pde-surrogates

FLARE++ is a low-rank attention architecture that replaces static learned queries with input-conditioned dynamic routing, improving on FLARE across PDE surrogate benchmarks and Long Range Arena while preserving linear complexity.

This paper proposes a diffusion-based framework for learning adaptive mesh discretization conditioned on observed PDE dynamics, using spectral guidance and physics constraints to allocate resolution where needed. The method achieves competitive or superior performance across five PDE regimes.

Proposes REEF-GP, a post-hoc uncertainty quantification framework that fits a Gaussian process to the residuals of a frozen neural operator using its internal embeddings, enabling geometry-aware and calibrated uncertainties at low cost.

Operator Boosting is a stagewise residual-learning framework that constructs compact neural operator surrogates for PDEs by training tiny models on residual fields. It achieves accuracy comparable to or better than full-size models while reducing parameters by up to 95%, demonstrating Pareto improvements on several benchmarks.