Physics-informed neural networks for inverse problems in supersonic flows

Jagtap, Ameya D.; Mao, Zhiping; Adams, Nikolaus A.; Karniadakis, George Em

doi:10.1016/j.jcp.2022.111402

Cited by 112 publications

(47 citation statements)

References 25 publications

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“…Their entropy pairs included density, Mach number, and specific entropy. Separately, Jagtap et al [34] used a flux pair based on density, both components of velocity, and specific entropy, coupled with a polytropic equation of state. Patel's formulation resulted in three loss components whereas Jagtap's method culminated in a scalar loss.…”

Section: Entropy Pair Regularizationmentioning

confidence: 99%

“…Mao et al [33] pioneered the use of a pseudo-schlieren loss to estimate 1D shock-laden airflow (they also developed a forward solver for a 2D oblique shock with no schlieren-type data). Cai et al [73] reconstructed a synthetic 2D bow shock in the same way, promptly followed by the paper of Jagtap et al [34], who utilized domain decomposition (via an extended PINN) to facilitate the representation of oblique and bow shocks as well as an expansion fan. All three studies utilized a dense array of noise-free, synthetic, multi-modal measurements.…”

Section: Pseudo-schlieren Data Lossmentioning

confidence: 99%

“…Including this region in the data loss term can cause the solution to blow up, resulting in nonsensical fields. We tested this using a BOS data loss as well as the local density gradient loss term employed by Jagtap et al [34]. The instability is present for both loss formulations.…”

Section: Planar Expansion Fanmentioning

confidence: 99%

“…Not only does physics-informed BOS yield better estimates of the density field than conventional techniques, it also generates estimates of the velocity and pressure fields. Furthermore, by processing noiseladen experimental LoS measurements with a realistic forward model instead of simulated point-wise data [33,34], this work represents an advance in the application of PINNs to high-speed flows.…”

Section: Introductionmentioning

confidence: 99%

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Estimating density, velocity, and pressure fields in supersonic flow using physics-informed BOS

Molnar¹,

Venkatakrishnan²,

Schmidt³

et al. 2022

Preprint

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We report a new workflow for background-oriented schlieren (BOS), termed "physics-informed BOS," to extract density, velocity, and pressure fields from a pair of reference and distorted images. Our method uses a physics-informed neural network (PINN) to produce flow fields that simultaneously satisfy the measurement data and governing equations. For the high-speed flows of interest in this work, we specify a physics loss based on the Euler and irrotationality equations. BOS is a quantitative fluid visualization technique that is used to characterize high-speed flows. Images of a background pattern, positioned behind the target flow, are processed using computer vision and tomography algorithms to determine the density field. Crucially, BOS features a series of ill-posed inverse problems that require supplemental information (i.e., in addition to the images) to accurately reconstruct the flow. Current BOS workflows rely upon interpolation of the images or a penalty term to promote a globally-or piecewise-smooth solution. However, these algorithms are invariably incompatible with the flow physics, leading to errors in the density field. Physics-informed BOS directly reconstructs all the flow fields using a PINN that includes the BOS measurement model and governing equations. This procedure improves the accuracy of density estimates and also yields velocity and pressure data, which was not previously available. We demonstrate our approach by reconstructing synthetic data that corresponds to analytical and numerical phantoms as well as experimental measurements. Our physics-informed reconstructions are significantly more accurate than conventional BOS estimates. Further, to the best of our knowledge, this work represents the first use of a PINN to reconstruct a supersonic flow from experimental data of any kind.

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Section: Entropy Pair Regularizationmentioning

confidence: 99%

Section: Pseudo-schlieren Data Lossmentioning

confidence: 99%

Section: Planar Expansion Fanmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Estimating density, velocity, and pressure fields in supersonic flow using physics-informed BOS

Molnar¹,

Venkatakrishnan²,

Schmidt³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The results show that given certain initial conditions and boundary conditions, PINNs can solve some partial differential equations very well. Since then, the door to solve partial differential equations using deep neural networks has been opened, and some works [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ] based on PINNs have been published one after another. For example, Even Lu Lu et al expounded the difference between the traditional finite element method and the deep neural network in solving partial differential equations from the selection of basis functions, the solution process, the error source, and the error order in [ 25 ].…”

Section: Introductionmentioning

confidence: 99%

Physics-Informed Neural Networks for Solving Coupled Stokes–Darcy Equation

Feng

2022

Entropy

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In this paper, a grid-free deep learning method based on a physics-informed neural network is proposed for solving coupled Stokes–Darcy equations with Bever–Joseph–Saffman interface conditions. This method has the advantage of avoiding grid generation and can greatly reduce the amount of computation when solving complex problems. Although original physical neural network algorithms have been used to solve many differential equations, we find that the direct use of physical neural networks to solve coupled Stokes–Darcy equations does not provide accurate solutions in some cases, such as rigid terms due to small parameters and interface discontinuity problems. In order to improve the approximation ability of a physics-informed neural network, we propose a loss-function-weighted function strategy, a parallel network structure strategy, and a local adaptive activation function strategy. In addition, the physical information neural network with an added strategy provides inspiration for solving other more complicated problems of multi-physical field coupling. Finally, the effectiveness of the proposed strategy is verified by numerical experiments.

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RoeNet: Predicting discontinuity of hyperbolic systems from continuous data

Tong,

Xiong,

et al. 2023

Numerical Meth Engineering

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Predicting future discontinuous phenomena that are unobservable from training data sets has long been a challenging problem in scientific machine learning. We introduce a novel paradigm to predict the emergence and evolution of various discontinuities of hyperbolic partial differential equations (PDEs) based on given training data over a short window with limited discontinuity information. Our method is inspired by the classical Roe solver [P. L. Roe, J Comput Phys., vol. 43, 1981], a basic tool for simulating various hyperbolic PDEs in computational physics. By carefully designing the computing primitives, the data flow, and the novel pseudoinverse processing module, we enable our data‐driven predictor to satisfy all the essential mathematical criteria of a Roe solver and hence deliver accurate predictions of hyperbolic PDEs. We demonstrate through various examples that our data‐driven Roe predictor outperforms original human‐designed Roe solver and deep neural networks with weak priors in terms of accuracy and robustness.

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Physics-informed neural networks for inverse problems in supersonic flows

Cited by 112 publications

References 25 publications

Estimating density, velocity, and pressure fields in supersonic flow using physics-informed BOS

Estimating density, velocity, and pressure fields in supersonic flow using physics-informed BOS

Physics-Informed Neural Networks for Solving Coupled Stokes–Darcy Equation

RoeNet: Predicting discontinuity of hyperbolic systems from continuous data

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