cite_note-ars-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-princeton_33-0" class="reference"><a href="#cite_note-princeton-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> Other <a href="/wiki/Programming_language" title="Programming language">programming languages</a> and <a href="/wiki/Computer_algebra_systems" class="mw-redirect" title="Computer algebra systems">computer algebra systems</a> commonly used for the more mathematical aspects of scientific computing applications include <a href="/wiki/GNU_Octave" title="GNU Octave">GNU Octave</a>, <a href="/wiki/Haskell_(programming_language)" class="mw-redirect" title="Haskell (programming language)">Haskell</a>,<sup id="cite_ref-ars_32-1" class="reference"><a href="#cite_note-ars-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Julia_(programming_language)" title="Julia (programming language)">Julia</a>,<sup id="cite_ref-ars_32-2" class="reference"><a href="#cite_note-ars-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Maple_(software)" title="Maple (software)">Maple</a>,<sup id="cite_ref-princeton_33-1" class="reference"><a href="#cite_note-princeton-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Mathematica" class="mw-redirect" title="Mathematica">Mathematica</a>,<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> <a href="/wiki/MATLAB" title="MATLAB">MATLAB</a>,<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-gh_40-0" class="reference"><a href="#cite_note-gh-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-bf_41-0" class="reference"><a href="#cite_note-bf-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Python_(programming_language)" title="Python (programming language)">Python</a> (with third-party <a href="/wiki/SciPy" title="SciPy">SciPy</a> library<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup>), <a href="/wiki/Perl" title="Perl">Perl</a> (with third-party <a href="/wiki/Perl_Data_Language" title="Perl Data Language">PDL</a> library),<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2008)">citation needed</span></a></i>]</sup> <a href="/wiki/R_(programming_language)" title="R (programming language)">R</a>,<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Scilab" title="Scilab">Scilab</a>,<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/TK_Solver" title="TK Solver">TK Solver</a>. The more computationally intensive aspects of scientific computing will often use some variation of <a href="/wiki/C_(programming_language)" title="C (programming language)">C</a> or <a href="/wiki/Fortran" title="Fortran">Fortran</a> and optimized algebra libraries such as <a href="/wiki/BLAS" class="mw-redirect" title="BLAS">BLAS</a> or <a href="/wiki/LAPACK" title="LAPACK">LAPACK</a>. In addition, <a href="/wiki/Parallel_computing" title="Parallel computing">parallel computing</a> is heavily used in scientific computing to find solutions of large problems in a reasonable amount of time. In this framework, the problem is either divided over many cores on a single CPU node (such as with <a href="/wiki/OpenMP" title="OpenMP">OpenMP</a>), divided over many CPU nodes networked together (such as with <a href="/wiki/Message_Passing_Interface" title="Message Passing Interface">MPI</a>), or is run on one or more <a href="/wiki/Graphics_processing_unit" title="Graphics processing unit">GPUs</a> (typically using either <a href="/wiki/CUDA" title="CUDA">CUDA</a> or <a href="/wiki/OpenCL" title="OpenCL">OpenCL</a>). </p><p>Computational science application programs often model real-world changing conditions, such as weather, airflow around a plane, automobile body distortions in a crash, the motion of stars in a galaxy, an explosive device, etc. Such programs might create a 'logical mesh' in computer memory where each item corresponds to an area in space and contains information about that space relevant to the model. For example, in <a href="/wiki/Numerical_weather_prediction" title="Numerical weather prediction">weather models</a>, each item might be a square kilometer; with land elevation, current wind direction, humidity, temperature, pressure, etc. The program would calculate the likely next state based on the current state, in simulated time steps, solving differential equations that describe how the system operates, and then repeat the process to calculate the next state.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2021)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading2"><h2 id="Conferences_and_journals">Conferences and journals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=10" title="Edit section: Conferences and journals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 2001, the <i>International Conference on Computational Science (ICCS)</i> was first organized. Since then, it has been organized yearly. ICCS is an A-rank conference in the <a href="/wiki/CORE_ranking" class="mw-redirect" title="CORE ranking">CORE ranking</a>.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p><p>The <i>Journal of Computational Science</i> published its first issue in May 2010.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> The <i>Journal of Open Research Software</i> was launched in 2012<i>.</i><sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/ReScience_C" title="ReScience C">ReScience C</a> initiative, which is dedicated to replicating computational results, was started on <a href="/wiki/GitHub" title="GitHub">GitHub</a> in 2015.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Education">Education</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=11" title="Edit section: Education"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At some institutions, a specialization in scientific computation can be earned as a "minor" within another program (which may be at varying levels). However, there are increasingly many <a href="/wiki/Bachelor%27s_degree" title="Bachelor's degree">bachelor's</a>, <a href="/wiki/Master%27s_degree" title="Master's degree">master's</a>, and <a href="/wiki/Doctoral_degree" class="mw-redirect" title="Doctoral degree">doctoral</a> programs in computational science. The joint degree program master program computational science at the <a href="/wiki/University_of_Amsterdam" title="University of Amsterdam">University of Amsterdam</a> and the <span title="Dutch-language text"><span lang="nl" style="font-style: normal;"><a href="/wiki/Vrije_Universiteit_Amsterdam" title="Vrije Universiteit Amsterdam">Vrije Universiteit</a></span></span> in computational science was first offered in 2004. In this program, students: </p> <ul><li>learn to build computational models from real-life observations;</li> <li>develop skills in turning these models into computational structures and in performing large-scale simulations;</li> <li>learn theories<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Avoid_weasel_words" class="mw-redirect" title="Wikipedia:Avoid weasel words"><span title="The material near this tag possibly uses too vague attribution or weasel words. (December 2021)">which?</span></a></i>]</sup> that will give a firm basis for the analysis of complex systems;</li> <li>learn to analyze the results of simulations in a virtual laboratory using advanced numerical algorithms.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Writing_better_articles#Stay_on_topic" title="Wikipedia:Writing better articles"><span title="The material near this tag may contain information that is not relevant to the article's main topic. (December 2021)">relevant?</span></a></i>]</sup></li></ul> <p><a href="/wiki/ETH_Zurich" title="ETH Zurich">ETH Zurich</a> offers a bachelor's and master's degree in Computational Science and Engineering. The degree equips students with the ability to understand scientific problem and apply numerical methods to solve such problems. The directions of specializations include Physics, Chemistry, Biology and other Scientific and Engineering disciplines. </p><p><a href="/wiki/George_Mason_University" title="George Mason University">George Mason University</a> has offered a multidisciplinary doctorate Ph.D. program in Computational Sciences and Informatics starting from 1992.<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p><p>The School of Computational and Integrative Sciences, <a href="/wiki/Jawaharlal_Nehru_University" title="Jawaharlal Nehru University">Jawaharlal Nehru University</a> (erstwhile School of Information Technology<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag needs to be fact-checked with the cited source(s). (December 2021)">verification needed</span></a></i>]</sup>) also offers<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="the link is dead (December 2021)">verification needed</span></a></i>]</sup> a vibrant master's science program for computational science with two specialties: <a href="/wiki/Computational_biology" title="Computational biology">Computational Biology</a> and <a href="/wiki/Complex_Systems" class="mw-redirect" title="Complex Systems">Complex Systems</a>.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Subfields">Subfields</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=12" title="Edit section: Subfields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 15em;"> <ul><li><a href="/wiki/Bioinformatics" title="Bioinformatics">Bioinformatics</a></li> <li><a href="/wiki/Car%E2%80%93Parrinello_molecular_dynamics" title="Car–Parrinello molecular dynamics">Car–Parrinello molecular dynamics</a></li> <li><a href="/wiki/Cheminformatics" title="Cheminformatics">Cheminformatics</a></li> <li><a href="/wiki/Chemometrics" title="Chemometrics">Chemometrics</a></li> <li><a href="/wiki/Computational_archaeology" title="Computational archaeology">Computational archaeology</a></li> <li><a href="/wiki/Computational_astrophysics" title="Computational astrophysics">Computational astrophysics</a></li> <li><a href="/wiki/Computational_biology" title="Computational biology">Computational biology</a></li> <li><a href="/wiki/Computational_chemistry" title="Computational chemistry">Computational chemistry</a></li> <li><a href="/wiki/Computational_materials_science" title="Computational materials science">Computational materials science</a></li> <li><a href="/wiki/Computational_economics" title="Computational economics">Computational economics</a></li> <li><a href="/wiki/Computational_electromagnetics" title="Computational electromagnetics">Computational electromagnetics</a></li> <li><a href="/wiki/Computational_engineering" title="Computational engineering">Computational engineering</a></li> <li><a href="/wiki/Computational_finance" title="Computational finance">Computational finance</a></li> <li><a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">Computational fluid dynamics</a></li> <li><a href="/wiki/Computational_forensics" class="mw-redirect" title="Computational forensics">Computational forensics</a></li> <li><a href="/wiki/Computational_geophysics" title="Computational geophysics">Computational geophysics</a></li> <li><a href="/wiki/Computational_history" title="Computational history">Computational history</a></li> <li><a href="/wiki/Computational_informatics" title="Computational informatics">Computational informatics</a></li> <li><a href="/wiki/Computational_intelligence" title="Computational intelligence">Computational intelligence</a></li> <li><a href="/wiki/Computational_law" title="Computational law">Computational law</a></li> <li><a href="/wiki/Computational_linguistics" title="Computational linguistics">Computational linguistics</a></li> <li><a href="/wiki/Computational_mathematics" title="Computational mathematics">Computational mathematics</a></li> <li><a href="/wiki/Computational_mechanics" title="Computational mechanics">Computational mechanics</a></li> <li><a href="/wiki/Computational_neuroscience" title="Computational neuroscience">Computational neuroscience</a></li> <li><a href="/wiki/Computational_particle_physics" title="Computational particle physics">Computational particle physics</a></li> <li><a href="/wiki/Computational_physics" title="Computational physics">Computational physics</a></li> <li><a href="/wiki/Computational_sociology" title="Computational sociology">Computational sociology</a></li> <li><a href="/wiki/Computational_statistics" title="Computational statistics">Computational statistics</a></li> <li><a href="/wiki/Computational_sustainability" title="Computational sustainability">Computational sustainability</a></li> <li><a href="/wiki/Computer_algebra" title="Computer algebra">Computer algebra</a></li> <li><a href="/wiki/Computer_simulation" title="Computer simulation">Computer simulation</a></li> <li><a href="/wiki/Financial_modeling" title="Financial modeling">Financial modeling</a></li> <li><a href="/wiki/Geographic_information_science" title="Geographic information science">Geographic information science</a> <ul><li><a href="/wiki/Geographic_information_system" title="Geographic information system">Geographic information system</a> (GIS)</li></ul></li> <li><a href="/wiki/High-performance_computing" title="High-performance computing">High-performance computing</a></li> <li><a href="/wiki/Machine_learning" title="Machine learning">Machine learning</a></li> <li><a href="/wiki/Network_theory" title="Network theory">Network analysis</a></li> <li><a href="/wiki/Neuroinformatics" title="Neuroinformatics">Neuroinformatics</a></li> <li><a href="/wiki/Numerical_linear_algebra" title="Numerical linear algebra">Numerical linear algebra</a></li> <li><a href="/wiki/Numerical_weather_prediction" title="Numerical weather prediction">Numerical weather prediction</a></li> <li><a href="/wiki/Pattern_recognition" title="Pattern recognition">Pattern recognition</a></li> <li><a href="/wiki/Scientific_visualization" title="Scientific visualization">Scientific visualization</a></li> <li><a href="/wiki/Simulation" title="Simulation">Simulation</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=13" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 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.references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Nonweiler T. R., 1986. 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Jose Paez, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=gtlaWucfu3YC">A Survey of Computational Physics: Introductory Computational Science</a>, <a href="/wiki/Princeton_University_Press" title="Princeton University Press">Princeton University Press</a> (2008)</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Computational_science&action=edit&section=16" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 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class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Differentiable_computing" title="Template:Differentiable computing"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Differentiable_computing" title="Template talk:Differentiable computing"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Differentiable_computing" title="Special:EditPage/Template:Differentiable computing"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Differentiable_computing254" style="font-size:114%;margin:0 4em">Differentiable computing</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Differentiable_function" title="Differentiable function">General</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><b><a href="/wiki/Differentiable_programming" title="Differentiable programming">Differentiable programming</a></b></li> <li><a href="/wiki/Information_geometry" title="Information geometry">Information geometry</a></li> <li><a href="/wiki/Statistical_manifold" title="Statistical manifold">Statistical manifold</a></li> <li><a href="/wiki/Automatic_differentiation" title="Automatic differentiation">Automatic differentiation</a></li> <li><a href="/wiki/Neuromorphic_computing" title="Neuromorphic computing">Neuromorphic computing</a></li> <li><a href="/wiki/Pattern_recognition" title="Pattern recognition">Pattern recognition</a></li> <li><a href="/wiki/Ricci_calculus" title="Ricci calculus">Ricci calculus</a></li> <li><a href="/wiki/Computational_learning_theory" title="Computational learning theory">Computational learning theory</a></li> <li><a href="/wiki/Inductive_bias" title="Inductive bias">Inductive bias</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Hardware</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Graphcore" title="Graphcore">IPU</a></li> <li><a href="/wiki/Tensor_Processing_Unit" title="Tensor Processing Unit">TPU</a></li> <li><a href="/wiki/Vision_processing_unit" title="Vision processing unit">VPU</a></li> <li><a href="/wiki/Memristor" title="Memristor">Memristor</a></li> <li><a href="/wiki/SpiNNaker" title="SpiNNaker">SpiNNaker</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Software libraries</th><td 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