4 papers
CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systems
Jiale Gong, Pengzhan Jin, Dongyang Kuang +2
Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification. For linearly damped H…
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…
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…