Multi-Objective Loss Function For Free Energy Calculations

Accurate estimation of binding free energy $\left(\Delta \Delta G\right)$ remains a critical challenge in drug discovery, directly influencing the development of effective therapeutics. Physics-based computational methods-such as molecular dynamics simulations and implicit solvent modeling-offer rigorous, atomistic insights into molecular recognition but are often constrained by computational costs and limited scalability. In contrast, deep learning models, particularly graph convolutional networks (GCNs), have demonstrated the ability to rapidly predict molecular properties by learning hierarchical representations from large-scale chemical data, yet frequently lack explicit incorporation of physical laws, leading to potential issues with interpretability and generalizability. Hybrid physics-guided neural networks seek to overcome these limitations by embedding physically meaningful features and constraints within deep learning architectures. In this study, we introduce a multi-objective loss function that simultaneously optimizes empirical error, structural similarity, and physical consistency by integrating molecular fingerprints with physics-based features such as electrostatic and van der Waals energies in a unified GCN framework. Applied to 65-75 host-guest systems, this approach yields substantial improvements in entropy $\left(T\Delta S\right)$ prediction accuracy, reducing the mean absolute difference (MAD) from 5.80 to 1.07 kcal/mol, while also enhancing the accuracy and convergence of binding free energy $\left(\Delta \Delta G\right)$ predictions (MAD reduced to 1.54 kcal/mol), mitigating overfitting, and improving model transferability to larger complexes. These results demonstrate that principled loss function engineering is pivotal not only for accurate entropy estimation but also for enhancing the reliability and interpretability of binding free energy predictions in molecular machine learning models.