Neural constitutive learning enables flexible reaction diffusion system modeling
Neural Constitutive Learning for Generalized Reaction-Diffusion Systems
Machine Learning
Summary
Modeling chemical and physical processes often requires solving complex equations that describe how substances move and react over time. The authors propose a new approach that teaches a neural network to learn the underlying rules (constituent laws) governing these processes, instead of the full solution paths. This method lets the model apply what it learns to new starting conditions and longer time periods without retraining. Their tests show it works well across various systems, enabling faster and more general predictions.
What this means in practice
- •For computational chemists: Simulate complex chemical transport and reaction processes more flexibly by reusing learned constitutive relations across diverse initial conditions and time periods.
- •For material simulation engineers: Implement shared neural frameworks for predicting material behaviors involving coupled transport and reactions without retraining for each scenario.
Authors
Shang-Ke Chen, Yu-Peng Wang, Shih-Hsuan Hung, Wei-Fang Sun, Chao-Shun Zhan, Simon See, Min-Jhe Lu
Abstract
Generalized reaction-diffusion systems encompass diverse transport mechanisms and coupled reaction kinetics. A central question for neural PDE solvers is what should be learned so that a common interface can accommodate phase-field and degenerate transport, local reactions, and multispecies coupling. We propose the Neural Constitutive Laws--Mass-Compression-Transport (NCL-MCT) Solver, which learns PDE-specific constitutive responses while retaining temporal evolution in a shared MCT integrator. Transport is represented through mobility and thermodynamic driving force, and reaction through relative reaction rates. These constitutive responses depend on the current density rather than explicitly on the initial condition or elapsed time, motivating their reuse across different initial conditions and time horizons. The same interface supports velocity-data supervision and known-law supervision, neither of which requires time integration during training. When constitutive laws are known, supervision can be evaluated on independently sampled density fields, enabling trajectory-free constitutive learning without generating solution trajectories. Across seven systems, separately trained constitutive modules share the same interface and MCT integrator and achieve relative rollout $L^2$ errors of $10^{-4}$ to $10^{-2}$. Tests with unseen initial-condition families and an extended time horizon assess reuse beyond training conditions, while separate experiments demonstrate trajectory-free constitutive learning. These results support constitutive responses as an effective learning target for a shared neural PDE framework.