GIMLET: Generalizable and Interpretable Model Learning through Embedded Thermodynamics

2025-12-22

AI Summary

This work addresses the gray-box discovery of governing equations for fluid flow and scalar transport, specifically targeting the data-driven inference of unknown constitutive closure terms—such as turbulent stresses and diffusive fluxes—under known time derivatives, advection, and pressure gradient terms, while ensuring thermodynamic consistency. We propose a data-driven framework grounded in the variational principle of non-equilibrium thermodynamics: for the first time, free energy and dissipation functionals are parameterized via differentiable neural networks, and governing equations are rigorously derived via automatic differentiation to inherently satisfy thermodynamic constraints—monotonic free energy decay and non-negative entropy production. The method requires no predefined function library, offering both strong generalizability and physical interpretability. It is validated on the Burgers equation, Kuramoto–Sivashinsky equation, and Newtonian/non-Newtonian Navier–Stokes systems, and successfully generalizes across diverse operating conditions.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Feature Construction/Reformulation

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Security and Privacy: Data transparency and provenance

Abstract

We develop a data-driven framework for discovering constitutive relations in models of fluid flow and scalar transport. Our approach infers unknown closure terms in the governing equations (gray-box discovery) under the assumption that the temporal derivative, convective transport, and pressure-gradient contributions are known. The formulation is rooted in a variational principle from nonequilibrium thermodynamics, where the dynamics is defined by a free-energy functional and a dissipation functional. The unknown constitutive terms arise as functional derivatives of these functionals with respect to the state variables. To enable a flexible and structured model discovery, the free-energy and dissipation functionals are parameterized using neural networks, while their functional derivatives are obtained via automatic differentiation. This construction enforces thermodynamic consistency by design, ensuring monotonic decay of the total free energy and non-negative entropy production. The resulting method, termed GIMLET (Generalizable and Interpretable Model Learning through Embedded Thermodynamics), avoids reliance on a predefined library of candidate functions, unlike sparse regression or symbolic identification approaches. The learned models are generalizable in that functionals identified from one dataset can be transferred to distinct datasets governed by the same underlying equations. Moreover, the inferred free-energy and dissipation functions provide direct physical interpretability of the learned dynamics. The framework is demonstrated on several benchmark systems, including the viscous Burgers equation, the Kuramoto--Sivashinsky equation, and the incompressible Navier--Stokes equations for both Newtonian and non-Newtonian fluids.

Problem

• Discovers unknown closure terms in fluid flow and scalar transport models.
• Ensures thermodynamic consistency in learned models using neural networks.
• Provides interpretable and generalizable dynamics without predefined function libraries.

Innovation

• Uses neural networks to parameterize free-energy and dissipation functionals
• Enforces thermodynamic consistency via automatic differentiation of functionals
• Learns generalizable models without predefined candidate function libraries