Physics-Constrained Neural Surrogate for Domain Growth Prediction in Systems with Conserved Kinetics
Abstract
The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs). Recently, deep neural network-based surrogate models have emerged as efficient alternatives to computationally expensive numerical PDE solvers. In this work, we propose a physics-constrained deep neural network as a surrogate model to learn the microstructural evolution of a binary mixture, in which conservation of the order parameter is imposed directly on the network output as a hard constraint. We train the model to accurately predict the time-evolution of phase separation in binary mixtures governed by the Cahn-Hilliard equation. We show that predictions from our trained surrogate model remain stable and accurate over long-time rollouts for both critical and off-critical mixtures and preserve the mixture composition throughout evolution. In contrast, a variant in which conservation is enforced only via a penalty term in the loss function drifts away from the initial composition and significantly loses predictive accuracy over the same rollout. This establishes that the hard constraint is essential for long-time stability and order parameter conservation. We also show that our model accurately captures the growth of domain size and is consistent with the Lifshitz-Slyozov domain-growth law. These results demonstrate the effectiveness of the proposed framework for modeling systems with conserved kinetics, and the construction extends directly to other systems with conserved quantities.
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BibTeX
@misc{yadav2026physicsconstrained,
title = {{Physics-Constrained Neural Surrogate for Domain Growth Prediction in Systems with Conserved Kinetics}},
author = {Vijay Yadav and Pallvi Pandey and Madhu Priya and Manish Dev Shrimali and Prabhat K. Jaiswal},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.26128},
eprint = {2606.26128},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.26128},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Physics-Constrained Neural Surrogate for Domain Growth Prediction in Systems with Conserved Kinetics
AU - Vijay Yadav
AU - Pallvi Pandey
AU - Madhu Priya
AU - Manish Dev Shrimali
AU - Prabhat K. Jaiswal
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2606.26128
UR - https://arxiv.org/abs/2606.26128
AB - The spatiotemporal evolution of many physical, chemical, and biological systems is described by nonlinear partial differential equations (PDEs). Recently, deep neural network-based surrogate models have emerged as efficient alternatives to computationally expensive numerical PDE solvers. In this work, we propose a physics-constrained deep neural network as a surrogate model to learn the microstructural evolution of a binary mixture, in which conservation of the order parameter is imposed directly on the network output as a hard constraint. We train the model to accurately predict the time-evolution of phase separation in binary mixtures governed by the Cahn-Hilliard equation. We show that predictions from our trained surrogate model remain stable and accurate over long-time rollouts for both critical and off-critical mixtures and preserve the mixture composition throughout evolution. In contrast, a variant in which conservation is enforced only via a penalty term in the loss function drifts away from the initial composition and significantly loses predictive accuracy over the same rollout. This establishes that the hard constraint is essential for long-time stability and order parameter conservation. We also show that our model accurately captures the growth of domain size and is consistent with the Lifshitz-Slyozov domain-growth law. These results demonstrate the effectiveness of the proposed framework for modeling systems with conserved kinetics, and the construction extends directly to other systems with conserved quantities.
ER -