The use of machine learning (ML) techniques to solve complex physical problems has been considere... more The use of machine learning (ML) techniques to solve complex physical problems has been considered recently as a promising approach. However, the evaluation of such learned physical models remains an important issue for industrial use. The aim of this competition is to encourage the development of new ML techniques to solve physical problems using a unified evaluation framework proposed recently, called Learning Industrial Physical Simulations (LIPS). We propose learning a task representing a well-known physical use case: the airfoil design simulation, using a dataset called AirfRANS. The global score calculated for each submitted solution is based on three main categories of criteria covering different aspects, namely: ML-related, Out-Of-Distribution, and physical compliance criteria. To the best of our knowledge, this is the first competition addressing the use of ML-based surrogate approaches to improve the trade-off computational cost/accuracy of physical simulation.The competition is hosted by the Codabench platform with online training and evaluation of all submitted solutions 1 .
Danan(a), Chiara Nardoni(a), Chetra Mang(a), Felipe Bordeu(b), Julien Cortial(b) IRT SystemX (a),... more Danan(a), Chiara Nardoni(a), Chetra Mang(a), Felipe Bordeu(b), Julien Cortial(b) IRT SystemX (a), Safran Tech (b) WCSMO-15, Cork, Ireland Many challenges remain ▪ Taking advantage of the design freedom provided by AM ▪ Accounting for actual design constraints, rules, practices ▪ Encompass and handle actual industrial criteria of interest ▪ Complex multi-physics environments ▪ Need for adjoint-enabled solvers ▪ Integration into complex workflows ▪ Large scale problems Multi-disciplinary environment ▪ Aeronautics ▪ High-pressure turbine cooling channels ▪ Heat sinks for electrical machines , fuel cells ▪ Heat exchangers, Surface coolers ▪ Automotive ▪ Car design ▪ Noise vibration harshness ▪ Energy ▪ Solar panels supports ▪ Wind farm ▪ Battery packs ▪ Medical implants Topology optimization in industry ▪ Mature technology to design structural, monoscale parts ▪ Many commercial off-the-shelf software packages available ▪ Alleviate workload at early stages of design ▪ Reducing environmental impact Need for R&T in topology optimization
Danan(a), Chiara Nardoni(a), Chetra Mang(a), Felipe Bordeu(b), Julien Cortial(b) IRT SystemX (a),... more Danan(a), Chiara Nardoni(a), Chetra Mang(a), Felipe Bordeu(b), Julien Cortial(b) IRT SystemX (a), Safran Tech (b) WCSMO-15, Cork, Ireland Many challenges remain ▪ Taking advantage of the design freedom provided by AM ▪ Accounting for actual design constraints, rules, practices ▪ Encompass and handle actual industrial criteria of interest ▪ Complex multi-physics environments ▪ Need for adjoint-enabled solvers ▪ Integration into complex workflows ▪ Large scale problems Multi-disciplinary environment ▪ Aeronautics ▪ High-pressure turbine cooling channels ▪ Heat sinks for electrical machines , fuel cells ▪ Heat exchangers, Surface coolers ▪ Automotive ▪ Car design ▪ Noise vibration harshness ▪ Energy ▪ Solar panels supports ▪ Wind farm ▪ Battery packs ▪ Medical implants Topology optimization in industry ▪ Mature technology to design structural, monoscale parts ▪ Many commercial off-the-shelf software packages available ▪ Alleviate workload at early stages of design ▪ Reducing environmental impact Need for R&T in topology optimization
Variational-hemivariational inequalities refer to the inequality problems where both convex and n... more Variational-hemivariational inequalities refer to the inequality problems where both convex and nonconvex functions are involved. In this paper, we consider the numerical solution of a family of stationary variational-hemivariational inequalities by the finite element method. For a variational-hemivariational inequality of a general form, we prove convergence of numerical solutions. For some particular variational-hemivariational inequalities, we provide error estimates of numerical solutions, which are of optimal order for the linear finite element method under appropriate solution regularity assumptions. Numerical results are reported on solving a variational-hemivariational inequality modeling the contact between an elastic body and a foundation with the linear finite element, illustrating the theoretically predicted optimal first order convergence and providing their mechanical interpretations.
HAL (Le Centre pour la Communication Scientifique Directe), Dec 3, 2022
Data-driven approaches to accelerate computation time on PDE-based physical problems have recentl... more Data-driven approaches to accelerate computation time on PDE-based physical problems have recently received growing interest. Deep Learning algorithms are applied to learn from samples of accurate approximations of the PDEs solutions computed by numerical solvers. However, generating a large-scale dataset with accurate solutions using these classical solvers remains challenging due to their high computational cost. In this work, we propose a multi-fidelity transfer learning approach that combines a large amount of low-cost data from poor approximations with a small but accurately computed dataset. Experiments on two physical problems (airfoil flow and wheel contact) show that by transferring prior-knowledge learned from the inaccurate dataset, our approach can predict well PDEs solutions, even when only a few samples of highly accurate solutions are available.
HAL (Le Centre pour la Communication Scientifique Directe), Nov 28, 2022
Data-driven approaches to accelerate computation time on PDE-based physical problems have recentl... more Data-driven approaches to accelerate computation time on PDE-based physical problems have recently received growing interest. Deep Learning algorithms are applied to learn from samples of accurate approximations of the PDEs solutions computed by numerical solvers. However, generating a large-scale dataset with accurate solutions using these classical solvers remains challenging due to their high computational cost. In this work, we propose a multi-fidelity transfer learning approach that combines a large amount of low-cost data from poor approximations with a small but accurately computed dataset. Experiments on two physical problems (airfoil flow and wheel contact) show that by transferring prior-knowledge learned from the inaccurate dataset, our approach can predict well PDEs solutions, even when only a few samples of highly accurate solutions are available.
The purpose of this work is to present an improved energy conservation method for hyperelastodyna... more The purpose of this work is to present an improved energy conservation method for hyperelastodynamic contact problems based on specific normal compliance conditions. In order to determine this Improved Normal Compliance (INC) law, we use a Moreau-Yosida α-regularization to approximate the unilateral contact law. Then, based on the work of Hauret-LeTallec [1], we propose in the discrete framework a specific approach allowing to respect the energy conservation of the system in adequacy with the continuous case. This strategy (INC) is characterized by a conserving behavior for frictionless impacts and admissible dissipation for friction phenomena while limiting penetration. Then, we detail the numerical treatment within the framework of the semi-smooth Newton method and primal-dual active set strategy for the normal compliance conditions with friction. We finally provide some numerical experiments to bring into light the energy conservation and the efficiency of the INC method by comparing with different classical methods from the literature throught representative contact problems.
The purpose of this work is to present an improved energy conservation method for hyperelastodyna... more The purpose of this work is to present an improved energy conservation method for hyperelastodynamic contact problems based on specific normal compliance conditions. In order to determine this Improved Normal Compliance (INC) law, we use a Moreau-Yosida α-regularization to approximate the unilateral contact law. Then, based on the work of Hauret-LeTallec [1], we propose in the discrete framework a specific approach allowing to respect the energy conservation of the system in adequacy with the continuous case. This strategy (INC) is characterized by a conserving behavior for frictionless impacts and admissible dissipation for friction phenomena while limiting penetration. Then, we detail the numerical treatment within the framework of the semi-smooth Newton method and primal-dual active set strategy for the normal compliance conditions with friction. We finally provide some numerical experiments to bring into light the energy conservation and the efficiency of the INC method by comparing with different classical methods from the literature throught representative contact problems.
HAL (Le Centre pour la Communication Scientifique Directe), Nov 28, 2022
Data-driven approaches to accelerate computation time on PDE-based physical problems have recentl... more Data-driven approaches to accelerate computation time on PDE-based physical problems have recently received growing interest. Deep Learning algorithms are applied to learn from samples of accurate approximations of the PDEs solutions computed by numerical solvers. However, generating a large-scale dataset with accurate solutions using these classical solvers remains challenging due to their high computational cost. In this work, we propose a multi-fidelity transfer learning approach that combines a large amount of low-cost data from poor approximations with a small but accurately computed dataset. Experiments on two physical problems (airfoil flow and wheel contact) show that by transferring prior-knowledge learned from the inaccurate dataset, our approach can predict well PDEs solutions, even when only a few samples of highly accurate solutions are available.
HAL (Le Centre pour la Communication Scientifique Directe), Nov 28, 2022
Physical simulations are at the core of many critical industrial systems. However, today's physic... more Physical simulations are at the core of many critical industrial systems. However, today's physical simulators have some limitations such as computation time, dealing with missing or uncertain data, or even non-convergence for some feasible cases. Recently, the use of data-driven approaches to learn complex physical simulations has been considered as a promising approach to address those issues. However, this comes often at the cost of some accuracy which may hinder the industrial use. To drive this new research topic towards a better real-world applicability, we propose a new benchmark suite "Learning Industrial Physical Simulations"(LIPS) to meet the need of developing efficient, industrial application-oriented, augmented simulators. To define how to assess such benchmark performance, we propose a set of four generic categories of criteria. The proposed benchmark suite is a modular and configurable framework that can deal with different physical problems. To demonstrate this ability, we propose in this paper to investigate two distinct use-cases with different physical simulations, namely: the power grid and the pneumatic. For each use case, several benchmarks are described and assessed with existing models. None of the models perform well under all expected criteria, inviting the community to develop new industry-applicable solutions and possibly showcase their performance publicly upon online LIPS instance on Codabench.
Le Centre pour la Communication Scientifique Directe - HAL - memSIC, 2021
Topology optimization is devoted to the optimal design of structures: It aims at finding the best... more Topology optimization is devoted to the optimal design of structures: It aims at finding the best material distribution inside a working domain while fulfilling mechanical, geometrical and manufacturing specifications. Conceptually different from parametric or size optimization, topology optimization relies on a freeform approach enabling to search for the optimal design in a larger space of configurations and promoting disruptive design. The need for lighter and efficient structural solutions has made topology optimization a vigorous research field in both academic and industrial structural engineering communities. This contribution presents a Research and Development software platform for shape and topology optimization where the computational process is carried out in a level set framework combined with a body-fitted approach.
The use of machine learning (ML) techniques to solve complex physical problems has been considere... more The use of machine learning (ML) techniques to solve complex physical problems has been considered recently as a promising approach. However, the evaluation of such learned physical models remains an important issue for industrial use. The aim of this competition is to encourage the development of new ML techniques to solve physical problems using a unified evaluation framework proposed recently, called Learning Industrial Physical Simulations (LIPS). We propose learning a task representing a well-known physical use case: the airfoil design simulation, using a dataset called AirfRANS. The global score calculated for each submitted solution is based on three main categories of criteria covering different aspects, namely: ML-related, Out-Of-Distribution, and physical compliance criteria. To the best of our knowledge, this is the first competition addressing the use of ML-based surrogate approaches to improve the trade-off computational cost/accuracy of physical simulation.The competition is hosted by the Codabench platform with online training and evaluation of all submitted solutions 1 .
Danan(a), Chiara Nardoni(a), Chetra Mang(a), Felipe Bordeu(b), Julien Cortial(b) IRT SystemX (a),... more Danan(a), Chiara Nardoni(a), Chetra Mang(a), Felipe Bordeu(b), Julien Cortial(b) IRT SystemX (a), Safran Tech (b) WCSMO-15, Cork, Ireland Many challenges remain ▪ Taking advantage of the design freedom provided by AM ▪ Accounting for actual design constraints, rules, practices ▪ Encompass and handle actual industrial criteria of interest ▪ Complex multi-physics environments ▪ Need for adjoint-enabled solvers ▪ Integration into complex workflows ▪ Large scale problems Multi-disciplinary environment ▪ Aeronautics ▪ High-pressure turbine cooling channels ▪ Heat sinks for electrical machines , fuel cells ▪ Heat exchangers, Surface coolers ▪ Automotive ▪ Car design ▪ Noise vibration harshness ▪ Energy ▪ Solar panels supports ▪ Wind farm ▪ Battery packs ▪ Medical implants Topology optimization in industry ▪ Mature technology to design structural, monoscale parts ▪ Many commercial off-the-shelf software packages available ▪ Alleviate workload at early stages of design ▪ Reducing environmental impact Need for R&T in topology optimization
Danan(a), Chiara Nardoni(a), Chetra Mang(a), Felipe Bordeu(b), Julien Cortial(b) IRT SystemX (a),... more Danan(a), Chiara Nardoni(a), Chetra Mang(a), Felipe Bordeu(b), Julien Cortial(b) IRT SystemX (a), Safran Tech (b) WCSMO-15, Cork, Ireland Many challenges remain ▪ Taking advantage of the design freedom provided by AM ▪ Accounting for actual design constraints, rules, practices ▪ Encompass and handle actual industrial criteria of interest ▪ Complex multi-physics environments ▪ Need for adjoint-enabled solvers ▪ Integration into complex workflows ▪ Large scale problems Multi-disciplinary environment ▪ Aeronautics ▪ High-pressure turbine cooling channels ▪ Heat sinks for electrical machines , fuel cells ▪ Heat exchangers, Surface coolers ▪ Automotive ▪ Car design ▪ Noise vibration harshness ▪ Energy ▪ Solar panels supports ▪ Wind farm ▪ Battery packs ▪ Medical implants Topology optimization in industry ▪ Mature technology to design structural, monoscale parts ▪ Many commercial off-the-shelf software packages available ▪ Alleviate workload at early stages of design ▪ Reducing environmental impact Need for R&T in topology optimization
Variational-hemivariational inequalities refer to the inequality problems where both convex and n... more Variational-hemivariational inequalities refer to the inequality problems where both convex and nonconvex functions are involved. In this paper, we consider the numerical solution of a family of stationary variational-hemivariational inequalities by the finite element method. For a variational-hemivariational inequality of a general form, we prove convergence of numerical solutions. For some particular variational-hemivariational inequalities, we provide error estimates of numerical solutions, which are of optimal order for the linear finite element method under appropriate solution regularity assumptions. Numerical results are reported on solving a variational-hemivariational inequality modeling the contact between an elastic body and a foundation with the linear finite element, illustrating the theoretically predicted optimal first order convergence and providing their mechanical interpretations.
HAL (Le Centre pour la Communication Scientifique Directe), Dec 3, 2022
Data-driven approaches to accelerate computation time on PDE-based physical problems have recentl... more Data-driven approaches to accelerate computation time on PDE-based physical problems have recently received growing interest. Deep Learning algorithms are applied to learn from samples of accurate approximations of the PDEs solutions computed by numerical solvers. However, generating a large-scale dataset with accurate solutions using these classical solvers remains challenging due to their high computational cost. In this work, we propose a multi-fidelity transfer learning approach that combines a large amount of low-cost data from poor approximations with a small but accurately computed dataset. Experiments on two physical problems (airfoil flow and wheel contact) show that by transferring prior-knowledge learned from the inaccurate dataset, our approach can predict well PDEs solutions, even when only a few samples of highly accurate solutions are available.
HAL (Le Centre pour la Communication Scientifique Directe), Nov 28, 2022
Data-driven approaches to accelerate computation time on PDE-based physical problems have recentl... more Data-driven approaches to accelerate computation time on PDE-based physical problems have recently received growing interest. Deep Learning algorithms are applied to learn from samples of accurate approximations of the PDEs solutions computed by numerical solvers. However, generating a large-scale dataset with accurate solutions using these classical solvers remains challenging due to their high computational cost. In this work, we propose a multi-fidelity transfer learning approach that combines a large amount of low-cost data from poor approximations with a small but accurately computed dataset. Experiments on two physical problems (airfoil flow and wheel contact) show that by transferring prior-knowledge learned from the inaccurate dataset, our approach can predict well PDEs solutions, even when only a few samples of highly accurate solutions are available.
The purpose of this work is to present an improved energy conservation method for hyperelastodyna... more The purpose of this work is to present an improved energy conservation method for hyperelastodynamic contact problems based on specific normal compliance conditions. In order to determine this Improved Normal Compliance (INC) law, we use a Moreau-Yosida α-regularization to approximate the unilateral contact law. Then, based on the work of Hauret-LeTallec [1], we propose in the discrete framework a specific approach allowing to respect the energy conservation of the system in adequacy with the continuous case. This strategy (INC) is characterized by a conserving behavior for frictionless impacts and admissible dissipation for friction phenomena while limiting penetration. Then, we detail the numerical treatment within the framework of the semi-smooth Newton method and primal-dual active set strategy for the normal compliance conditions with friction. We finally provide some numerical experiments to bring into light the energy conservation and the efficiency of the INC method by comparing with different classical methods from the literature throught representative contact problems.
The purpose of this work is to present an improved energy conservation method for hyperelastodyna... more The purpose of this work is to present an improved energy conservation method for hyperelastodynamic contact problems based on specific normal compliance conditions. In order to determine this Improved Normal Compliance (INC) law, we use a Moreau-Yosida α-regularization to approximate the unilateral contact law. Then, based on the work of Hauret-LeTallec [1], we propose in the discrete framework a specific approach allowing to respect the energy conservation of the system in adequacy with the continuous case. This strategy (INC) is characterized by a conserving behavior for frictionless impacts and admissible dissipation for friction phenomena while limiting penetration. Then, we detail the numerical treatment within the framework of the semi-smooth Newton method and primal-dual active set strategy for the normal compliance conditions with friction. We finally provide some numerical experiments to bring into light the energy conservation and the efficiency of the INC method by comparing with different classical methods from the literature throught representative contact problems.
HAL (Le Centre pour la Communication Scientifique Directe), Nov 28, 2022
Data-driven approaches to accelerate computation time on PDE-based physical problems have recentl... more Data-driven approaches to accelerate computation time on PDE-based physical problems have recently received growing interest. Deep Learning algorithms are applied to learn from samples of accurate approximations of the PDEs solutions computed by numerical solvers. However, generating a large-scale dataset with accurate solutions using these classical solvers remains challenging due to their high computational cost. In this work, we propose a multi-fidelity transfer learning approach that combines a large amount of low-cost data from poor approximations with a small but accurately computed dataset. Experiments on two physical problems (airfoil flow and wheel contact) show that by transferring prior-knowledge learned from the inaccurate dataset, our approach can predict well PDEs solutions, even when only a few samples of highly accurate solutions are available.
HAL (Le Centre pour la Communication Scientifique Directe), Nov 28, 2022
Physical simulations are at the core of many critical industrial systems. However, today's physic... more Physical simulations are at the core of many critical industrial systems. However, today's physical simulators have some limitations such as computation time, dealing with missing or uncertain data, or even non-convergence for some feasible cases. Recently, the use of data-driven approaches to learn complex physical simulations has been considered as a promising approach to address those issues. However, this comes often at the cost of some accuracy which may hinder the industrial use. To drive this new research topic towards a better real-world applicability, we propose a new benchmark suite "Learning Industrial Physical Simulations"(LIPS) to meet the need of developing efficient, industrial application-oriented, augmented simulators. To define how to assess such benchmark performance, we propose a set of four generic categories of criteria. The proposed benchmark suite is a modular and configurable framework that can deal with different physical problems. To demonstrate this ability, we propose in this paper to investigate two distinct use-cases with different physical simulations, namely: the power grid and the pneumatic. For each use case, several benchmarks are described and assessed with existing models. None of the models perform well under all expected criteria, inviting the community to develop new industry-applicable solutions and possibly showcase their performance publicly upon online LIPS instance on Codabench.
Le Centre pour la Communication Scientifique Directe - HAL - memSIC, 2021
Topology optimization is devoted to the optimal design of structures: It aims at finding the best... more Topology optimization is devoted to the optimal design of structures: It aims at finding the best material distribution inside a working domain while fulfilling mechanical, geometrical and manufacturing specifications. Conceptually different from parametric or size optimization, topology optimization relies on a freeform approach enabling to search for the optimal design in a larger space of configurations and promoting disruptive design. The need for lighter and efficient structural solutions has made topology optimization a vigorous research field in both academic and industrial structural engineering communities. This contribution presents a Research and Development software platform for shape and topology optimization where the computational process is carried out in a level set framework combined with a body-fitted approach.
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Papers by David Danan