# RSI-PDEbench

Recovering a partial differential equation from sampled solution data demands expert work in equation discovery, coefficient estimation and numerical solver configuration. RSI-PDEbench turns that workflow into a benchmark of 1,001 cases over 42 equation templates, split into noise-free, 50% Gaussian-noise and unseen-template-with-shifted-coefficient settings; the accompanying RSI-PDE agent shortlists candidate equations by residual, refines coefficients and solvers with relative feedback, and keeps improvements behind a validation gate. Across four frontier models its mean pass rate rises 106.5–181.9% over single-run baselines and 3.0–19.6% over native agent harnesses.

Recovering a partial differential equation from sampled solution data demands expert work in equation discovery, coefficient estimation and numerical solver configuration. RSI-PDEbench turns that workflow into a benchmark of 1,001 cases over 42 equation templates, split into noise-free, 50% Gaussian-noise and unseen-template-with-shifted-coefficient settings; the accompanying RSI-PDE agent shortlists candidate equations by residual, refines coefficients and solvers with relative feedback, and keeps improvements behind a validation gate. Across four frontier models its mean pass rate rises 106.5–181.9% over single-run baselines and 3.0–19.6% over native agent harnesses.