Learning Reaction-Diffusion Kinetics from Mechanical Information

TL;DR

This paper introduces a novel framework that uses mechanical strain data to accurately infer complex chemical kinetics and properties in materials, enabling characterization where direct measurement is challenging.

Contribution

The study presents a PDE-constrained learning method that reconstructs chemical kinetics from mechanical observations in coupled systems, applicable to various complex scenarios.

Findings

Successfully identified diffusion and reaction laws in battery materials

Robustly inferred spatial heterogeneity and thermodynamic properties

Achieved accurate learning with limited data and noise

Abstract

A central challenge in materials science is characterizing chemical processes that are elusive to direct measurement, particularly in functional materials operating under realistic conditions. Here, we demonstrate that mechanical strain fields contain sufficient information to reconstruct hidden chemical kinetics in coupled chemomechanical systems. Our partial differential equation-constrained learning framework decodes concentration-dependent diffusion kinetics, thermodynamic driving forces, and spatially heterogeneous reaction rates solely from mechanical observations. Using battery electrode materials as a model system, we demonstrate that the framework can accurately identify complex constitutive laws governing three distinct scenarios: classical Fickian diffusion, spinodal decomposition with pattern formation, and heterogeneous electrochemical reactions with spatial rate variations. The approach demonstrates robustness while maintaining accuracy with limited spatial data and reasonable experimental noise levels. Most significantly, the framework simultaneously infers multiple fundamental processes and properties, including diffusivity, reaction kinetics, chemical potential, and spatial heterogeneity maps, all from mechanical information alone. This method establishes a paradigm for materials characterization, enabling accurate learning of chemical processes in energy storage systems, catalysts, and phase-change materials where conventional diagnostics prove difficult. By revealing that mechanical deformation patterns serve as information-rich fingerprints of the underlying chemical processes, this work follows the pathway of inversely learning constitutive laws, with broad implications in materials science and engineering.