4 papers
A Fixed-Point Neural Operator for Size- and Functional-Transferable Hamiltonian Prediction
Yunhong Lou, Xihang Yue, Xinran Wei +2
Predicting the Kohn-Sham Hamiltonian with machine learning can accelerate density functional theory while retaining access to molecular orbitals, energy levels, and electronic-stru…
PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation
Zhen Hang, Yushan Yashengjiang, Junhui Li +21
PDE-to-solver code generation aims to automatically synthesize executable numerical solvers from partial differential equation (PDE) specifications. This task requires not only und…
DeltaPhi: Physical States Residual Learning for Neural Operators in Data-Limited PDE Solving
Xihang Yue, Yi Yang, Linchao Zhu
The limited availability of high-quality training data poses a major obstacle in data-driven PDE solving, where expensive data collection and resolution constraints severely impact…
Holistic Physics Solver: Learning PDEs in a Unified Spectral-Physical Space
Xihang Yue, Yi Yang, Linchao Zhu
Recent advances in operator learning have produced two distinct approaches for solving partial differential equations (PDEs): attention-based methods offering point-level adaptabil…