Description
I will present a versatile computational framework that employs Physics-Informed Neural Networks (PINNs) to discover constitutive equations for the extra-stress in rheological models of polymer solutions [1]. In this framework, the training of the neural network is guided by a meta-model for the conformation tensor that adheres to the GENERIC formalism (General Equation for Non-Equilibrium Reversible–Irreversible Coupling) [2]. The use of GENERIC enables a reduction of the parameter space by restricting the search to thermodynamically admissible fluid models—that is, those that strictly satisfy the First and Second Laws of Thermodynamics. The discovery of different geometric blocks within GENERIC includes irreversible entropic contributions, anisotropic mobility terms related to the friction tensor, and specific choices of the objective derivative for the microstructural variables. We discuss the potential of data-driven PINN approaches to identify such models and compare various training strategies, including viscometric and complex flow data. The PINN strategy is incorporated into CFD tools for the simulation of polymeric flows using RheoTool-OpenFOAM. Fluid dynamics results will be presented to assess the accuracy of the aforementioned methodology. Finally, I will discuss possible outlooks and perspectives on using this approach to accelerate multiscale polymer simulations and/or to directly incorporate experimental data into the model.
References:
[1] DN Simavilla et al. “Hammering at the entropy: a GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs”, J. Fluid Mechanics v. 1016, A11 (2025). doi.org/10.1017/jfm.2025.10325
[2] HC Oettinger, “Beyond Equilibrium Thermodynamics”, Wiley (2005).