Inferring incompressible two-phase flow fields from the interface motion using physics-informed neural networks

Buhendwa, Aaron B.; Adami, Stefan; Adams, Nikolaus A.

doi:10.1016/j.mlwa.2021.100029

Cited by 18 publications

(4 citation statements)

References 24 publications

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“…Many works (e.g. [19,24,35,37]) often treat λ j as hyper-parameters, which are fixed prior to training, hence, we refer to such weight tuning as 'static weight tuning'. In many cases, the choice of λ j is problem specific, making the cost to find the optimal λ j prohibitively expensive, although several techniques can exploit these difficulties [38,39].…”

Section: îmentioning

confidence: 99%

“…Lately, there has been a surge in attempts to evaluate physical phenomena using machine learning, with many of them seeking to couple known physical laws (governing equations) with machine learning models [15,16]. Among them, Physics-Informed Neural Networks (PINNs) [17] has been one of the most successful approaches to tackle a wide range of problems [18][19][20][21][22]. PINNs incorporates constraints given by the governing partial differential equations (PDEs), initial conditions (ICs), and boundary conditions (BCs) into the loss function via automatic differentiation [23].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic & norm-based weights to normalize imbalance in back-propagated gradients of physics-informed neural networks

Deguchi

Asai

2023

J. Phys. Commun.

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Physics-Informed Neural Networks (PINNs) have been a promising machine learning model for evaluating various physical problems. Despite their success in solving many types of partial differential equations (PDEs), some problems have been found to be difficult to learn, implying that the baseline PINNs is biased towards learning the governing PDEs while relatively neglecting given initial or boundary conditions. In this work, we propose Dynamically Normalized Physics-Informed Neural Networks (DN-PINNs), a method to train PINNs while evenly distributing multiple back-propagated gradient components. DN-PINNs determine the relative weights assigned to initial or boundary condition losses based on gradient norms, and the weights are updated dynamically during training. Through several numerical experiments, we demonstrate that DN-PINNs effectively avoids the imbalance in multiple gradients and improves the inference accuracy while keeping the additional computational cost within a reasonable range. Furthermore, we compare DN-PINNs with other PINNs variants and empirically show that DN-PINNs is competitive with or outperforms them. In addition, since DN-PINN uses exponential decay to update the relative weight, the weights obtained are biased toward the initial values. We study this initialization bias and show that a simple bias correction technique can alleviate this problem.

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Section: îmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic & norm-based weights to normalize imbalance in back-propagated gradients of physics-informed neural networks

Deguchi

Asai

2023

J. Phys. Commun.

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“…The loss components L IB , L BC don't depend on the interior spatial coordinates, and L IC considers a data snapshot only at t/T = 0. They play an important role in ensuring the hidden variables are recovered appropriately [12,13]. However, L Bulk and L P hy are computed from spatial coordinates interior to Ω r f .…”

Section: Moving Boundary Enabled Pinns (Mb-pinns)mentioning

confidence: 99%

Surrogate modeling of unsteady aerodynamic loads acting on a plunging airfoil

Rahul¹,

Kumar²,

Majumdar³

et al. 2022

8th European Congress on Computational Methods in Applied Sciences and Engineering

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“…Natural and engineering sciences can profit from ML methods as they have capabilities to learn complex relations from data and enable novel strategies for modelling physics as well as new avenues of post-processing. For example, machine learning has been successfully used to identify PDEs from data [28], and physics-informed neural networks provide new ways for solving inverse problems [29,30] by combining data and PDE knowledge.…”

Section: Introductionmentioning

confidence: 99%

JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows

Bezgin¹,

Buhendwa²,

Adams³

2022

Preprint

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Physical systems are governed by partial differential equations (PDEs). The Navier-Stokes equations describe fluid flows and are representative of nonlinear physical systems with complex spatio-temporal interactions. Fluid flows are omnipresent in nature and engineering applications, and their accurate simulation is essential for providing insights into these processes. While PDEs are typically solved with numerical methods, the recent success of machine learning (ML) has shown that ML methods can provide novel avenues of finding solutions to PDEs. ML is becoming more and more present in computational fluid dynamics (CFD). However, up to this date, there does not exist a generalpurpose ML-CFD package which provides 1) powerful state-of-the-art numerical methods, 2) seamless hybridization of ML with CFD, and 3) automatic differentiation (AD) capabilities. AD in particular is essential to ML-CFD research as it provides gradient information and enables optimization of preexisting and novel CFD models. In this work, we propose JAX-FLUIDS: a comprehensive fullydifferentiable CFD Python solver for compressible two-phase flows. JAX-FLUIDS allows the simulation of complex fluid dynamics with phenomena like three-dimensional turbulence, compressibility effects, and two-phase flows. Written entirely in JAX, it is straightforward to include existing ML models into the proposed framework. Furthermore, JAX-FLUIDS enables end-to-end optimization. I.e., ML models can be optimized with gradients that are backpropagated through the entire CFD algorithm, and therefore contain not only information of the underlying PDE but also of the applied numerical methods. We believe that a Python package like JAX-FLUIDS is crucial to facilitate research at the intersection of ML and CFD and may pave the way for an era of differentiable fluid dynamics.

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Inferring incompressible two-phase flow fields from the interface motion using physics-informed neural networks

Cited by 18 publications

References 24 publications

Dynamic & norm-based weights to normalize imbalance in back-propagated gradients of physics-informed neural networks

Dynamic & norm-based weights to normalize imbalance in back-propagated gradients of physics-informed neural networks

Surrogate modeling of unsteady aerodynamic loads acting on a plunging airfoil

JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows

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