A GENERIC-Informed Neural Network for Generative Rheology

Abstract

We present GINNGER (GENERIC-Informed Neural Network for GEnerative Rheology), a framework for discovering thermodynamically admissible constitutive equations from microstructural flow data. Unlike existing approaches that learn constitutive operators, GINNGER reformulates constitutive discovery as the learning of the underlying thermodynamic generators from which constitutive equations emerge. Embedding the GENERIC formalism into the learning process restricts the search to constitutive models that satisfy the first and second laws of thermodynamics by construction, eliminating the need to prescribe phenomenological constitutive equations a priori. A second conceptual advance is a spectral formulation of constitutive discovery in the intrinsic eigenspace of the polymer conformation tensor. This provides a kinematics-independent thermodynamic state space in which the thermodynamic generators depend only on the instantaneous microstructural state, while flow kinematics acts solely as an external driver transporting the system through this space. Consequently, data from shear, extensional, and mixed flows contribute to the discovery of a single constitutive model that generalizes across deformation protocols and flow geometries. By learning thermodynamic generators rather than high-dimensional constitutive operators, GINNGER substantially reduces the complexity of the discovery problem while preserving thermodynamic consistency, material objectivity, and physical interpretability by construction. The framework is validated using high-fidelity simulations, accurately reconstructing constitutive behavior and predicting complex flow fields across previously unseen geometries. GINNGER establishes a new paradigm for constitutive discovery by combining generative, spectral, and thermodynamically grounded learning within a unified framework for data-driven modeling of complex fluids.