Neural Constitutive Learning for Generalized Reaction-Diffusion Systems
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 L2 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.
Related
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- Gradient flow formulation and discrete approximation of reaction-cross-diffusion systems with size exclusion
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BibTeX
@misc{chen2026neural,
title = {{Neural Constitutive Learning for Generalized Reaction-Diffusion Systems}},
author = {Shang-Ke Chen and Yu-Peng Wang and Shih-Hsuan Hung and Wei-Fang Sun and Chao-Shun Zhan and Simon See and Min-Jhe Lu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37113},
eprint = {2609.37113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37113},
}
RIS
TY - UNPB
TI - Neural Constitutive Learning for Generalized Reaction-Diffusion Systems
AU - Shang-Ke Chen
AU - Yu-Peng Wang
AU - Shih-Hsuan Hung
AU - Wei-Fang Sun
AU - Chao-Shun Zhan
AU - Simon See
AU - Min-Jhe Lu
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37113
UR - https://arxiv.org/abs/2609.37113
AB - 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.
ER -