no code implementations • 23 Feb 2024 • 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.
no code implementations • 8 Jan 2024 • Shanshan Xiao, Jiawei Zhang, Yifa Tang
Then in this article, we introduce a groundbreaking extension (Genralized Lagrangian Neural Networks) to Lagrangian Neural Networks (LNNs), innovatively tailoring them for non-conservative systems.
no code implementations • 31 Mar 2023 • Aiqing Zhu, Tom Bertalan, Beibei Zhu, Yifa Tang, Ioannis G. Kevrekidis
We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss.
1 code implementation • 15 Jun 2022 • Aiqing Zhu, Pengzhan Jin, Beibei Zhu, Yifa Tang
The combination of ordinary differential equations and neural networks, i. e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles.
1 code implementation • 29 Apr 2022 • Aiqing Zhu, Beibei Zhu, Jiawei Zhang, Yifa Tang, Jian Liu
We propose volume-preserving networks (VPNets) for learning unknown source-free dynamical systems using trajectory data.
no code implementations • 21 Jun 2021 • Aiqing Zhu, Pengzhan Jin, Yifa Tang
Measure-preserving neural networks are well-developed invertible models, however, their approximation capabilities remain unexplored.
1 code implementation • 11 Jan 2020 • Pengzhan Jin, Zhen Zhang, Aiqing Zhu, Yifa Tang, George Em. Karniadakis
We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules.
1 code implementation • 27 May 2019 • Pengzhan Jin, Lu Lu, Yifa Tang, George Em. Karniadakis
To derive a meaningful bound, we study the generalization error of neural networks for classification problems in terms of data distribution and neural network smoothness.