pde-solving

AutoPDE is a code agent that explicitly represents solver strategies for partial differential equations, improving pass rate by 14.2% over baselines on the PDE Agent Bench.

Functional Attention is a novel attention mechanism that reinterprets attention as a functional correspondence between adaptive bases, replacing softmax affinities with structured linear operators inspired by geometric functional maps. The method achieves state-of-the-art performance on operator learning tasks including PDE solving and 3D segmentation while remaining resolution-invariant.

This paper investigates the generalization behavior of Fourier Neural Operators and Deep Operator Networks under distribution shifts in a variable-coefficient wave equation, revealing that FNO struggles with high-frequency inputs while DeepONet shows milder degradation.

This paper proposes a new architecture that augments Flux Neural Operators with recurrent Vision Transformers to solve conservation laws as a foundation model. It demonstrates robust generalization and long-time prediction capabilities across diverse conservative systems without explicit access to governing equations.