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H.B. Keller Colloquium

Monday, October 25, 2021
4:00pm to 5:00pm
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Online Event
Neural Operator: Learning in Infinite Dimensions with Applications to PDEs
Animashree Anandkumar, Bren Professor, Computing and Mathematical Sciences Dept., California Institute of Technology,

Standard neural networks assume finite-dimensional inputs and outputs, and hence, are unsuitable for modeling phenomena such as those arising from the solutions of Partial Differential Equations (PDE). We introduce neural operators that can learn operators, which are mappings between infinite dimensional spaces. By framing neural operators as non-linear compositions of kernel integrations, we establish that they can universally approximate any operator. They are independent of the resolution or grid of training data and allow for zero-shot generalization to higher resolution evaluations. We find that the Fourier neural operator can solve turbulent fluid flows with a 1000x speedup compared to numerical solvers. I will outline several applications where neural operator has shown orders of magnitude speedup.

For more information, please contact Diana Bohler by phone at 6263951768 or by email at dbohler@caltech.edu.