Learning Diffusion from Sparse Data: A Machine-Learning Bridge between Molecular Motion and Macroscopic Transport

Abstract

Predicting molecular self-diffusion coefficients (D*) across chemical space remains challenging due to sparse experimental data and the high computational cost of molecular simulations. We present a data-centric machine learning framework that integrates experimental diffusion measurements with molecular dynamics simulations through a semisupervised distillation strategy. Unlike conventional approaches that treat limited experiments or simulations as direct ground truth, our method selectively incorporates simulation-derived D* only when they align with the uncertainty bounds of a Random Forest model initially trained on experimental D*. This enables controlled data set expansion, from 130 unique experimentally measured molecules to over 1,000 unique substances, while preserving label reliability. We further employ pretrained large language model embeddings to encode transferable chemical context beyond conventional descriptors, reducing predictive variance and improving generalization across chemically diverse systems. The resulting model achieves improved accuracy, with a held-out test set R2 of 0.87, an overall R2 of 0.92, and a test set mean absolute error of 0.13 × 10-9 m2 s-1 after iterative distillation across more than 1,000 chemically diverse molecules under near-ambient conditions (295-300 K). We further demonstrate that learned D* act as transferable, physically interpretable descriptors in skin permeability modeling, where their inclusion reduces test set error and improves correlation relative to models relying solely on conventional physicochemical descriptors. This work establishes a scalable framework for bridging sparse experimental measurements with broadly generalizable predictions, enabling interpretable and transferable modeling across distinct molecular transport phenomena.