4 papers
Kernel Localization and Whole-Trajectory Generalization for Linear Multistep Methods in Deep Learning-Based Discovery of Dynamical Systems
Yaru Liu, Yiqi Gu
Linear multistep methods (LMMs) combined with neural-network approximation provide a high-order framework for learning governing vector fields of dynamical systems from discrete tr…
Layer Separation Deep Learning Model with Auxiliary Variables for Partial Differential Equations
Yaru Liu, Yiqi Gu
In this paper, we propose a new optimization framework, the layer separation (LySep) model, to improve the deep learning-based methods in solving partial differential equations. Du…
Deep Learning Optimization Using Self-Adaptive Weighted Auxiliary Variables
Yaru Liu, Yiqi Gu, Michael K. Ng
In this paper, we develop a new optimization framework for the least squares learning problem via fully connected neural networks or physics-informed neural networks. The gradient…
Discover physical concepts and equations with machine learning
Bao-Bing Li, Yi Gu, Shao-Feng Wu
Machine learning can uncover physical concepts or physical equations when prior knowledge from the other is available. However, these two aspects are often intertwined and cannot b…