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is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2409.13038">arXiv:2409.13038</a> <span> [<a href="https://arxiv.org/pdf/2409.13038">pdf</a>, <a href="https://arxiv.org/format/2409.13038">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> </div> </div> <p class="title is-5 mathjax"> HeadCT-ONE: Enabling Granular and Controllable Automated Evaluation of Head CT Radiology Report Generation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Acosta%2C+J+N">Juli谩n N. Acosta</a>, <a href="/search/cs?searchtype=author&query=Zhang%2C+X">Xiaoman Zhang</a>, <a href="/search/cs?searchtype=author&query=Dogra%2C+S">Siddhant Dogra</a>, <a href="/search/cs?searchtype=author&query=Zhou%2C+H">Hong-Yu Zhou</a>, <a href="/search/cs?searchtype=author&query=Payabvash%2C+S">Seyedmehdi Payabvash</a>, <a href="/search/cs?searchtype=author&query=Falcone%2C+G+J">Guido J. Falcone</a>, <a href="/search/cs?searchtype=author&query=Oermann%2C+E+K">Eric K. Oermann</a>, <a href="/search/cs?searchtype=author&query=Rajpurkar%2C+P">Pranav Rajpurkar</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2409.13038v1-abstract-short" style="display: inline;"> We present Head CT Ontology Normalized Evaluation (HeadCT-ONE), a metric for evaluating head CT report generation through ontology-normalized entity and relation extraction. HeadCT-ONE enhances current information extraction derived metrics (such as RadGraph F1) by implementing entity normalization through domain-specific ontologies, addressing radiological language variability. HeadCT-ONE compare… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.13038v1-abstract-full').style.display = 'inline'; document.getElementById('2409.13038v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.13038v1-abstract-full" style="display: none;"> We present Head CT Ontology Normalized Evaluation (HeadCT-ONE), a metric for evaluating head CT report generation through ontology-normalized entity and relation extraction. HeadCT-ONE enhances current information extraction derived metrics (such as RadGraph F1) by implementing entity normalization through domain-specific ontologies, addressing radiological language variability. HeadCT-ONE compares normalized entities and relations, allowing for controllable weighting of different entity types or specific entities. Through experiments on head CT reports from three health systems, we show that HeadCT-ONE's normalization and weighting approach improves the capture of semantically equivalent reports, better distinguishes between normal and abnormal reports, and aligns with radiologists' assessment of clinically significant errors, while offering flexibility to prioritize specific aspects of report content. Our results demonstrate how HeadCT-ONE enables more flexible, controllable, and granular automated evaluation of head CT reports. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.13038v1-abstract-full').style.display = 'none'; document.getElementById('2409.13038v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2110.03210">arXiv:2110.03210</a> <span> [<a href="https://arxiv.org/pdf/2110.03210">pdf</a>, <a href="https://arxiv.org/format/2110.03210">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Statistical Mechanics">cond-mat.stat-mech</span> </div> </div> <p class="title is-5 mathjax"> Universality of Winning Tickets: A Renormalization Group Perspective </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Redman%2C+W+T">William T. Redman</a>, <a href="/search/cs?searchtype=author&query=Chen%2C+T">Tianlong Chen</a>, <a href="/search/cs?searchtype=author&query=Wang%2C+Z">Zhangyang Wang</a>, <a href="/search/cs?searchtype=author&query=Dogra%2C+A+S">Akshunna S. Dogra</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2110.03210v3-abstract-short" style="display: inline;"> Foundational work on the Lottery Ticket Hypothesis has suggested an exciting corollary: winning tickets found in the context of one task can be transferred to similar tasks, possibly even across different architectures. This has generated broad interest, but methods to study this universality are lacking. We make use of renormalization group theory, a powerful tool from theoretical physics, to add… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.03210v3-abstract-full').style.display = 'inline'; document.getElementById('2110.03210v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2110.03210v3-abstract-full" style="display: none;"> Foundational work on the Lottery Ticket Hypothesis has suggested an exciting corollary: winning tickets found in the context of one task can be transferred to similar tasks, possibly even across different architectures. This has generated broad interest, but methods to study this universality are lacking. We make use of renormalization group theory, a powerful tool from theoretical physics, to address this need. We find that iterative magnitude pruning, the principal algorithm used for discovering winning tickets, is a renormalization group scheme, and can be viewed as inducing a flow in parameter space. We demonstrate that ResNet-50 models with transferable winning tickets have flows with common properties, as would be expected from the theory. Similar observations are made for BERT models, with evidence that their flows are near fixed points. Additionally, we leverage our framework to study winning tickets transferred across ResNet architectures, observing that smaller models have flows with more uniform properties than larger models, complicating transfer between them. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.03210v3-abstract-full').style.display = 'none'; document.getElementById('2110.03210v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, 3 figures, 8 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Proceedings of the 39th International Conference on Machine Learning, PMLR Vol. 162, pp. 18483-18498 (ICML 2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2008.12190">arXiv:2008.12190</a> <span> [<a href="https://arxiv.org/pdf/2008.12190">pdf</a>, <a href="https://arxiv.org/format/2008.12190">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Local error quantification for Neural Network Differential Equation solvers </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Dogra%2C+A+S">Akshunna S. Dogra</a>, <a href="/search/cs?searchtype=author&query=Redman%2C+W+T">William T Redman</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2008.12190v3-abstract-short" style="display: inline;"> Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide variety of differential equations. Such solvers produce robust functional expressions, are well suited for further manipulations on the quantities of interest… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.12190v3-abstract-full').style.display = 'inline'; document.getElementById('2008.12190v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2008.12190v3-abstract-full" style="display: none;"> Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide variety of differential equations. Such solvers produce robust functional expressions, are well suited for further manipulations on the quantities of interest (for example, taking derivatives), and capable of leveraging the modern advances in parallelization and computing power. However, there is a lack of work on the role precise error quantification can play in their predictions: usually, the focus is on ambiguous and/or global measures of performance like the loss function and/or obtaining global bounds on the errors associated with the predictions. Precise, local error quantification is seldom possible without external means or outright knowledge of the true solution. We address these concerns in the context of dynamical system NN DE solvers, leveraging learnt information within the NN DE solvers to develop methods that allow them to be more accurate and efficient, while still pursuing an unsupervised approach that does not rely on external tools or data. We achieve this via methods that can precisely estimate NN DE solver prediction errors point-wise, thus allowing the user the capacity for efficient and targeted error correction. We exemplify the utility of our methods by testing them on a nonlinear and a chaotic system each. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.12190v3-abstract-full').style.display = 'none'; document.getElementById('2008.12190v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 3 figures, 2 Tables, 1 appendix with a new proposed algorithm. Modifications in the statement and proof of Equation 7 compared to the previous version. Text overlap with arXiv:2004.11826</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2008.01774">arXiv:2008.01774</a> <span> [<a href="https://arxiv.org/pdf/2008.01774">pdf</a>, <a href="https://arxiv.org/format/2008.01774">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Image and Video Processing">eess.IV</span> </div> </div> <p class="title is-5 mathjax"> An artificial intelligence system for predicting the deterioration of COVID-19 patients in the emergency department </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Shamout%2C+F+E">Farah E. Shamout</a>, <a href="/search/cs?searchtype=author&query=Shen%2C+Y">Yiqiu Shen</a>, <a href="/search/cs?searchtype=author&query=Wu%2C+N">Nan Wu</a>, <a href="/search/cs?searchtype=author&query=Kaku%2C+A">Aakash Kaku</a>, <a href="/search/cs?searchtype=author&query=Park%2C+J">Jungkyu Park</a>, <a href="/search/cs?searchtype=author&query=Makino%2C+T">Taro Makino</a>, <a href="/search/cs?searchtype=author&query=Jastrz%C4%99bski%2C+S">Stanis艂aw Jastrz臋bski</a>, <a href="/search/cs?searchtype=author&query=Witowski%2C+J">Jan Witowski</a>, <a href="/search/cs?searchtype=author&query=Wang%2C+D">Duo Wang</a>, <a href="/search/cs?searchtype=author&query=Zhang%2C+B">Ben Zhang</a>, <a href="/search/cs?searchtype=author&query=Dogra%2C+S">Siddhant Dogra</a>, <a href="/search/cs?searchtype=author&query=Cao%2C+M">Meng Cao</a>, <a href="/search/cs?searchtype=author&query=Razavian%2C+N">Narges Razavian</a>, <a href="/search/cs?searchtype=author&query=Kudlowitz%2C+D">David Kudlowitz</a>, <a href="/search/cs?searchtype=author&query=Azour%2C+L">Lea Azour</a>, <a href="/search/cs?searchtype=author&query=Moore%2C+W">William Moore</a>, <a href="/search/cs?searchtype=author&query=Lui%2C+Y+W">Yvonne W. Lui</a>, <a href="/search/cs?searchtype=author&query=Aphinyanaphongs%2C+Y">Yindalon Aphinyanaphongs</a>, <a href="/search/cs?searchtype=author&query=Fernandez-Granda%2C+C">Carlos Fernandez-Granda</a>, <a href="/search/cs?searchtype=author&query=Geras%2C+K+J">Krzysztof J. Geras</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2008.01774v2-abstract-short" style="display: inline;"> During the coronavirus disease 2019 (COVID-19) pandemic, rapid and accurate triage of patients at the emergency department is critical to inform decision-making. We propose a data-driven approach for automatic prediction of deterioration risk using a deep neural network that learns from chest X-ray images and a gradient boosting model that learns from routine clinical variables. Our AI prognosis s… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.01774v2-abstract-full').style.display = 'inline'; document.getElementById('2008.01774v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2008.01774v2-abstract-full" style="display: none;"> During the coronavirus disease 2019 (COVID-19) pandemic, rapid and accurate triage of patients at the emergency department is critical to inform decision-making. We propose a data-driven approach for automatic prediction of deterioration risk using a deep neural network that learns from chest X-ray images and a gradient boosting model that learns from routine clinical variables. Our AI prognosis system, trained using data from 3,661 patients, achieves an area under the receiver operating characteristic curve (AUC) of 0.786 (95% CI: 0.745-0.830) when predicting deterioration within 96 hours. The deep neural network extracts informative areas of chest X-ray images to assist clinicians in interpreting the predictions and performs comparably to two radiologists in a reader study. In order to verify performance in a real clinical setting, we silently deployed a preliminary version of the deep neural network at New York University Langone Health during the first wave of the pandemic, which produced accurate predictions in real-time. In summary, our findings demonstrate the potential of the proposed system for assisting front-line physicians in the triage of COVID-19 patients. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.01774v2-abstract-full').style.display = 'none'; document.getElementById('2008.01774v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2020. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2007.04433">arXiv:2007.04433</a> <span> [<a href="https://arxiv.org/pdf/2007.04433">pdf</a>, <a href="https://arxiv.org/ps/2007.04433">ps</a>, <a href="https://arxiv.org/format/2007.04433">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Numerical Analysis">math.NA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> Error Estimation and Correction from within Neural Network Differential Equation Solvers </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Dogra%2C+A+S">Akshunna S. Dogra</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2007.04433v2-abstract-short" style="display: inline;"> Neural Network Differential Equation (NN DE) solvers have surged in popularity due to a combination of factors: computational advances making their optimization more tractable, their capacity to handle high dimensional problems, easy interpret-ability of their models, etc. However, almost all NN DE solvers suffer from a fundamental limitation: they are trained using loss functions that depend only… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.04433v2-abstract-full').style.display = 'inline'; document.getElementById('2007.04433v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2007.04433v2-abstract-full" style="display: none;"> Neural Network Differential Equation (NN DE) solvers have surged in popularity due to a combination of factors: computational advances making their optimization more tractable, their capacity to handle high dimensional problems, easy interpret-ability of their models, etc. However, almost all NN DE solvers suffer from a fundamental limitation: they are trained using loss functions that depend only implicitly on the error associated with the estimate. As such, validation and error analysis of solution estimates requires knowledge of the true solution. Indeed, if the true solution is unknown, we are often reduced to simply hoping that a "low enough" loss implies "small enough" errors, since explicit relationships between the two are not available/well defined. In this work, we describe a general strategy for efficiently constructing error estimates and corrections for Neural Network Differential Equation solvers. Our methods do not require advance knowledge of the true solutions and obtain explicit relationships between loss functions and the error associated with solution estimates. In turn, these explicit relationships directly allow us to estimate and correct for the errors. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.04433v2-abstract-full').style.display = 'none'; document.getElementById('2007.04433v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 July, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2020. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2006.02361">arXiv:2006.02361</a> <span> [<a href="https://arxiv.org/pdf/2006.02361">pdf</a>, <a href="https://arxiv.org/format/2006.02361">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Neural and Evolutionary Computing">cs.NE</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Signal Processing">eess.SP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computational Physics">physics.comp-ph</span> </div> </div> <p class="title is-5 mathjax"> Optimizing Neural Networks via Koopman Operator Theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Dogra%2C+A+S">Akshunna S. Dogra</a>, <a href="/search/cs?searchtype=author&query=Redman%2C+W+T">William T Redman</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2006.02361v3-abstract-short" style="display: inline;"> Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in making use of this connection. As Koopman operator theory is a linear theory, a successful implementation of it in evolving network weights and biases offers the pro… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.02361v3-abstract-full').style.display = 'inline'; document.getElementById('2006.02361v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2006.02361v3-abstract-full" style="display: none;"> Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in making use of this connection. As Koopman operator theory is a linear theory, a successful implementation of it in evolving network weights and biases offers the promise of accelerated training, especially in the context of deep networks, where optimization is inherently a non-convex problem. We show that Koopman operator theoretic methods allow for accurate predictions of weights and biases of feedforward, fully connected deep networks over a non-trivial range of training time. During this window, we find that our approach is >10x faster than various gradient descent based methods (e.g. Adam, Adadelta, Adagrad), in line with our complexity analysis. We end by highlighting open questions in this exciting intersection between dynamical systems and neural network theory. We highlight additional methods by which our results could be expanded to broader classes of networks and larger training intervals, which shall be the focus of future work. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.02361v3-abstract-full').style.display = 'none'; document.getElementById('2006.02361v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 October, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 June, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 main content pages (7 supplementary pages), 3 main content figures (3 supplementary figures), 2 main content Tables (5 supplementary Tables). 34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Advances in Neural Information Processing Systems 33, 2087-2097 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2001.11107">arXiv:2001.11107</a> <span> [<a href="https://arxiv.org/pdf/2001.11107">pdf</a>, <a href="https://arxiv.org/format/2001.11107">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computational Physics">physics.comp-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevE.105.065305">10.1103/PhysRevE.105.065305 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Hamiltonian neural networks for solving equations of motion </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Mattheakis%2C+M">Marios Mattheakis</a>, <a href="/search/cs?searchtype=author&query=Sondak%2C+D">David Sondak</a>, <a href="/search/cs?searchtype=author&query=Dogra%2C+A+S">Akshunna S. Dogra</a>, <a href="/search/cs?searchtype=author&query=Protopapas%2C+P">Pavlos Protopapas</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2001.11107v5-abstract-short" style="display: inline;"> There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine learning method where the optimization process of the network depends solely on the predicted functions without using any ground truth data. The model learns soluti… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.11107v5-abstract-full').style.display = 'inline'; document.getElementById('2001.11107v5-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2001.11107v5-abstract-full" style="display: none;"> There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine learning method where the optimization process of the network depends solely on the predicted functions without using any ground truth data. The model learns solutions that satisfy, up to an arbitrarily small error, Hamilton's equations and, therefore, conserve the Hamiltonian invariants. The choice of an appropriate activation function drastically improves the predictability of the network. Moreover, an error analysis is derived and states that the numerical errors depend on the overall network performance. The Hamiltonian network is then employed to solve the equations for the nonlinear oscillator and the chaotic Henon-Heiles dynamical system. In both systems, a symplectic Euler integrator requires two orders more evaluation points than the Hamiltonian network in order to achieve the same order of the numerical error in the predicted phase space trajectories. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.11107v5-abstract-full').style.display = 'none'; document.getElementById('2001.11107v5-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 April, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. E 105, 065305 (2022) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1904.08991">arXiv:1904.08991</a> <span> [<a href="https://arxiv.org/pdf/1904.08991">pdf</a>, <a href="https://arxiv.org/format/1904.08991">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computational Physics">physics.comp-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> </div> </div> <p class="title is-5 mathjax"> Physical Symmetries Embedded in Neural Networks </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Mattheakis%2C+M">M. Mattheakis</a>, <a href="/search/cs?searchtype=author&query=Protopapas%2C+P">P. Protopapas</a>, <a href="/search/cs?searchtype=author&query=Sondak%2C+D">D. Sondak</a>, <a href="/search/cs?searchtype=author&query=Di+Giovanni%2C+M">M. Di Giovanni</a>, <a href="/search/cs?searchtype=author&query=Kaxiras%2C+E">E. Kaxiras</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1904.08991v3-abstract-short" style="display: inline;"> Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations. Two fundamental challenges facing the development of neural networks in physics applications is their lack of interpretability and their physics-agnostic design… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.08991v3-abstract-full').style.display = 'inline'; document.getElementById('1904.08991v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1904.08991v3-abstract-full" style="display: none;"> Neural networks are a central technique in machine learning. Recent years have seen a wave of interest in applying neural networks to physical systems for which the governing dynamics are known and expressed through differential equations. Two fundamental challenges facing the development of neural networks in physics applications is their lack of interpretability and their physics-agnostic design. The focus of the present work is to embed physical constraints into the structure of the neural network to address the second fundamental challenge. By constraining tunable parameters (such as weights and biases) and adding special layers to the network, the desired constraints are guaranteed to be satisfied without the need for explicit regularization terms. This is demonstrated on upervised and unsupervised networks for two basic symmetries: even/odd symmetry of a function and energy conservation. In the supervised case, the network with embedded constraints is shown to perform well on regression problems while simultaneously obeying the desired constraints whereas a traditional network fits the data but violates the underlying constraints. Finally, a new unsupervised neural network is proposed that guarantees energy conservation through an embedded symplectic structure. The symplectic neural network is used to solve a system of energy-conserving differential equations and out-performs an unsupervised, non-symplectic neural network. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.08991v3-abstract-full').style.display = 'none'; document.getElementById('1904.08991v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">This is the same manuscript with version 1 (arXiv:1904.08991v1) which accidentally was replaced 16 pages, 8 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0911.0402">arXiv:0911.0402</a> <span> [<a href="https://arxiv.org/pdf/0911.0402">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Cryptography and Security">cs.CR</span> </div> </div> <p class="title is-5 mathjax"> A Cost Effective RFID Based Customized DVD-ROM to Thwart Software Piracy </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/cs?searchtype=author&query=Dogra%2C+S">Sudip Dogra</a>, <a href="/search/cs?searchtype=author&query=Ray%2C+R">Ritwik Ray</a>, <a href="/search/cs?searchtype=author&query=Ghosh%2C+S">Saustav Ghosh</a>, <a href="/search/cs?searchtype=author&query=Bhattacharya%2C+D">Debharshi Bhattacharya</a>, <a href="/search/cs?searchtype=author&query=Sarkar%2C+S+K">Subir Kr. Sarkar</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0911.0402v1-abstract-short" style="display: inline;"> Software piracy has been a very perilous adversary of the software based industry, from the very beginning of the development of the latter into a significant business. There has been no developed foolproof system that has been developed to appropriately tackle this vile issue. We have in our scheme tried to develop a way to embark upon this problem using a very recently developed technology of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0911.0402v1-abstract-full').style.display = 'inline'; document.getElementById('0911.0402v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0911.0402v1-abstract-full" style="display: none;"> Software piracy has been a very perilous adversary of the software based industry, from the very beginning of the development of the latter into a significant business. There has been no developed foolproof system that has been developed to appropriately tackle this vile issue. We have in our scheme tried to develop a way to embark upon this problem using a very recently developed technology of RFID. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0911.0402v1-abstract-full').style.display = 'none'; document.getElementById('0911.0402v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 November, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages IEEE format, International Journal of Computer Science and Information Security, IJCSIS 2009, ISSN 1947 5500, Impact Factor 0.423, http://sites.google.com/site/ijcsis/</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> ISSN 1947 5500 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> International Journal of Computer Science and Information Security, IJCSIS, Vol. 6, No. 1, pp. 034-039, October 2009, USA </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact 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