Learning unknown physics of non-Newtonian fluids

Howard, Amanda A.; Perdikaris, Paris; Tartakovsky, Alexandre M.

doi:10.1103/physrevfluids.6.073301

Cited by 46 publications

(11 citation statements)

References 16 publications

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“…( 29) as a constraint on the learning process, the PINN "smooths out" the physically-questionable singularity of the ODE at y * = 0. Note that this feature of the PINN approach was also mentioned in [31], in the context of the shear stress singularity at the channel centerline under a power-law rheological model. Importantly, by training the PINN, we deduce best-fit K c /K η values different from the traditional value of 0.66, which has only been validated for the concentric Couette flow (Sec.…”

Section: Comparison Between Pinn Theory and Experimentsmentioning

confidence: 58%

“…It should be re-emphasized that using the parameter values (calibrated in 1992 only for annular Couette flow) in varied flow scenarios strongly enforces physics that may or may not be manifested in the particular flow under consideration. We have demonstrated that, to gain an understanding of the "unknown physics" (to use the terminology of Reyes et al [31]) of particle migration in a variety of flow experiments, PINNs can be effectively employed to simultaneously solve the inverse and forward problems and to significantly extend the practical utility of the standard phenomenological models.…”

Section: Discussionmentioning

confidence: 99%

“…PINNs are a deep learning framework for solving problems involving PDEs by embedding (in a suitable sense) the physics into the neural network. Due to their versatility, PINNs have been applied to solve forward and inverse problems in fluid mechanics [27][28][29][30][31][32], solid mechanics [33,34], material science [35,36], and heat transfer [37], amongst many other applications. PINNs are appealing due to their standardized implementation.…”

Section: Pinn Algorithm Description and Implementationmentioning

confidence: 99%

“…Similarly to the approach of Reyes et al [31], Eq. ( 25) will be enforced via the PINN's loss function to account for the blunted (non-parabolic) velocity profiles of dense suspensions.…”

Section: Poiseuille Flow 41 Governing Physics Equationsmentioning

confidence: 99%

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Physics-informed neural networks for understanding shear migration of particles in viscous flow

Lu¹,

Christov

2021

Preprint

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We harness the physics-informed neural network (PINN) approach to extend the utility of phenomenological models for particle migration in shear flow. Specifically, we propose to constrain the neural network training via a model for the physics of shear-induced particle migration in suspensions. Then, we train the PINN against experimental data from the literature, showing that this approach provides both better fidelity to the experiments, and novel understanding of the relative roles of the hypothesized migration fluxes. We first verify the PINN approach for solving the inverse problem of radial particle migration in a non-Brownian suspension in an annular Couette flow. In this classical case, the PINN yields the same value (as reported in the literature) for the ratio of the two parameters of the empirical model. Next, we apply the PINN approach to analyze experiments on particle migration in both non-Brownian and Brownian suspensions in Poiseuille slot flow, for which a definitive calibration of the phenomenological migration model has been lacking. Using the PINN approach, we identify the unknown/empirical parameters in the physical model through the inverse solver capability of PINNs. Specifically, the values are significantly different from those for the Couette cell, highlighting an inconsistency in the literature that uses the latter value for Poiseuille flow. Importantly, the PINN results also show that the inferred values of the empirical model's parameters vary with the shear Péclet number and the particle bulk volume fraction of the suspension, instead of being constant as assumed in some previous literature.

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Section: Comparison Between Pinn Theory and Experimentsmentioning

confidence: 58%

Section: Discussionmentioning

confidence: 99%

Section: Pinn Algorithm Description and Implementationmentioning

confidence: 99%

“…Similarly to the approach of Reyes et al [31], Eq. ( 25) will be enforced via the PINN's loss function to account for the blunted (non-parabolic) velocity profiles of dense suspensions.…”

Section: Poiseuille Flow 41 Governing Physics Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Physics-informed neural networks for understanding shear migration of particles in viscous flow

Lu¹,

Christov

2021

Preprint

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“…A PINN solver uses fully connected neural networks to approximate the solution variables, and is trained using the strong form of the governing equations, which are evaluated readily using Automatic Differentiation [5]. This convenience has made the framework very popular and has been explored extensively for a wide range of problems, including fluid mechanics (e.g., [30,61,10,51,41,53,13]), solid mechanics (e.g., [24,52]), and heat transfer [9,42] (for a detailed review see [32]).…”

Section: Introductionmentioning

confidence: 99%

Physics-informed neural network solution of thermo-hydro-mechanical (THM) processes in porous media

Amini¹,

Haghighat²,

Juanes³

2022

Preprint

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Physics-Informed Neural Networks (PINNs) have received increased interest for forward, inverse, and surrogate modeling of problems described by partial differential equations (PDE). However, their application to multiphysics problem, governed by several coupled PDEs, present unique challenges that have hindered the robustness and widespread applicability of this approach. Here we investigate the application of PINNs to the forward solution of problems involving thermohydro-mechanical (THM) processes in porous media, which exhibit disparate spatial and temporal scales in thermal conductivity, hydraulic permeability, and elasticity. In addition, PINNs are faced with the challenges of the multi-objective and non-convex nature of the optimization problem. To address these fundamental issues, we: (1) rewrite the THM governing equations in dimensionless form that is best suited for deep-learning algorithms; (2) propose a sequential training strategy that circumvents the need for a simultaneous solution of the multiphysics problem and facilitates the task of optimizers in the solution search; and (3) leverage adaptive weight strategies to overcome the stiffness in the gradient flow of the multi-objective optimization problem. Finally, we apply this framework to the solution of several synthetic problems in 1D and 2D.

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Fractional rheology-informed neural networks for data-driven identification of viscoelastic constitutive models

Dabiri,

Saadat,

Mangal

et al. 2023

Rheol Acta

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Developing constitutive models that can describe a complex fluid’s response to an applied stimulus has been one of the critical pursuits of rheologists. The complexity of the models typically goes hand-in-hand with that of the observed behaviors and can quickly become prohibitive depending on the choice of materials and/or flow protocols. Therefore, reducing the number of fitting parameters by seeking compact representations of those constitutive models can obviate extra experimentation to confine the parameter space. To this end, fractional derivatives in which the differential response of matter accepts non-integer orders have shown promise. Here, we develop neural networks that are informed by a series of different fractional constitutive models. These fractional rheology-informed neural networks (RhINNs) are then used to recover the relevant parameters (fractional derivative orders) of three fractional viscoelastic constitutive models, i.e., fractional Maxwell, Kelvin-Voigt, and Zener models. We find that for all three studied models, RhINNs recover the observed behavior accurately, although in some cases, the fractional derivative order is recovered with significant deviations from what is known as ground truth. This suggests that extra fractional elements are redundant when the material response is relatively simple. Therefore, choosing a fractional constitutive model for a given material response is contingent upon the response complexity, as fractional elements embody a wide range of transient material behaviors.

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Learning unknown physics of non-Newtonian fluids

Cited by 46 publications

References 16 publications

Physics-informed neural networks for understanding shear migration of particles in viscous flow

Physics-informed neural networks for understanding shear migration of particles in viscous flow

Physics-informed neural network solution of thermo-hydro-mechanical (THM) processes in porous media

Fractional rheology-informed neural networks for data-driven identification of viscoelastic constitutive models

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