README.md

PIFT Python JAX

This study reproduced the main ideas and key empirical findings of Alberts and Bilionis' physics-informed information field theory (PIFT) framework in a JAX/Python implementation translated from the original C++ codebase. Component-level verification (sec. 2) showed that covariance, KLE, and constrained-field gradient calculations matched the reference implementation up to expected numerical precision.

The reproduced experiments (sec. 3) also captured the paper's main qualitative conclusions. In the forward problem, increasing $\beta$ caused the prior to concentrate around the PDE solution, confirming its role as a measure of trust in the physics. In the inverse problem, inferred $\beta$ was large when the model was correct and small when the physics were wrong, showing that PIFT can detect model-form error.

Although the JAX version was slower and used fewer SGLD iterations than the original implementation, it reproduced the essential trends reported in the paper. Overall, this replication supports the paper's central claim that PIFT provides a principled Bayesian framework for combining physical laws and data while using $\beta$ to balance trust between them.

Referenced Paper: ArXiv Elsevier GitHub