Learning constitutive models and rheology from partial flow measurements

TL;DR

This paper introduces a physics-informed, data-driven framework that learns constitutive laws of complex fluids from partial flow measurements, enabling geometry-independent predictions and interpretable models.

Contribution

It develops an end-to-end differentiable simulation framework with a neural network-based tensor basis, allowing for constitutive law discovery directly from flow data in various geometries.

Findings

Successfully learns stress-strain relationships from flow data

Predicts fluid behavior in unseen geometries

Extracts interpretable physical parameters via Bayesian model selection

Abstract

Constitutive laws relate fluid stress to deformation and underpin predictions of non-Newtonian behavior in industrial and biological fluids. Standard characterization relies on measurements in idealized flows that often miss physics relevant to complex geometries. Existing data-driven methods overfit sparse data, lack geometry portability, or presuppose constitutive forms. To unify measurement and constitutive discovery, we developed an end-to-end framework that leverages automatic differentiation through a full physics simulation. By embedding a frame-invariant tensor basis neural network (TBNN) within a differentiable non-Newtonian solver, we learn form-agnostic stress-strain mappings from any flow observable. Unlike coordinate-dependent methods, learning local material response enables prediction in unseen geometries. We then distill this closure into symbolic form via automated Bayesian model selection, extracting interpretable physical parameters. This work establishes a foundation for comprehensive characterization of complex fluids directly within their operating environment ("digital rheometry") with broad applicability to constitutive discovery across engineering and the physical sciences.