Nithin Chalapathi

Nithin Chalapathi

Ph.D. student ยท AI for Science

PDEInvBench: A Comprehensive Dataset and Design Space Exploration of Neural Networks for PDE Inverse Problems

Published in Transactions on Machine Learning Research (TMLR), 2026

Divyam Goel, Nithin Chalapathi, Sanjeev Raja, Aditi S. Krishnapriyan

PDF Code Dataset TMLR DOI BibTeX

PDEInvBench overview showing inverse parameter estimation, neural-network design axes, PDE datasets, and evaluation splits.

Figure 1. Benchmark overview. Source paper.

Abstract summary

PDEInvBench benchmarks how neural networks recover physical parameters from observed PDE solutions. It covers time-dependent and steady-state equations, with evaluation across familiar and unfamiliar parameter regimes. The study compares training objectives, network representations, and model and dataset scaling. Results favor supervised initialization followed by physics-based test-time refinement, show benefits from providing PDE derivatives as input, and highlight the value of diverse initial conditions. The released dataset and evaluation code support reproducible comparisons of methods for PDE inverse problems.