Hammering at the entropy: A GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs

Abstract

We present a versatile framework that employs Physics-Informed Neural Networks (PINNs) to discover the entropic contribution that leads to the constitutive equation for the extra-stress in rheological models of polymer solutions. In this framework the training of the Neural Network is guided by an evolution equation for the conformation tensor which is GENERIC-compliant. We compare two training methodologies for the data-driven PINN constitutive models: one trained on data from the analytical solution of the Oldroyd-B model under steady-state rheometric flows (PINN-rheometric), and another trained on in-silico data generated from complex flow CFD simulations around a cylinder that use the Oldroyd-B model (PINN-complex). The capacity of the PINN models to provide good predictions are evaluated by comparison with CFD simulations using the underlying Oldroyd-B model as a reference. Both models are capable of predicting flow behavior in transient and complex conditions; however, the PINN-complex model, trained on a broader range of mixed flow data, outperforms the PINN-rheometric model in complex flow scenarios. The geometry agnostic character of our methodology allows us to apply the learned PINN models to flows with different topologies than the ones used for training.

References in corpus (9)

• PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs
• Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
• A new family of Constitutive Artificial Neural Networks towards automated model discovery
• Structure-preserving neural networks
• Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows
• Active- and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows
• Machine learning based non-Newtonian fluid model with molecular fidelity
• Learning the constitutive relation of polymeric flows with memory
• A general approach for running Python codes in OpenFOAM using an embedded pybind11 Python interpreter