Search Results for author:
Found 8 papers, 4 papers with code
Learning solution operators of PDEs defined on varying domains via MIONet
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.
Generalized Lagrangian Neural Networks
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.
Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-nets
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.
On Numerical Integration in Neural Ordinary Differential Equations
The combination of ordinary differential equations and neural networks, i. e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles.
VPNets: Volume-preserving neural networks for learning source-free dynamics
We propose volume-preserving networks (VPNets) for learning unknown source-free dynamical systems using trajectory data.
Approximation capabilities of measure-preserving neural networks
Measure-preserving neural networks are well-developed invertible models, however, their approximation capabilities remain unexplored.
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules.
Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness
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.
