Physics-conforming Latent Twins

2026-06-12

AI Summary

Existing surrogate models struggle to preserve essential physical consistency—such as conservation laws, invariants, and dissipative structures—in time-varying physical systems. This work proposes a latent-space surrogate operator framework that jointly trains an encoder, decoder, and latent flow map to explicitly constrain dynamics in the latent space, thereby accurately preserving or dissipating prescribed physical structures. The approach innovatively introduces a constrained transfer perspective, establishing a correspondence between physical structures in the original and latent spaces, and derives algebraic conditions for latent flow dynamics that guarantee preservation of linear or quadratic invariants or satisfaction of dissipation inequalities. Built upon a Latent Twin architecture with embedded physical constraints and structure-preserving optimization, the method significantly enhances physical consistency, structural fidelity, and long-term simulation stability on canonical ODE/PDE benchmarks while maintaining high predictive accuracy.

Abstract

Surrogate models are central to scientific machine learning, where they enable fast prediction, simulation, inference, and control for complex physical systems. For time-dependent problems, however, accurate interpolation of training trajectories is not sufficient: reliable surrogates should also respect the conservation laws, invariants, admissibility conditions, and dissipative structures that give those trajectories physical meaning. We introduce Physics-conforming Latent Twins, a framework for learning latent surrogate solution operators whose dynamics satisfy selected physical principles by design. The method builds on the Latent Twin formulation by jointly learning an encoder, a decoder, and a latent flow map between arbitrary time-indexed states, while constraining the latent dynamics to preserve or dissipate prescribed structural quantities. We develop a constraint-transfer viewpoint that connects physical structure in the original state space with compatible constraints in latent space, and prove structure-preservation bounds showing how latent enforcement improves control of physical defects after decoding. We also derive algebraic conditions for latent flow maps that preserve linear and quadratic invariants or enforce dissipative inequalities. Numerical experiments on representative ODE and PDE benchmarks demonstrate improved constraint satisfaction, structural fidelity, and qualitative long-time behavior while maintaining accurate surrogate prediction.

Problem

• surrogate models
• physical constraints
• conservation laws
• invariants
• dissipative structures

Innovation

• Physics-conforming
• Latent Twins
• Structure-preserving
• Surrogate modeling
• Dissipative systems