From Physics-Informed Machine Learning to Physics-Informed Machine Intelligence: Quo Vadimus?

분야Field
날짜Date	2023-05-03 ~ 2023-05-03	시간Time	09:30 ~ 11:00
장소Place	Online Streaming (Zoom)	초청자Host	Minseok Choi
연사Speaker	George Em Karniadakis	소속Affiliation	The Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and Engineering, Brown University
TOPIC	From Physics-Informed Machine Learning to Physics-Informed Machine Intelligence: Quo Vadimus?
소개 및 안내사항Content	Abstract: We will review physics-informed neural networks (NNs) and summarize available extensions for applications in computational science and engineering. We will also introduce new NNs that learn functionals and nonlinear operators from functions and corresponding responses for system identification. The universal approximation theorem of operators is suggestive of the potential of NNs in learning from scattered data any continuous operator or complex system. We first generalize the theorem to deep neural networks, and subsequently we apply it to design a new composite NN with small generalization error, the deep operator network (DeepONet), consisting of a NN for encoding the discrete input function space (branch net) and another NN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, e.g., integrals, Laplace transforms and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. More generally, DeepOnet can learn multiscale operators spanning across many scales and trained by diverse sources of data simultaneously. Finally, we will present first results on the next generation of these architectures to biologically plausible designs based on spiking neural networks and Hebbian learning that are more efficient and closer to human intelligence. Online Streaming (Zoom): https://us06web.zoom.us/j/6888961076?pwd=ejYxN05jNmhUa25PU2JzSUJvQ1haQT09 ID: 688 896 1076  PW: 54321

학회명Field	From Physics-Informed Machine Learning to Physics-Informed Machine Intelligence: Quo Vadimus?
날짜Date	2023-05-03 ~ 2023-05-03	시간Time	09:30 ~ 11:00
장소Place	Online Streaming (Zoom)	초청자Host	Minseok Choi
소개 및 안내사항Content	Abstract: We will review physics-informed neural networks (NNs) and summarize available extensions for applications in computational science and engineering. We will also introduce new NNs that learn functionals and nonlinear operators from functions and corresponding responses for system identification. The universal approximation theorem of operators is suggestive of the potential of NNs in learning from scattered data any continuous operator or complex system. We first generalize the theorem to deep neural networks, and subsequently we apply it to design a new composite NN with small generalization error, the deep operator network (DeepONet), consisting of a NN for encoding the discrete input function space (branch net) and another NN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, e.g., integrals, Laplace transforms and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. More generally, DeepOnet can learn multiscale operators spanning across many scales and trained by diverse sources of data simultaneously. Finally, we will present first results on the next generation of these architectures to biologically plausible designs based on spiking neural networks and Hebbian learning that are more efficient and closer to human intelligence. Online Streaming (Zoom): https://us06web.zoom.us/j/6888961076?pwd=ejYxN05jNmhUa25PU2JzSUJvQ1haQT09 ID: 688 896 1076  PW: 54321

성명Field	From Physics-Informed Machine Learning to Physics-Informed Machine Intelligence: Quo Vadimus?
날짜Date	2023-05-03 ~ 2023-05-03	시간Time	09:30 ~ 11:00
소속Affiliation	The Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and Engineering, Brown University	초청자Host	Minseok Choi
소개 및 안내사항Content	Abstract: We will review physics-informed neural networks (NNs) and summarize available extensions for applications in computational science and engineering. We will also introduce new NNs that learn functionals and nonlinear operators from functions and corresponding responses for system identification. The universal approximation theorem of operators is suggestive of the potential of NNs in learning from scattered data any continuous operator or complex system. We first generalize the theorem to deep neural networks, and subsequently we apply it to design a new composite NN with small generalization error, the deep operator network (DeepONet), consisting of a NN for encoding the discrete input function space (branch net) and another NN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, e.g., integrals, Laplace transforms and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. More generally, DeepOnet can learn multiscale operators spanning across many scales and trained by diverse sources of data simultaneously. Finally, we will present first results on the next generation of these architectures to biologically plausible designs based on spiking neural networks and Hebbian learning that are more efficient and closer to human intelligence. Online Streaming (Zoom): https://us06web.zoom.us/j/6888961076?pwd=ejYxN05jNmhUa25PU2JzSUJvQ1haQT09 ID: 688 896 1076  PW: 54321

성명Field	From Physics-Informed Machine Learning to Physics-Informed Machine Intelligence: Quo Vadimus?
날짜Date	2023-05-03 ~ 2023-05-03	시간Time	09:30 ~ 11:00
호실Host		인원수Affiliation	George Em Karniadakis
사용목적Affiliation	Minseok Choi	신청방식Host	The Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and Engineering, Brown University
소개 및 안내사항Content	Abstract: We will review physics-informed neural networks (NNs) and summarize available extensions for applications in computational science and engineering. We will also introduce new NNs that learn functionals and nonlinear operators from functions and corresponding responses for system identification. The universal approximation theorem of operators is suggestive of the potential of NNs in learning from scattered data any continuous operator or complex system. We first generalize the theorem to deep neural networks, and subsequently we apply it to design a new composite NN with small generalization error, the deep operator network (DeepONet), consisting of a NN for encoding the discrete input function space (branch net) and another NN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, e.g., integrals, Laplace transforms and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. More generally, DeepOnet can learn multiscale operators spanning across many scales and trained by diverse sources of data simultaneously. Finally, we will present first results on the next generation of these architectures to biologically plausible designs based on spiking neural networks and Hebbian learning that are more efficient and closer to human intelligence. Online Streaming (Zoom): https://us06web.zoom.us/j/6888961076?pwd=ejYxN05jNmhUa25PU2JzSUJvQ1haQT09 ID: 688 896 1076  PW: 54321