18 citations · 28 across the 9 of their papers we have counts for
5 papers · 1 filter
Manifold Function Encoder: Identifying Different Functions Defined on Different Manifolds
Jun Hu, Pengzhan Jin, Weijun Zhang
We propose the Manifold Function Encoder (MFE) for identifying different functions defined on different manifolds. Both a manifold in Euclidean space and a function defined on this…
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…
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…
Deep Hamiltonian networks based on symplectic integrators
Aiqing Zhu, Pengzhan Jin, Yifa Tang
HNets is a class of neural networks on grounds of physical prior for learning Hamiltonian systems. This paper explains the influences of different integrators as hyper-parameters o…