A rheologist's guideline to data-driven recovery of complex fluids' parameters from constitutive models

Predicting the response of complex fluids to different flow conditions has been the focal point of rheology and is generally done via constitutive relations. There are, nonetheless, scenarios in which not much is known from the material mathematically, while data collection from samples is elusive, resource-intensive, or both. In such cases, meta-modeling of observables using a parametric surrogate model called multi-fidelity neural networks (MFNNs) may obviate the constitutive equation development step by leveraging only a handful of high-fidelity (Hi-Fi) data collected from experiments (or high-resolution simulations) and an abundance of low-fidelity (Lo-Fi) data generated synthetically to compensate for Hi-Fi data scarcity. To this end, MFNNs are employed to meta-model the material responses of a thermo-viscoelastic (TVE) fluid, consumer product Johnson’s® Baby Shampoo, under four flow protocols: steady shear, step growth, oscillatory, and small/large amplitude oscillatory shear (S/LAOS). In addition, the time–temperature superposition (TTS) of the material response and MFNN predictions are explored. By applying simple linear regression (without induction of any constitutive equation) on log-spaced Hi-Fi data, a series of Lo-Fi data were generated and found sufficient to obtain accurate material response recovery in terms of either interpolation or extrapolation for all flow protocols except for S/LAOS. This insufficiency is resolved by informing the MFNN platform with a linear constitutive model (Maxwell viscoelastic) resulting in simultaneous interpolation and extrapolation capabilities in S/LAOS material response recovery. The roles of data volume, flow type, and deformation range are discussed in detail, providing a practical pathway to multifidelity meta-modeling of different complex fluids.

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Short Review on Machine Learning-Based Multi-Scale Simulation in Rheology

Miyamoto

2024

J. Soc. Rheol., Jpn

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We briefly review the machine-learning (ML) applications for rheological research, particularly on the multi-scale simulation (MSS) techniques for complex fluid flows. For such simulations, it is essential to accurately model the constitutive relation (i.e., the strain-rate and stress relation) of complex fluids. Several past studies have found that ML applications for modeling the constitutive relation can reasonably accelerate the flow predictions from a microscopically resolved description of complex fluids such as polymers and colloidal suspensions. Nevertheless, even when the proposed regression models are consistent with the physical knowledge, several outstanding questions remain to be answered, for example, how to ensure the robustness of the predictions. This review summarizes the methods to obtain constitutive models using ML techniques and those applications based on molecular and phenomenological knowledge. Furthermore, we provide a perspective on how to develop the ML framework starting from a microscopic description.

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A rheologist's guideline to data-driven recovery of complex fluids' parameters from constitutive models

Abstract: Rheology-informed neural networks (RhINNs) have recently been popularized as data-driven platforms for solving rheologically relevant differential equations. While RhINNs can be employed to solve different constitutive equations of interest in...

Cited by 3 publications

References 43 publications

Data-driven techniques in rheology: Developments, challenges and perspective

Data-driven techniques in rheology: Developments, challenges and perspective

Data-driven constitutive meta-modeling of nonlinear rheology via multifidelity neural networks

Short Review on Machine Learning-Based Multi-Scale Simulation in Rheology

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