9 papers
Large language models for partial differential equation workflows
Han Wan, Rui Zhang, Hao Sun
Partial differential equations (PDEs) become actionable in science and engineering not as isolated formulae, but as executable workflows that connect modelling assumptions, governi…
Learning, Solving and Optimizing PDEs with TensorGalerkin: an efficient high-performance Galerkin assembly algorithm
Shizheng Wen, Mingyuan Chi, Tianwei Yu +5
We present a unified algorithmic framework for the numerical solution, constrained optimization, and physics-informed learning of PDEs with a variational structure. Our framework i…
Spectral-inspired Operator Learning with Limited Data and Unknown Physics
Han Wan, Rui Zhang, Hao Sun
Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals…
Hierarchical Physics-Embedded Learning for Partially Known Spatiotemporal Dynamics
Xizhe Wang, Xiaobin Song, Qingshan Jia +4
Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems. Existing scientific machine learning para…
PIMRL: Physics-Informed Multi-Scale Recurrent Learning for Burst-Sampled Spatiotemporal Dynamics
Han Wan, Qi Wang, Yuan Mi +2
Deep learning has shown strong potential in modeling complex spatiotemporal dynamics. However, most existing methods depend on densely and uniformly sampled data, which is often un…
Stable spectral neural operator for learning stiff PDE systems from limited data
Rui Zhang, Han Wan, Yang Liu +1
Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the…