Generalised dissipative solutions for a non-isothermal phase-field system: existence, weak-strong uniqueness, and long-time behaviour

What the math gives to ML

The paper develops a thermodynamically consistent formulation for two interacting order parameters and inverse temperature, using a fully non-diagonal Onsager mobility while preserving conservation and entropy production. The transferable asset is a parameterization of learned dynamics that permits cross-variable coupling without allowing the learned dissipative operator to become indefinite. A neural PDE simulator can use a positive-semidefinite mobility factor, explicit free-energy and entropy functionals, and positivity-preserving temperature coordinates to obtain stable long-horizon rollouts.