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Exact Representation of Piecewise Polynomial Finite Element Functions by Two-Hidden-Layer Multilayer Perceptrons
Jun Hu, Pengzhan Jin, Shengyang Xu
We construct exact representations of finite element functions of arbitrary polynomial degree on simplicial meshes in any spatial dimension by two-hidden-layer multilayer perceptro…
Learning Operators of Geometry with an Interface Autoencoder
Aiqing Zhu, Pengzhan Jin
Geometry-dependent PDEs define operators whose inputs and outputs may each consist of an oriented interface and a function on that interface, whereas most existing neural operators…
MENO: Memory-Efficient Neural Operator
Shengyang Xu, Weijun Zhang, Jun Hu +1
We propose the Memory-Efficient Neural Operator (MENO) as a high-performance PDE neural solver based on the Manifold Function Encoder (MFE). MENO features three primary advantages:…
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…