PATHNet: A Thermodynamic Path-Integral-Inspired Neural Network for Protein-Ligand Interaction Prediction

Protein-ligand scoring functions must capture strongly nonlinear, target-dependent binding physics while remaining generalizable beyond their training data, a balance that purely analytic and purely data-driven models each struggle to achieve on their own. We present PATHNet, a physics-informed framework that learns this unknown functional relationship from molecular-mechanics descriptors using a non-monotonic piecewise-linear mapper with a bounded neural-network correction, trained through a variational, least-action-inspired objective and regulated by a renormalization-group-inspired spectral constraint, with model selection performed through multi-start basin optimization. Across seven DUD-E targets, PATHNet achieved the highest mean active inactive/decoy classification accuracy among the methods tested, outperforming three literature baselines representing distinct architectural families. These results support a physics-grounded, variationally constrained approach to neural-network scoring as a practical route toward more interpretable and transferable protein-ligand interaction models.