A probabilistic data-driven constitutive modeling framework for complex fluids

초록

Conventional constitutive modeling of complex fluids typically relies on deterministic parameter fitting or discrete mode selection, which limits flexibility in representing diverse rheological responses. We propose the Rheological Probabilistic (RheoPro) framework, a data-driven constitutive modeling approach that extends physics-based kinetic models into stochastic ensembles and infers parameter-generating distributions from differentiable, closed-form evaluations of small-amplitude oscillatory shear moduli and steady-shear viscosity. As a representative implementation, we formulate a Generalized Dumbbell Soft Glassy Rheology (GDSGR) model that couples activated yielding dynamics with bead-spring kinematics. A reparameterization trick enables stable gradient-based optimization without repeated time stepping during training. When trained on single- and multi-mode Giesekus and thixotropic elasto-viscoplastic benchmarks, the optimized GDSGR model reproduces linear moduli and nonlinear flow curves with log-space coefficients of determination near unity. For the multi-mode benchmark, the inferred distribution represents the relaxation spectrum as a continuous lifetime distribution without a prescribed mode count. In the thixotropic benchmark, it captures the yield-dominated low-shear response and viscoelastic-plastic coupling, while showing that moduli and steady-shear viscosity alone may not uniquely constrain transient kinetics. This constitutive modeling framework remains robust under moderate synthetic measurement noise and provides an interpretable, extensible foundation for distribution inference across linear viscoelastic and nonlinear steady-shear regimes.

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