DiscretizationNet: A machine-learning based solver for Navier–Stokes equations using finite volume discretization

Ranade, Rishikesh; Hill, Chris; Pathak, Jay

doi:10.1016/j.cma.2021.113722

Cited by 100 publications

(34 citation statements)

References 30 publications

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“…In the past couple of years, the PINN framework has been extended to solve complicated PDEs representing complex physics (Jin et al, 2021;Mao et al, 2020;Rao et al, 2020;Wu et al, 2018;Qian et al, 2020;Dwivedi et al, 2021;Nabian et al, 2021;Kharazmi et al, 2021;Cai et al, 2021a;Bode et al, 2021;Taghizadeh et al, 2021;Lu et al, 2021c;Shukla et al, 2021;Hennigh et al, 2020;Li et al, 2021). More recently, alternate approaches that use discretization techniques using higher order derivatives and specialize numerical schemes to compute derivatives have shown to provide better regularization for faster convergence (Ranade et al, 2021b;Gao et al, 2021;Wandel et al, 2020;He & Pathak, 2020). Differentiable solver frameworks for learning PDEs: Training NNs within differentiable solver frameworks has shown to improve learning and provide better control of PDE solutions and transient system dynamics (Amos & Kolter, 2017;Um et al, 2020;de Avila Belbute-Peres et al, 2018;Toussaint et al, 2018;Wang et al, 2020;Portwood et al, 2019).…”

Section: Related Workmentioning

confidence: 99%

A composable autoencoder-based iterative algorithm for accelerating numerical simulations

Ranade,

Hill,

et al. 2021

Preprint

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Numerical simulations for engineering applications solve partial differential equations (PDE) to model various physical processes. Traditional PDE solvers are very accurate but computationally costly. On the other hand, Machine Learning (ML) methods offer a significant computational speedup but face challenges with accuracy and generalization to different PDE conditions, such as geometry, boundary conditions, initial conditions and PDE source terms. In this work, we propose a novel ML-based approach, CoAE-MLSim (Composable AutoEncoder Machine Learning Simulation), which is an unsupervised, lower-dimensional, local method, that is motivated from key ideas used in commercial PDE solvers. This allows our approach to learn better with relatively fewer samples of PDE solutions. The proposed ML-approach is compared against commercial solvers for better benchmarks as well as latest ML-approaches for solving PDEs. It is tested for a variety of complex engineering cases to demonstrate its computational speed, accuracy, scalability, and generalization across different PDE conditions. The results show that our approach captures physics accurately across all metrics of comparison (including measures such as results on section cuts and lines).

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Section: Related Workmentioning

confidence: 99%

A composable autoencoder-based iterative algorithm for accelerating numerical simulations

Ranade,

Hill,

et al. 2021

Preprint

Self Cite

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“…ML can be applied to develop explicit substitution models that relate the cost function and control/optimization parameters [86] [86] [87] [88]. Substitution models such as neural networks can then lend themselves to methods based on gradients, even if they often remain stuck in local minima [89] [90] [91].…”

Section: Related Workmentioning

confidence: 99%

Proof of Concept: Calibration of an Overhead Line Conductors’ Movements Simulation Model Using Ensemble-Based Machine Learning Model

Amroun¹,

Ammi

Hafid³

2021

IEEE Access

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In this paper, we present a new approach to use machine learning (ML) for the calibration of a physical model allowing the reproduction of the vibratory behavior of an overhead line conductor. This physical model known as Strip Theory (ST) has the advantage of being very precise but very complicated and cumbersome in its software operations and manipulations. A second model known as the Wake Oscillator (WO) has been implemented in order to meet the limitations of the ST model. In order to be able to use the WO model instead of the ST model, very heavy manual adjustments are required, which makes its use complicated.Precisely, the WO must be able to generate a time series similar to a time series generated by the ST model. In order to respond to this limitation, a machine learning model known as ENS has been proposed. The machine learning model will therefore take as input the data from the WO model and output the data from the ST model. A series of Machine learning models have been implemented and tested. The ENS algorithm was retained with a best Pearson's linear coefficient of determination (R2 Score) of almost 0.7 and a Root mean square deviation (RMSE) of 7.57e-09. This type of approach therefore makes it possible to calibrate the WO model so that simulations of the behavior of overhead line conductors are carried out only with the WO model.

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“…CNNs are more prevalent in deep learning due to their efficacy in capturing the topological information in datasets such as images, videos, voxels, etc. Several recent papers have utilized such neural networks for producing field predictions 29,34,45,46 . In the next section, we provide details of the network used in this paper.…”

Section: Convolutional Neural Network (Cnns)mentioning

confidence: 99%

Distributed Multigrid Neural Solvers on Megavoxel Domains

Balu¹,

Botelho²,

Khara³

et al. 2021

Preprint

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DiscretizationNet: A machine-learning based solver for Navier–Stokes equations using finite volume discretization

Cited by 100 publications

References 30 publications

A composable autoencoder-based iterative algorithm for accelerating numerical simulations

A composable autoencoder-based iterative algorithm for accelerating numerical simulations

Proof of Concept: Calibration of an Overhead Line Conductors’ Movements Simulation Model Using Ensemble-Based Machine Learning Model

Distributed Multigrid Neural Solvers on Megavoxel Domains

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