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stat.CO2025
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…
stat.ML2025
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.…
stat.ML2025
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…