3 papers
math.DS2026
Incorporating Continuous Dependence Qualifies Physics-Informed Neural Networks for Operator Learning
Guojie Li, Wuyue Yang, Liu Hong
Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irr…
physics.comp-ph2025
Extracting Interaction Kernels for Many-Particle Systems by a Two-Phase Approach
Yangxuan Shi, Wuyue Yang, Liu Hong
This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the p…
stat.ML2024
MEP-Net: Generating Solutions to Scientific Problems with Limited Knowledge by Maximum Entropy Principle
Wuyue Yang, Liangrong Peng, Guojie Li +1
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networ…