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H.B. Keller Colloquium

Monday, November 15, 2021
4:00pm to 5:00pm
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Physics-Informed Machine Learning
George Em Karniadakis, The Charles Pitts Robinson and John Palmer Barstow Professor, Applied Mathematics and Engineering, Brown University,

We will review physics-informed neural network and summarize available theoretical results. 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.

For more information, please contact Diana Bohler by phone at 626-395-1768 or by email at [email protected].