Physics-Conforming Latent Twins Enhance Scientific Machine Learning Surrogates

Surrogate models are crucial in scientific machine learning for accelerating predictions and simulations of complex physical systems. However, ensuring these models respect fundamental physical laws like conservation and dissipation has been a challenge. Researchers introduce Physics-conforming Latent Twins, a framework that learns latent surrogate solution operators. This approach constrains the latent dynamics to inherently preserve or dissipate specific structural quantities, thereby embedding physical principles directly into the model's design. The method provides a constraint-transfer viewpoint, connecting physical structure in the original state space to compatible constraints in the latent space. Numerical experiments demonstrate that this latent enforcement significantly improves constraint satisfaction, structural fidelity, and long-term qualitative behavior of the surrogate models, while maintaining predictive accuracy.