3.4k citations · 3.4k across the 19 of their papers we have counts for
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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…
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…
Experimental observation on a low-rank tensor model for eigenvalue problems
Jun Hu, Pengzhan Jin
Here we utilize a low-rank tensor model (LTM) as a function approximator, combined with the gradient descent method, to solve eigenvalue problems including the Laplacian operator a…
On Numerical Integration in Neural Ordinary Differential Equations
Aiqing Zhu, Pengzhan Jin, Beibei Zhu +1
The combination of ordinary differential equations and neural networks, i.e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles. Howe…
MIONet: Learning multiple-input operators via tensor product
Pengzhan Jin, Shuai Meng, Lu Lu
As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several…
Approximation capabilities of measure-preserving neural networks
Aiqing Zhu, Pengzhan Jin, Yifa Tang
Measure-preserving neural networks are well-developed invertible models, however, their approximation capabilities remain unexplored. This paper rigorously analyses the approximati…
Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks
Pengzhan Jin, Zhen Zhang, Ioannis G. Kevrekidis +1
We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data. Based on the Darboux-Lie theorem, the phase flow of a Poiss…
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
Pengzhan Jin, Zhen Zhang, Aiqing Zhu +2
We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we def…
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
Lu Lu, Pengzhan Jin, George Em Karniadakis
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a sin…