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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…
math.DS2023
Entropy Structure Informed Learning for Inverse XDE Problems
Yan Jiang, Wuyue Yang, Yi Zhu +1
Entropy, since its first discovery by Ludwig Boltzmann in 1877, has been widely applied in diverse disciplines, including thermodynamics, continuum mechanics, mathematical analysis…
math.DS2020
Revealing hidden dynamics from time-series data by ODENet
Pipi Hu, Wuyue Yang, Yi Zhu +1
To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpret…