Neural Operators for Solving PDEs and Inverse Design
Anima Anandkumar
California Institute of Technology
, and NVIDIA
ABSTRACT
Deep learning surrogate models have shown promise in
modeling complex physical phenomena such as photonics, fluid
flows, molecular dynamics and material properties. However,
standard neural networks assume finite
-
dimensional inputs and
outputs, and hence, cannot withstand a change in resolution or
discretization between training and testing. We introduce Fourier
neural operators that can learn operators, which are mappings
bet
ween infinite dimensional spaces. They are discretization
-
invariant and can generalize beyond the discretization or
resolution of training data. They can efficiently solve
partial
differential equations (
PDEs
)
on general geometries. We consider
a variety o
f PDEs for both forward modeling and inverse design
problems, as well as show practical gains in the lithography
domain.
CCS Concepts/ACM Classifier
s
•
Computing methodologies
→
Machine learning
→
Machine learning approaches
→
Neural networks
Author Keywords
Deep learning; neural networks; Fourier neural operators;
partial differential equations; lithography.
BIOGRAPHY
Anima Anandkumar is Bren Professor at Caltech and Senior
Director of AI Research at NVIDIA. She received her B.Tech from
the
Indian Institute of Technology Madras, and her Ph.D. from
Cornell University. She did her postdoctoral research at MIT and
an assistant professorship at the University of California Irvine.
She has received several honors such as the IEEE fellowship,
Alfre
d. P. Sloan Fellowship, NSF Career Award, and Faculty
Fellowships from Microsoft, Google, Facebook, and Adobe. She is
part of the World Economic Forum's Expert Network.
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-
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3
, March 2
6
–
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Copyright is held by the owner/author(s).
ACM ISBN
978
-
1
-
450
3
-
9978
-
4/23/03
.
DOI:
https://doi.org/10.1145/3569052.3578911
195