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arXiv Machine Learning By Jaehyeon Park, Mingu Kang, Dongseok Lee, Woojin Cho, Kookjin Lee, Anthony Gruber, Youngjoon Hong, Noseong Park

PDE-PFN: Prior-Data Fitted Neural PDE Solver

Read the original on arXiv Machine Learning →

PDE-PFN is a prior‑data fitted neural solver that uses in‑context learning to approximate the posterior predictive mean of partial differential equation (PDE) solutions. It builds on a Transformer‑based PFN architecture with self‑ and cross‑attention, and is pre‑trained on noisy approximate solutions generated by physics‑informed neural networks. Experiments on various two‑dimensional PDEs show that PDE‑PFN generalizes across heterogeneous equations, remains robust to noisy priors, and can perform zero‑gradient‑update inference while achieving competitive or better predictive accuracy compared to baselines.

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