Encode physics
Use governing equations, boundary conditions, and variational energies as direct learning signals rather than relying on labels alone.
Equations · learning · verification
About AI4PDE
AI4PDE primarily presents Xiaoying Zhuang's machine-learning research at the intersection of computational mechanics, materials, and partial differential equations.
Our direction
Intelligence grounded in physical principles.
Xiaoying Zhuang's work combines rigorous mechanics formulations with learning methods trained from physical laws, variational energies, boundary conditions, and computational data.
Core themes include energy-based PDE solvers, physics-informed deep collocation, material transfer learning, domain adaptation, neural architecture search, sensitivity analysis, multiscale modeling, stochastic heterogeneous media, neural operators, and real-time digital twins.
Recent collaborations with Mohammad Sadegh Eshaghi and other researchers extend these themes to variational neural operators, learned solver warm starts, long-time interfacial dynamics, and scientific machine learning. The objective is to build methods that remain physically interpretable while adapting efficiently across materials, geometries, scales, boundary conditions, and uncertain parameters.
Working principles
Adapt efficiently
Transfer learned features across material parameters, geometric domains, and related PDE families.
Quantify uncertainty
Use sensitivity analysis and architecture search to make stochastic simulation more efficient and transparent.