Enforcing physical conservation in neural network surrogate models for complex chemical kinetics

The "AI for Science" movement has sparked a paradigm shift toward incorporating fundamental physical understanding into neural networks, moving beyond pure data-driven approaches. In this context, we propose a novel ANN approach with hard physical constraints (ANN-hard) for chemical source term calculations that strictly enforce conservation laws (mass, energy, and element). We compare ANN-hard against two baselines: a conventional ANN and an ANN with soft conservation constraints implemented through loss function optimization (ANN-soft). Our systematic evaluation spans multiple combustion scenarios using H₂/air mixtures, including zero-dimensional autoignition, one-dimensional premixed laminar flames, two-dimensional triple flames, and outwardly expanding turbulent spherical flames. We further extend validation to dimethyl ether (DME)/air mixtures, demonstrating the models’ capabilities in capturing complex combustion chemistry through simulations of premixed laminar flames and penta-branchial flames exhibiting simultaneous cool, warm, and hot flame structures. Our analysis reveals a critical insight: traditional training or testing error metrics can be misleading indicators of ANN performance, as they may mask violations of physical principles. Even small violations in physics can accumulate, leading to significant physical violations and explaining why conventional ANNs often produce non-physical predictions or diverge during long-term continuous evolution. While both ANN-soft and ANN-hard show improved robustness over conventional ANNs, ANN-hard demonstrates superior stability and physical accuracy by preventing error accumulation, all while maintaining computational efficiency with negligible additional cost. These findings underscore the importance of enforcing physical constraints in machine learning models for reliable combustion simulations, contributing to the broader goal of physics-informed artificial intelligence.