7 papers
Inverse Problems for Partial Differential Equations with Jump Discontinuities in Coefficients via Two-Stage Physics-Informed Deep Learning and Statistical Mixture Models
Zhikun Zhang, Guanyu Pan, Xiangjun Wang +2
This work proposes a two-stage physics-informed deep learning framework that combines neural-network-based sampling with statistical inference and constrained parameter refinement.…
Wasserstein Geometry of Information Loss in Nonlinear Dynamical Systems
Yiting Duan, Zhikun Zhang, Yi Guo
Time-delay embedding is a powerful technique for reconstructing the dynamics of nonlinear systems. However, the reconstruction map is not always an embedding, a condition rarely ve…
Residual-loss Anomaly Analysis of Physics-Informed Neural Networks: An Inverse Method for Change-point Detection in Nonlinear Dynamical Systems with Regime Switching
Yuhe Bai, Chengli Tan, Jiaqi Li +2
Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat c…
Reconstruction and Prediction of Volterra Integral Equations Driven by Gaussian Noise
Zhihao Xu, Saisai Ding, Zhikun Zhang +1
Integral equations are widely used in fields such as applied modeling, medical imaging, and system identification, providing a powerful framework for solving deterministic problems…
Solving Fokker-Planck-Kolmogorov Equation by Distribution Self-adaptation Normalized Physics-informed Neural Networks
Yi Zhang, Yiting Duan, Xiangjun Wang +1
Stochastic dynamical systems provide essential mathematical frameworks for modeling complex real-world phenomena. The Fokker-Planck-Kolmogorov (FPK) equation governs the evolution…
Parameters Inference for Nonlinear Wave Equations with Markovian Switching
Yi Zhang, Zhikun Zhang, Xiangjun Wang
Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coeff…