A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics

Haghighat, Ehsan; Raissi, Maziar; Moure, Adrian; Gómez, Héctor; Juanes, Rubén

doi:10.1016/j.cma.2021.113741

Cited by 529 publications

(218 citation statements)

References 33 publications

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“…Although, inputting physical parameters to guide prediction, perhaps by introducing a regularising term in the loss function, may be beneficial [56,57]. To demonstrate the learnt HFQ® dynamics, Figure 24 visualises an interpolation of stamping speeds from 50mm/s to 500mm/s for an arbitrary shrink corner with tight radii formed at two initial blank temperatures 350°C and 500°C.…”

Section: Discussionmentioning

confidence: 99%

Rapid feasibility assessment of components to be formed through hot stamping: A deep learning approach

Attar

Zhou

Foster

et al. 2021

Journal of Manufacturing Processes

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Section: Discussionmentioning

confidence: 99%

Rapid feasibility assessment of components to be formed through hot stamping: A deep learning approach

Attar

Zhou

Foster

et al. 2021

Journal of Manufacturing Processes

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“…In addition, PINNs have been applied successfully in a wide range of applications, including fluid dynamics [113,115,117,160,177], continuum mechanics and elastodynamics [66,132,162], inverse problems [91,121], fractional advection–diffusion equations [135], stochastic advection–diffusion–reaction equations [34], stochastic differential equations [179] and power systems [127]. Finally, we mention that Gaussian processes as an alternative to neural networks for approximating complex multivariate functions have also been studied extensively for solving PDEs and inverse problems [136,155,158,164].…”

Section: Physics‐informed Neural Networkmentioning

confidence: 99%

Three ways to solve partial differential equations with neural networks — A review

2021

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Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and their suitability for high‐dimensional problems: physics‐informed neural networks, methods based on the Feynman–Kac formula and methods based on the solution of backward stochastic differential equations. The article is accompanied by a suite of expository software in the form of Jupyter notebooks in which each basic methodology is explained step by step, allowing for a quick assimilation and experimentation. An extensive bibliography summarizes the state of the art.

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“…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%

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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A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics

Cited by 529 publications

References 33 publications

Rapid feasibility assessment of components to be formed through hot stamping: A deep learning approach

Rapid feasibility assessment of components to be formed through hot stamping: A deep learning approach

Three ways to solve partial differential equations with neural networks — A review

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

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