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A deformation-based framework for learning solution mappings of PDEs defined on varying domains
Shanshan Xiao, Pengzhan Jin, Yifa Tang
In this work, we establish a deformation-based framework for learning solution mappings of PDEs defined on varying domains. The union of functions defined on varying domains can be…
Learning solution operators of PDEs defined on varying domains via MIONet
Shanshan Xiao, Pengzhan Jin, Yifa Tang
In this work, we propose a method to learn the solution operators of PDEs defined on varying domains via MIONet, and theoretically justify this method. We first extend the approxim…
Two-hidden-layer ReLU neural networks and finite elements
Pengzhan Jin
We point out that (continuous or discontinuous) piecewise linear functions on a convex polytope mesh can be represented by two-hidden-layer ReLU neural networks in a weak sense. In…
A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples
Jun Hu, Pengzhan Jin
We propose a hybrid iterative method based on MIONet for PDEs, which combines the traditional numerical iterative solver and the recent powerful machine learning method of neural o…