Discovering Equations that Govern Experimental Materials Stability under Environmental Stress using Scientific Machine Learning

TL;DR

This study uses scientific machine learning to infer the differential equations governing the degradation of perovskite materials under environmental stress, revealing a minimal three-term polynomial model that aids mechanistic understanding.

Contribution

The paper introduces a sparse regression approach to identify the governing differential equations from experimental data, providing new insights into material degradation mechanisms.

Findings

The governing DE is a three-term polynomial, not a simple reaction order.

The DE aligns with the Verhulst logistic function, indicating autocatalytic behavior.

The methodology is robust to noise and experimental variability.

Abstract

While machine learning (ML) in experimental research has demonstrated impressive predictive capabilities, inductive reasoning and knowledge extraction remain elusive tasks, in part because of the difficulty extracting fungible knowledge representations from experimental data. In this manuscript, we use ML to infer the underlying dynamical differential equation (DE) from experimental data of degrading organic-inorganic methylammonium lead iodide (MAPI) perovskite thin films under environmental stressors (elevated temperature, humidity, and light). We apply a sparse regression algorithm that automatically identifies the differential equation describing the dynamics from time-series data. We find that the underlying DE governing MAPI degradation across a broad temperature range of 35 to 85{\deg}C is described minimally with three terms (specifically, a second-order polynomial), and not a simple single-order reaction (i.e. 0th, 1st, or 2nd-order reaction). We demonstrate how computer-derived results can aid the researcher to develop profound mechanistic insights. This DE corresponds to the Verhulst logistic function, which describes reaction kinetics analogous in functional form to autocatalytic or self-propagating reactions, suggesting future strategies to suppress MAPI degradation. We examine the robustness of our conclusions to experimental luck-of-the-draw variance and Gaussian noise using a combination of experiment and simulation, and describe the experimental limits within which this methodology can be applied. Our study demonstrates the application of scientific ML in experimental chemical and materials systems, highlighting the promise and challenges associated with ML-aided scientific discovery.