4 papers
Physics-Consistent Diffusion for Efficient Fluid Super-Resolution via Multiscale Residual Correction
Zhihao Li, Shengwei Dong, Chuang Yi +5
Existing image SR and generic diffusion models transfer poorly to fluid SR: they are sampling-intensive, ignore physical constraints, and often yield spectral mismatch and spurious…
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.…
A Priori Error Estimation of Physics-Informed Neural Networks Solving Allen--Cahn and Cahn--Hilliard Equations
Guangtao Zhang, Jiani Lin, Qijia Zhai +4
Physics-Informed Neural Networks (PINNs) encounter accuracy limitations when solving the Allen--Cahn (AC) and Cahn--Hilliard (CH) partial differential equations (PDEs). To overcome…
Parameter Identification for Partial Differential Equations with Spatiotemporal Varying Coefficients
Guangtao Zhang, Yiting Duan, Guanyu Pan +3
To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing thes…