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Broyden</title> <meta name="description" content="Search results for: mulit-step Broyden"> <meta name="keywords" content="mulit-step Broyden"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="mulit-step Broyden"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 10</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: mulit-step Broyden</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10</span> A Multistep Broyden’s-Type Method for Solving Systems of Nonlinear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Y.%20Waziri">M. Y. Waziri</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20Aliyu"> M. A. Aliyu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mulit-step%20Broyden" title="mulit-step Broyden">mulit-step Broyden</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20systems%20of%20equations" title=" nonlinear systems of equations"> nonlinear systems of equations</a>, <a href="https://publications.waset.org/abstracts/search?q=computational%20efficiency" title=" computational efficiency"> computational efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=iterate" title=" iterate"> iterate</a> </p> <a href="https://publications.waset.org/abstracts/13750/a-multistep-broydens-type-method-for-solving-systems-of-nonlinear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13750.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">638</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">9</span> On Direct Matrix Factored Inversion via Broyden's Updates</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Adel%20Mohsen">Adel Mohsen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Broyden%27s%20updates" title="Broyden's updates">Broyden's updates</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20inverse" title=" matrix inverse"> matrix inverse</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20factorization" title=" inverse factorization"> inverse factorization</a>, <a href="https://publications.waset.org/abstracts/search?q=solution%20of%20linear%20algebraic%20equations" title=" solution of linear algebraic equations"> solution of linear algebraic equations</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-conditioned%20matrices" title=" ill-conditioned matrices"> ill-conditioned matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=preconditioning" title=" preconditioning"> preconditioning</a> </p> <a href="https://publications.waset.org/abstracts/22126/on-direct-matrix-factored-inversion-via-broydens-updates" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22126.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">479</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">8</span> Prediction of the Thermal Parameters of a High-Temperature Metallurgical Reactor Using Inverse Heat Transfer</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Hafid">Mohamed Hafid</a>, <a href="https://publications.waset.org/abstracts/search?q=Marcel%20Lacroix"> Marcel Lacroix</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study presents an inverse analysis for predicting the thermal conductivities and the heat flux of a high-temperature metallurgical reactor simultaneously. Once these thermal parameters are predicted, the time-varying thickness of the protective phase-change bank that covers the inside surface of the brick walls of a metallurgical reactor can be calculated. The enthalpy method is used to solve the melting/solidification process of the protective bank. The inverse model rests on the Levenberg-Marquardt Method (LMM) combined with the Broyden method (BM). A statistical analysis for the thermal parameter estimation is carried out. The effect of the position of the temperature sensors, total number of measurements and measurement noise on the accuracy of inverse predictions is investigated. Recommendations are made concerning the location of temperature sensors. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inverse%20heat%20transfer" title="inverse heat transfer">inverse heat transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=phase%20change" title=" phase change"> phase change</a>, <a href="https://publications.waset.org/abstracts/search?q=metallurgical%20reactor" title=" metallurgical reactor"> metallurgical reactor</a>, <a href="https://publications.waset.org/abstracts/search?q=Levenberg%E2%80%93Marquardt%20method" title=" Levenberg–Marquardt method"> Levenberg–Marquardt method</a>, <a href="https://publications.waset.org/abstracts/search?q=Broyden%20method" title=" Broyden method"> Broyden method</a>, <a href="https://publications.waset.org/abstracts/search?q=bank%20thickness" title=" bank thickness"> bank thickness</a> </p> <a href="https://publications.waset.org/abstracts/50511/prediction-of-the-thermal-parameters-of-a-high-temperature-metallurgical-reactor-using-inverse-heat-transfer" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50511.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">334</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">7</span> Parameter Estimation of Gumbel Distribution with Maximum-Likelihood Based on Broyden Fletcher Goldfarb Shanno Quasi-Newton</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dewi%20Retno%20Sari%20Saputro">Dewi Retno Sari Saputro</a>, <a href="https://publications.waset.org/abstracts/search?q=Purnami%20Widyaningsih"> Purnami Widyaningsih</a>, <a href="https://publications.waset.org/abstracts/search?q=Hendrika%20Handayani"> Hendrika Handayani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Extreme data on an observation can occur due to unusual circumstances in the observation. The data can provide important information that can’t be provided by other data so that its existence needs to be further investigated. The method for obtaining extreme data is one of them using maxima block method. The distribution of extreme data sets taken with the maxima block method is called the distribution of extreme values. Distribution of extreme values is Gumbel distribution with two parameters. The parameter estimation of Gumbel distribution with maximum likelihood method (ML) is difficult to determine its exact value so that it is necessary to solve the approach. The purpose of this study was to determine the parameter estimation of Gumbel distribution with quasi-Newton BFGS method. The quasi-Newton BFGS method is a numerical method used for nonlinear function optimization without constraint so that the method can be used for parameter estimation from Gumbel distribution whose distribution function is in the form of exponential doubel function. The quasi-New BFGS method is a development of the Newton method. The Newton method uses the second derivative to calculate the parameter value changes on each iteration. Newton's method is then modified with the addition of a step length to provide a guarantee of convergence when the second derivative requires complex calculations. In the quasi-Newton BFGS method, Newton's method is modified by updating both derivatives on each iteration. The parameter estimation of the Gumbel distribution by a numerical approach using the quasi-Newton BFGS method is done by calculating the parameter values that make the distribution function maximum. In this method, we need gradient vector and hessian matrix. This research is a theory research and application by studying several journals and textbooks. The results of this study obtained the quasi-Newton BFGS algorithm and estimation of Gumbel distribution parameters. The estimation method is then applied to daily rainfall data in Purworejo District to estimate the distribution parameters. This indicates that the high rainfall that occurred in Purworejo District decreased its intensity and the range of rainfall that occurred decreased. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=parameter%20estimation" title="parameter estimation">parameter estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=Gumbel%20distribution" title=" Gumbel distribution"> Gumbel distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum%20likelihood" title=" maximum likelihood"> maximum likelihood</a>, <a href="https://publications.waset.org/abstracts/search?q=broyden%20fletcher%20goldfarb%20shanno%20%28BFGS%29quasi%20newton" title=" broyden fletcher goldfarb shanno (BFGS)quasi newton "> broyden fletcher goldfarb shanno (BFGS)quasi newton </a> </p> <a href="https://publications.waset.org/abstracts/73714/parameter-estimation-of-gumbel-distribution-with-maximum-likelihood-based-on-broyden-fletcher-goldfarb-shanno-quasi-newton" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/73714.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">324</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6</span> Inverse Heat Transfer Analysis of a Melting Furnace Using Levenberg-Marquardt Method </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Hafid">Mohamed Hafid</a>, <a href="https://publications.waset.org/abstracts/search?q=Marcel%20Lacroix"> Marcel Lacroix</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=melting%20furnace" title="melting furnace">melting furnace</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20heat%20transfer" title=" inverse heat transfer"> inverse heat transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=enthalpy%20method" title=" enthalpy method"> enthalpy method</a>, <a href="https://publications.waset.org/abstracts/search?q=levenberg%E2%80%93marquardt%20method" title=" levenberg–marquardt method"> levenberg–marquardt method</a> </p> <a href="https://publications.waset.org/abstracts/49891/inverse-heat-transfer-analysis-of-a-melting-furnace-using-levenberg-marquardt-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/49891.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">324</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5</span> Artificial Neural Network Regression Modelling of GC/MS Retention of Terpenes Present in Satureja montana Extracts Obtained by Supercritical Carbon Dioxide</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Strahinja%20Kova%C4%8Devi%C4%87">Strahinja Kovačević</a>, <a href="https://publications.waset.org/abstracts/search?q=Jelena%20Vladi%C4%87"> Jelena Vladić</a>, <a href="https://publications.waset.org/abstracts/search?q=Senka%20Vidovi%C4%87"> Senka Vidović</a>, <a href="https://publications.waset.org/abstracts/search?q=Zoran%20Zekovi%C4%87"> Zoran Zeković</a>, <a href="https://publications.waset.org/abstracts/search?q=Lidija%20Jevri%C4%87"> Lidija Jevrić</a>, <a href="https://publications.waset.org/abstracts/search?q=Sanja%20Podunavac%20Kuzmanovi%C4%87"> Sanja Podunavac Kuzmanović</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Supercritical extracts of highly valuated medicinal plant Satureja montana were prepared by application of supercritical carbon dioxide extraction in the carbon dioxide pressure range from 125 to 350 bar and temperature range from 40 to 60°C. Using GC/MS method of analysis chemical profiles (aromatic constituents) of S. montana extracts were obtained. Self-training artificial neural networks were applied to predict the retention time of the analyzed terpenes in GC/MS system. The best ANN model obtained was multilayer perceptron (MLP 11-11-1). Hidden activation was tanh and output activation was identity with Broyden–Fletcher–Goldfarb–Shanno training algorithm. Correlation measures of the obtained network were the following: R(training) = 0.9975, R(test) = 0.9971 and R(validation) = 0.9999. The comparison of the experimental and predicted retention times of the analyzed compounds showed very high correlation (R = 0.9913) and significant predictive power of the established neural network. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=ANN%20regression" title="ANN regression">ANN regression</a>, <a href="https://publications.waset.org/abstracts/search?q=GC%2FMS" title=" GC/MS"> GC/MS</a>, <a href="https://publications.waset.org/abstracts/search?q=Satureja%20montana" title=" Satureja montana"> Satureja montana</a>, <a href="https://publications.waset.org/abstracts/search?q=terpenes" title=" terpenes"> terpenes</a> </p> <a href="https://publications.waset.org/abstracts/2742/artificial-neural-network-regression-modelling-of-gcms-retention-of-terpenes-present-in-satureja-montana-extracts-obtained-by-supercritical-carbon-dioxide" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2742.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">452</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4</span> An Inverse Heat Transfer Algorithm for Predicting the Thermal Properties of Tumors during Cryosurgery</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Hafid">Mohamed Hafid</a>, <a href="https://publications.waset.org/abstracts/search?q=Marcel%20Lacroix"> Marcel Lacroix</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study aimed at developing an inverse heat transfer approach for predicting the time-varying freezing front and the temperature distribution of tumors during cryosurgery. Using a temperature probe pressed against the layer of tumor, the inverse approach is able to predict simultaneously the metabolic heat generation and the blood perfusion rate of the tumor. Once these parameters are predicted, the temperature-field and time-varying freezing fronts are determined with the direct model. The direct model rests on one-dimensional <em>Pennes</em> bioheat equation. The phase change problem is handled with the enthalpy method. The <em>Levenberg-Marquardt</em> Method (LMM) combined to the <em>Broyden</em> Method (BM) is used to solve the inverse model. The effect (a) of the thermal properties of the diseased tissues; (b) of the initial guesses for the unknown thermal properties; (c) of the data capture frequency; and (d) of the noise on the recorded temperatures is examined. It is shown that the proposed inverse approach remains accurate for all the cases investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cryosurgery" title="cryosurgery">cryosurgery</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20heat%20transfer" title=" inverse heat transfer"> inverse heat transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=Levenberg-Marquardt%20method" title=" Levenberg-Marquardt method"> Levenberg-Marquardt method</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20properties" title=" thermal properties"> thermal properties</a>, <a href="https://publications.waset.org/abstracts/search?q=Pennes%20model" title=" Pennes model"> Pennes model</a>, <a href="https://publications.waset.org/abstracts/search?q=enthalpy%20method" title=" enthalpy method"> enthalpy method</a> </p> <a href="https://publications.waset.org/abstracts/71945/an-inverse-heat-transfer-algorithm-for-predicting-the-thermal-properties-of-tumors-during-cryosurgery" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/71945.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">200</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3</span> The Data-Driven Localized Wave Solution of the Fokas-Lenells Equation using PINN</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gautam%20Kumar%20Saharia">Gautam Kumar Saharia</a>, <a href="https://publications.waset.org/abstracts/search?q=Sagardeep%20Talukdar"> Sagardeep Talukdar</a>, <a href="https://publications.waset.org/abstracts/search?q=Riki%20Dutta"> Riki Dutta</a>, <a href="https://publications.waset.org/abstracts/search?q=Sudipta%20Nandy"> Sudipta Nandy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The physics informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary condition to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful to study various optical phenomena. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=deep%20learning" title="deep learning">deep learning</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20Soliton" title=" optical Soliton"> optical Soliton</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation" title=" partial differential equation"> partial differential equation</a> </p> <a href="https://publications.waset.org/abstracts/165868/the-data-driven-localized-wave-solution-of-the-fokas-lenells-equation-using-pinn" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165868.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">126</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2</span> The Data-Driven Localized Wave Solution of the Fokas-Lenells Equation Using Physics-Informed Neural Network</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gautam%20Kumar%20Saharia">Gautam Kumar Saharia</a>, <a href="https://publications.waset.org/abstracts/search?q=Sagardeep%20Talukdar"> Sagardeep Talukdar</a>, <a href="https://publications.waset.org/abstracts/search?q=Riki%20Dutta"> Riki Dutta</a>, <a href="https://publications.waset.org/abstracts/search?q=Sudipta%20Nandy"> Sudipta Nandy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The physics-informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on a strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary conditions to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of the Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful in studying various optical phenomena. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=deep%20learning" title="deep learning">deep learning</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20soliton" title=" optical soliton"> optical soliton</a>, <a href="https://publications.waset.org/abstracts/search?q=physics%20informed%20neural%20network" title=" physics informed neural network"> physics informed neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation" title=" partial differential equation"> partial differential equation</a> </p> <a href="https://publications.waset.org/abstracts/165242/the-data-driven-localized-wave-solution-of-the-fokas-lenells-equation-using-physics-informed-neural-network" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165242.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">70</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1</span> Market Solvency Capital Requirement Minimization: How Non-linear Solvers Provide Portfolios Complying with Solvency II Regulation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abraham%20Castellanos">Abraham Castellanos</a>, <a href="https://publications.waset.org/abstracts/search?q=Christophe%20Durville"> Christophe Durville</a>, <a href="https://publications.waset.org/abstracts/search?q=Sophie%20Echenim"> Sophie Echenim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, a portfolio optimization problem is performed in a Solvency II context: it illustrates how advanced optimization techniques can help to tackle complex operational pain points around the monitoring, control, and stability of Solvency Capital Requirement (SCR). The market SCR of a portfolio is calculated as a combination of SCR sub-modules. These sub-modules are the results of stress-tests on interest rate, equity, property, credit and FX factors, as well as concentration on counter-parties. The market SCR is non convex and non differentiable, which does not make it a natural optimization criteria candidate. In the SCR formulation, correlations between sub-modules are fixed, whereas risk-driven portfolio allocation is usually driven by the dynamics of the actual correlations. Implementing a portfolio construction approach that is efficient on both a regulatory and economic standpoint is not straightforward. Moreover, the challenge for insurance portfolio managers is not only to achieve a minimal SCR to reduce non-invested capital but also to ensure stability of the SCR. Some optimizations have already been performed in the literature, simplifying the standard formula into a quadratic function. But to our knowledge, it is the first time that the standard formula of the market SCR is used in an optimization problem. Two solvers are combined: a bundle algorithm for convex non- differentiable problems, and a BFGS (Broyden-Fletcher-Goldfarb- Shanno)-SQP (Sequential Quadratic Programming) algorithm, to cope with non-convex cases. A market SCR minimization is then performed with historical data. This approach results in significant reduction of the capital requirement, compared to a classical Markowitz approach based on the historical volatility. A comparative analysis of different optimization models (equi-risk-contribution portfolio, minimizing volatility portfolio and minimizing value-at-risk portfolio) is performed and the impact of these strategies on risk measures including market SCR and its sub-modules is evaluated. A lack of diversification of market SCR is observed, specially for equities. This was expected since the market SCR strongly penalizes this type of financial instrument. It was shown that this direct effect of the regulation can be attenuated by implementing constraints in the optimization process or minimizing the market SCR together with the historical volatility, proving the interest of having a portfolio construction approach that can incorporate such features. The present results are further explained by the Market SCR modelling. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=financial%20risk" title="financial risk">financial risk</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20optimization" title=" numerical optimization"> numerical optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=portfolio%20management" title=" portfolio management"> portfolio management</a>, <a href="https://publications.waset.org/abstracts/search?q=solvency%20capital%20requirement" title=" solvency capital requirement"> solvency capital requirement</a> </p> <a href="https://publications.waset.org/abstracts/127464/market-solvency-capital-requirement-minimization-how-non-linear-solvers-provide-portfolios-complying-with-solvency-ii-regulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127464.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">117</span> </span> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); 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