TY - JOUR
T1 - A Theory of Inductive Biases for Thermal Transport Prediction in Disordered Materials Using Equivariant GNNs
AU - Patrick O’Connor
AU - Sean Murphy
JF - Journal of Computational and Data-Driven Materials Engineering
JO - J. Comput. Data-Driven Mater. Eng.
SN - 3149-9368
Y1 - 2025
VL - 4
IS - 2
DO - 10.68159/d564214712
SP - 53
N2 - Thermal transport, specifically lattice thermal conductivity, in disordered materials such as glasses, high-entropy alloys, and polymers is critical for applications ranging from thermoelectric energy conversion and thermal barrier coatings to electronic cooling and flexible electronics. The structural disorder inherent in these systems breaks translational symmetry, generates heterogeneous local atomic environments, and produces complex, non-perturbative phonon scattering that defies conventional analytical or simulation-based prediction. Equivariant graph neural networks (GNNs) have demonstrated strong empirical promise in this domain by embedding specific inductive biases directly into their architecture. This paper delivers a purely theoretical analysis of the inductive biases that are necessary and sufficient for reliable thermal transport prediction in disordered materials using equivariant GNNs. We formally define inductive bias as any assumption that constrains the hypothesis space and thereby enables generalization from limited data. Through conceptual arguments we identify three key biases—rotational equivariance, locality (finite cutoff), and energy conservation—as fundamental, while showing how supporting biases of smoothness, permutation invariance, and size extensivity reinforce them. Rotational equivariance ensures that tensorial thermal conductivity transforms correctly under arbitrary material rotations; locality reflects the short-range nature of phonon scattering even in globally disordered systems; and energy conservation guarantees that derived forces remain physically consistent for phonon-frequency calculations. We prove conceptually that these biases collectively reduce sample complexity by shrinking the effective dimension of the hypothesis space, improve extrapolation to new disorder realizations provided local environments remain statistically similar, and enforce physical consistency without requiring explicit regularization. Disordered materials constitute a worst-case regime for machine learning because they lack the global symmetries that crystalline systems implicitly exploit; the biases therefore become not merely advantageous but essential. The analysis concludes with direct implications for GNN architecture design, establishing equivariant GNNs as the theoretically preferred framework for thermal transport in disordered materials. This work supplies the missing theoretical foundation that explains why equivariant architectures succeed where generic models fail and offers precise guidance for future model development in computational materials engineering.
UR - https://iamrp.net/d564214712
ER -