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MINDS Seminar on Machine LearningㅣNumerical approximation of PDEs via deep neural networks: analysis and computation

기간 : 2023-03-21 ~ 2023-03-21
시간 : 17:00 ~ 18:00
개최 장소 : Online Streaming
개요
MINDS Seminar on Machine LearningㅣNumerical approximation of PDEs via deep neural networks: analysis and computation
분야Field
날짜Date 2023-03-21 ~ 2023-03-21 시간Time 17:00 ~ 18:00
장소Place Online Streaming 초청자Host
연사Speaker Seungchan Ko 소속Affiliation Inha University
TOPIC MINDS Seminar on Machine LearningㅣNumerical approximation of PDEs via deep neural networks: analysis and computation
소개 및 안내사항Content
Abstract: In recent years, due to the tremendous success of machine learning in various fields, it has recently begun to gain more attention to solve partial differential equations (PDEs) using a deep learning algorithm. In particular, by utilizing the approximation properties of deep neural networks and statistical learning theory to numerical PDEs, this new approach opened a new area of research which is recently called scientific machine learning. In this talk, I will introduce some well-known algorithms in scientific machine learning, for example, Deep Ritz Method or Physics-Informed Neural Network. And then I will also address the mathematical analysis of these methods in the context of the classical numerical analysis framework. Finally, I will introduce my recent result on the analysis and approximation of unsupervised Legendre–Galerkin neural network (ULGNet), which is based on the techniques both from numerical analysis and machine learning. Unlike existing deep learning-based numerical methods for PDEs, the ULGNet expresses the solution as a spectral expansion with respect to the Legendre basis and predicts the coefficients with deep neural networks by solving a variational residual minimization problem. Numerical evidence will also be provided to support the theoretical result.
 
 
ID : 688 896 1076 / PW : 54321
학회명Field MINDS Seminar on Machine LearningㅣNumerical approximation of PDEs via deep neural networks: analysis and computation
날짜Date 2023-03-21 ~ 2023-03-21 시간Time 17:00 ~ 18:00
장소Place Online Streaming 초청자Host
소개 및 안내사항Content
Abstract: In recent years, due to the tremendous success of machine learning in various fields, it has recently begun to gain more attention to solve partial differential equations (PDEs) using a deep learning algorithm. In particular, by utilizing the approximation properties of deep neural networks and statistical learning theory to numerical PDEs, this new approach opened a new area of research which is recently called scientific machine learning. In this talk, I will introduce some well-known algorithms in scientific machine learning, for example, Deep Ritz Method or Physics-Informed Neural Network. And then I will also address the mathematical analysis of these methods in the context of the classical numerical analysis framework. Finally, I will introduce my recent result on the analysis and approximation of unsupervised Legendre–Galerkin neural network (ULGNet), which is based on the techniques both from numerical analysis and machine learning. Unlike existing deep learning-based numerical methods for PDEs, the ULGNet expresses the solution as a spectral expansion with respect to the Legendre basis and predicts the coefficients with deep neural networks by solving a variational residual minimization problem. Numerical evidence will also be provided to support the theoretical result.
 
 
ID : 688 896 1076 / PW : 54321
성명Field MINDS Seminar on Machine LearningㅣNumerical approximation of PDEs via deep neural networks: analysis and computation
날짜Date 2023-03-21 ~ 2023-03-21 시간Time 17:00 ~ 18:00
소속Affiliation Inha University 초청자Host
소개 및 안내사항Content
Abstract: In recent years, due to the tremendous success of machine learning in various fields, it has recently begun to gain more attention to solve partial differential equations (PDEs) using a deep learning algorithm. In particular, by utilizing the approximation properties of deep neural networks and statistical learning theory to numerical PDEs, this new approach opened a new area of research which is recently called scientific machine learning. In this talk, I will introduce some well-known algorithms in scientific machine learning, for example, Deep Ritz Method or Physics-Informed Neural Network. And then I will also address the mathematical analysis of these methods in the context of the classical numerical analysis framework. Finally, I will introduce my recent result on the analysis and approximation of unsupervised Legendre–Galerkin neural network (ULGNet), which is based on the techniques both from numerical analysis and machine learning. Unlike existing deep learning-based numerical methods for PDEs, the ULGNet expresses the solution as a spectral expansion with respect to the Legendre basis and predicts the coefficients with deep neural networks by solving a variational residual minimization problem. Numerical evidence will also be provided to support the theoretical result.
 
 
ID : 688 896 1076 / PW : 54321
성명Field MINDS Seminar on Machine LearningㅣNumerical approximation of PDEs via deep neural networks: analysis and computation
날짜Date 2023-03-21 ~ 2023-03-21 시간Time 17:00 ~ 18:00
호실Host 인원수Affiliation Seungchan Ko
사용목적Affiliation 신청방식Host Inha University
소개 및 안내사항Content
Abstract: In recent years, due to the tremendous success of machine learning in various fields, it has recently begun to gain more attention to solve partial differential equations (PDEs) using a deep learning algorithm. In particular, by utilizing the approximation properties of deep neural networks and statistical learning theory to numerical PDEs, this new approach opened a new area of research which is recently called scientific machine learning. In this talk, I will introduce some well-known algorithms in scientific machine learning, for example, Deep Ritz Method or Physics-Informed Neural Network. And then I will also address the mathematical analysis of these methods in the context of the classical numerical analysis framework. Finally, I will introduce my recent result on the analysis and approximation of unsupervised Legendre–Galerkin neural network (ULGNet), which is based on the techniques both from numerical analysis and machine learning. Unlike existing deep learning-based numerical methods for PDEs, the ULGNet expresses the solution as a spectral expansion with respect to the Legendre basis and predicts the coefficients with deep neural networks by solving a variational residual minimization problem. Numerical evidence will also be provided to support the theoretical result.
 
 
ID : 688 896 1076 / PW : 54321
Admin Admin · 2023-03-06 17:33 · 조회 68
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