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A physics-informed neural network approach to the point defect model for electrochemical oxide film growth

Mohid Farooqi, Ingmar Bösing, Conrard G. Tetsassi Feugmo

TL;DR

This work addresses efficient, high-fidelity electrochemical oxide-film growth modeling within the Point Defect Model by embedding governing PDEs into physics-informed neural networks. A segregated PINN framework solves the coupled Nernst–Planck and Poisson equations with moving boundary L(t) and Butler–Volmer kinetics, powered by non-dimensionalization and Neural Tangent Kernel-based loss balancing. The authors show that pure PINNs overpredict film growth, but a minimally supervised hybrid approach—anchoring with a single FEM data point—yields sub-$1\%$ relative error across voltages and robust predictive fidelity. Loss landscape diagnostics and sparse data strategies expand the practical use of PINNs for multiphysics electrochemistry, offering a path toward autonomous, data-efficient simulations and parameter studies.

Abstract

Physics-informed neural networks (PINNs) offer a novel AI-driven framework for integrating physical laws directly into neural network models, facilitating the solution of complex multiphysics problems in materials engineering. This study systematically explores the application of PINNs to simulate oxide film layer growth in halide-free solutions using the point defect model (PDM). We identify and analyze four key failure modes in this context: imbalanced loss components across different physical processes, numerical instabilities due to variable scale disparities, challenges in enforcing boundary conditions within multiphysics systems, and convergence to mathematically valid but physically meaningless solutions. To overcome these challenges, we implement and validate established techniques including nondimensionalization for training stabilization, Neural Tangent Kernel-based adaptive loss balancing, robust enforcement of boundary conditions and hybrid training with sparse data. Our results demonstrate the effectiveness of these strategies in enhancing the reliability and physical fidelity of PINNs, achieving sub $1\%$ relative error as compared to Finite Element Benchmarks with the hybrid model. Thereby showing that PINNs can be used for high fidelity electrochemical simulations with minimal data requirements and highlight necesary factors for fully autonomous PINN simulations.

A physics-informed neural network approach to the point defect model for electrochemical oxide film growth

TL;DR

This work addresses efficient, high-fidelity electrochemical oxide-film growth modeling within the Point Defect Model by embedding governing PDEs into physics-informed neural networks. A segregated PINN framework solves the coupled Nernst–Planck and Poisson equations with moving boundary L(t) and Butler–Volmer kinetics, powered by non-dimensionalization and Neural Tangent Kernel-based loss balancing. The authors show that pure PINNs overpredict film growth, but a minimally supervised hybrid approach—anchoring with a single FEM data point—yields sub- relative error across voltages and robust predictive fidelity. Loss landscape diagnostics and sparse data strategies expand the practical use of PINNs for multiphysics electrochemistry, offering a path toward autonomous, data-efficient simulations and parameter studies.

Abstract

Physics-informed neural networks (PINNs) offer a novel AI-driven framework for integrating physical laws directly into neural network models, facilitating the solution of complex multiphysics problems in materials engineering. This study systematically explores the application of PINNs to simulate oxide film layer growth in halide-free solutions using the point defect model (PDM). We identify and analyze four key failure modes in this context: imbalanced loss components across different physical processes, numerical instabilities due to variable scale disparities, challenges in enforcing boundary conditions within multiphysics systems, and convergence to mathematically valid but physically meaningless solutions. To overcome these challenges, we implement and validate established techniques including nondimensionalization for training stabilization, Neural Tangent Kernel-based adaptive loss balancing, robust enforcement of boundary conditions and hybrid training with sparse data. Our results demonstrate the effectiveness of these strategies in enhancing the reliability and physical fidelity of PINNs, achieving sub relative error as compared to Finite Element Benchmarks with the hybrid model. Thereby showing that PINNs can be used for high fidelity electrochemical simulations with minimal data requirements and highlight necesary factors for fully autonomous PINN simulations.

Paper Structure

This paper contains 33 sections, 26 equations, 11 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Point Defect Model
  3. Reactions at the Metal--Film Interface (mf-interface)
  4. Reactions at the Film--Solution Interface (fs-interface)
  5. Current Densities
  6. Model and Methodology
  7. PINN Architecture for Multiphysics Modeling
  8. Loss Function Design in the PINN Framework
  9. Sampling Strategy
  10. Parameterization of Applied Potential
  11. Non-Dimensionalization and Scale Disparity
  12. NTK-Based Loss Balancing
  13. Training Summary
  14. Result and Discussion
  15. Best Model Results
  16. ...and 18 more sections

Figures (11)

  • Figure 1: Full PINN Structure Schematic
  • Figure 2: Predictions Overview using NTK weighting with Xavier Initialization simulating 250 hours. Top row left to right: potential profile time evolution on $y$-axis, space on $x$-axis, cation vacancy concentration profile time evolution on $y$-axis, space on $x$-axis, anion vacancy concentration profile time evolution on $y$-axis, space on $x$-axis. Bottom row left to right: film size vs time at representative potentials, film size vs time for $E=0.8$, potential vs $x$ at 125 hours at $E=0.8$
  • Figure 3: Film Thickness Predictions: Pure PINN vs FEM
  • Figure 4: Film Thickness Predictions: Hybrid PINN vs FEM
  • Figure 5: Potential profiles, showing potential vs $x$ at representative time between dimensional and non-dimensional model
  • ...and 6 more figures