Physics-Inspired Latent Dynamics for Predicting Olfactory Mixture Similarity

Predicting olfactory similarity between molecular mixtures remains a fundamental challenge due to the absence of a universal structure-percept mapping. Existing approaches often rely on pretrained molecular representations or graph neural networks that require larger labeled data sets than are currently available for mixture similarity. Here we introduce PhysSim, a physics-inspired latent dynamics network that tests whether mixture similarity can be represented as relaxation in a descriptor-initialized latent field. Molecular embeddings evolve under three distance-dependent functional forms─inverse-square attraction, charge-based coupling, and Lennard-Jones-like short-range interaction─with scaling constants learned end-to-end. These operations are not proposed as literal molecular forces, a receptor-level model, or a complete first-principles theory of olfaction; rather, they provide a field-like functional inductive bias in a learned 128-dimensional latent space. The PyTorch implementation contains 162,059 trainable parameters (162 K), with five active dimensionless constants in the core model. On molecule-level cross-validation (Snitz 2013, 10 seeds × 5 folds, n = 50), the parsimonious core model achieves Spearman ρ = 0.610, while the extended model reaches ρ = 0.613 (95% bootstrap CI for the extended model mean: 0.600-0.626) and does not significantly improve over the core model. Relative to baselines, PhysSim is separated from descriptor MLP, Morgan fingerprint MLP, and MPNN baselines; the difference versus the attention-based mixture model is small (Δρ = 0.011, nominal p = 0.050, d = 0.25) and is therefore interpreted cautiously. Without fine-tuning, PhysSim transfers zero-shot to Ravia 2020 (ρ = 0.408, 2.0× cosine baseline) and to cross-task discriminability prediction on Bushdid 2014 (|ρ| = 0.492, 264 pairs). Monomolecular evaluation on 473 DREAM challenge stimuli yields near-zero correlation (r = -0.018), indicating that the current architecture is useful for mixture-level similarity but not for single-molecule odor character prediction. Ablation results suggest that charge-based coupling contributes to performance, but component-level attributions are exploratory after multiple-comparison correction.