Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation. General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more easily harvested by classical Bayesian optimization techniques than a mixed space would. Discrete variables are recovered either subsequently to the continuous optimization, or simultaneously with an additional continuous-discrete compatibility constraint that is handled with augmented Lagrangians. Several possible implementations of such Bayesian mixed optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with searches working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, a particular attention is devoted to the Lagrange multipliers for which a local and a global estimation techniques are studied. The comparisons are based on the repeated optimization of three analytical functions and a beam design problem.
{"title":"A comparison of mixed-variables Bayesian optimization approaches","authors":"Cuesta Ramirez, Jhouben, Le Riche, Rodolphe, Roustant, Olivier, Perrin, Guillaume, Durantin, Cédric, Glière, Alain","doi":"10.1186/s40323-022-00218-8","DOIUrl":"https://doi.org/10.1186/s40323-022-00218-8","url":null,"abstract":"Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation. General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more easily harvested by classical Bayesian optimization techniques than a mixed space would. Discrete variables are recovered either subsequently to the continuous optimization, or simultaneously with an additional continuous-discrete compatibility constraint that is handled with augmented Lagrangians. Several possible implementations of such Bayesian mixed optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with searches working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, a particular attention is devoted to the Lagrange multipliers for which a local and a global estimation techniques are studied. The comparisons are based on the repeated optimization of three analytical functions and a beam design problem.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"29 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nowadays, in the Scientific Machine Learning (SML) research field, the traditional machine learning (ML) tools and scientific computing approaches are fruitfully intersected for solving problems modelled by Partial Differential Equations (PDEs) in science and engineering applications. Challenging SML methodologies are the new computational paradigms named Physics-Informed Neural Networks (PINNs). PINN has revolutionized the classical adoption of ML in scientific computing, representing a novel class of promising algorithms where the learning process is constrained to satisfy known physical laws described by differential equations. In this paper, we propose a PINN-based computational study to deal with a non-linear partial differential equations system. In particular, using this approach, we solve the Gray-Scott model, a reaction–diffusion system that involves an irreversible chemical reaction between two reactants. In the unstable region of the model, we consider some a priori information related to dynamical behaviors, i. e. a supervised approach that relies on a finite difference method (FDM). Finally, simulation results show that PINNs can successfully provide an approximated Grey-Scott system solution, reproducing the characteristic Turing patterns for different parameter configurations.
{"title":"Physics-informed neural networks approach for 1D and 2D Gray-Scott systems","authors":"Giampaolo, Fabio, De Rosa, Mariapia, Qi, Pian, Izzo, Stefano, Cuomo, Salvatore","doi":"10.1186/s40323-022-00219-7","DOIUrl":"https://doi.org/10.1186/s40323-022-00219-7","url":null,"abstract":"Nowadays, in the Scientific Machine Learning (SML) research field, the traditional machine learning (ML) tools and scientific computing approaches are fruitfully intersected for solving problems modelled by Partial Differential Equations (PDEs) in science and engineering applications. Challenging SML methodologies are the new computational paradigms named Physics-Informed Neural Networks (PINNs). PINN has revolutionized the classical adoption of ML in scientific computing, representing a novel class of promising algorithms where the learning process is constrained to satisfy known physical laws described by differential equations. In this paper, we propose a PINN-based computational study to deal with a non-linear partial differential equations system. In particular, using this approach, we solve the Gray-Scott model, a reaction–diffusion system that involves an irreversible chemical reaction between two reactants. In the unstable region of the model, we consider some a priori information related to dynamical behaviors, i. e. a supervised approach that relies on a finite difference method (FDM). Finally, simulation results show that PINNs can successfully provide an approximated Grey-Scott system solution, reproducing the characteristic Turing patterns for different parameter configurations.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"30 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-17DOI: 10.1186/s40323-023-00243-1
R. Meethal, A. Kodakkal, Mohamed Khalil, A. Ghantasala, B. Obst, K. Bletzinger, R. Wüchner
{"title":"Finite element method-enhanced neural network for forward and inverse problems","authors":"R. Meethal, A. Kodakkal, Mohamed Khalil, A. Ghantasala, B. Obst, K. Bletzinger, R. Wüchner","doi":"10.1186/s40323-023-00243-1","DOIUrl":"https://doi.org/10.1186/s40323-023-00243-1","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"30 3","pages":"1-23"},"PeriodicalIF":0.0,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41301471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-16DOI: 10.1186/s40323-022-00217-9
M. Chapelier, R. Bouclier, J. Passieux
{"title":"Spline-based specimen shape optimization for robust material model calibration","authors":"M. Chapelier, R. Bouclier, J. Passieux","doi":"10.1186/s40323-022-00217-9","DOIUrl":"https://doi.org/10.1186/s40323-022-00217-9","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47862139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-11DOI: 10.1186/s40323-022-00215-x
N. Akkari, F. Casenave, D. Ryckelynck, C. Rey
{"title":"An updated Gappy-POD to capture non-parameterized geometrical variation in fluid dynamics problems","authors":"N. Akkari, F. Casenave, D. Ryckelynck, C. Rey","doi":"10.1186/s40323-022-00215-x","DOIUrl":"https://doi.org/10.1186/s40323-022-00215-x","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44599949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-07DOI: 10.1186/s40323-022-00216-w
M. Kazemzadeh-Parsi, A. Ammar, F. Chinesta
{"title":"Domain decomposition involving subdomain separable space representations for solving parametric problems in complex geometries","authors":"M. Kazemzadeh-Parsi, A. Ammar, F. Chinesta","doi":"10.1186/s40323-022-00216-w","DOIUrl":"https://doi.org/10.1186/s40323-022-00216-w","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44537571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-18DOI: 10.1186/s40323-022-00214-y
Hanane Khatouri, T. Benamara, P. Breitkopf, Jean Demange
{"title":"Metamodeling techniques for CPU-intensive simulation-based design optimization: a survey","authors":"Hanane Khatouri, T. Benamara, P. Breitkopf, Jean Demange","doi":"10.1186/s40323-022-00214-y","DOIUrl":"https://doi.org/10.1186/s40323-022-00214-y","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65854177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-05DOI: 10.21203/rs.3.rs-1153344/v1
M. Chapelier, R. Bouclier, J. Passieux
Identification from field measurements allows several parameters to be identified from a single test, provided that the measurements are sensitive enough to the parameters to be identified. To do this, authors use empirically defined geometries (with holes, notches...). The first attempts to optimize the specimen to maximize the sensitivity of the measurement are linked to a design space that is either very small (parametric optimization), which does not allow the exploration of very different designs, or, conversely, very large (topology optimization), which sometimes leads to designs that are not regular and cannot be manufactured. In this paper, an intermediate approach based on a non-invasive CAD-inspired optimization strategy is proposed. It relies on the definition of univariate spline Free-Form Deformation boxes to reduce the design space and thus regularize the problem. Then, from the modeling point of view, a new objective function is proposed that takes into account the experimental setup and constraint functions are added to ensure that the gain is real and the shape physically sound. Several examples show that with this method and at low cost, one can significantly improve the identification of constitutive parameters without changing the experimental setup.
{"title":"Spline-based specimen shape optimization for robust material model calibration","authors":"M. Chapelier, R. Bouclier, J. Passieux","doi":"10.21203/rs.3.rs-1153344/v1","DOIUrl":"https://doi.org/10.21203/rs.3.rs-1153344/v1","url":null,"abstract":"Identification from field measurements allows several parameters to be identified from a single test, provided that the measurements are sensitive enough to the parameters to be identified. To do this, authors use empirically defined geometries (with holes, notches...). The first attempts to optimize the specimen to maximize the sensitivity of the measurement are linked to a design space that is either very small (parametric optimization), which does not allow the exploration of very different designs, or, conversely, very large (topology optimization), which sometimes leads to designs that are not regular and cannot be manufactured. In this paper, an intermediate approach based on a non-invasive CAD-inspired optimization strategy is proposed. It relies on the definition of univariate spline Free-Form Deformation boxes to reduce the design space and thus regularize the problem. Then, from the modeling point of view, a new objective function is proposed that takes into account the experimental setup and constraint functions are added to ensure that the gain is real and the shape physically sound. Several examples show that with this method and at low cost, one can significantly improve the identification of constitutive parameters without changing the experimental setup.","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"9 1","pages":"1-28"},"PeriodicalIF":0.0,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48655754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-22DOI: 10.1186/s40323-023-00242-2
Saddam Hijazi, M. Freitag, Niels Landwehr
{"title":"POD-Galerkin reduced order models and physics-informed neural networks for solving inverse problems for the Navier–Stokes equations","authors":"Saddam Hijazi, M. Freitag, Niels Landwehr","doi":"10.1186/s40323-023-00242-2","DOIUrl":"https://doi.org/10.1186/s40323-023-00242-2","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"10 1","pages":"1-38"},"PeriodicalIF":0.0,"publicationDate":"2021-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42836277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-10DOI: 10.1186/s40323-022-00231-x
M. Xiao, Jun Ma, Dongcheng Lu, B. Raghavan, Weihong Zhang
{"title":"Stress-constrained topology optimization using approximate reanalysis with on-the-fly reduced order modeling","authors":"M. Xiao, Jun Ma, Dongcheng Lu, B. Raghavan, Weihong Zhang","doi":"10.1186/s40323-022-00231-x","DOIUrl":"https://doi.org/10.1186/s40323-022-00231-x","url":null,"abstract":"","PeriodicalId":37424,"journal":{"name":"Advanced Modeling and Simulation in Engineering Sciences","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43501253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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