Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next

Cuomo, Salvatore; Cola, Vincenzo Schiano di; Giampaolo, Fabio; Rozza, Gianluigi; Raissi, Maziar; Piccialli, Francesco

doi:10.48550/arxiv.2201.05624

Cited by 30 publications

(32 citation statements)

References 119 publications

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“…1) Regularization approaches in power systems: Many recent results have focused on a particular regularization architecture, known as Physics Informed Neural Networks (PINNs) [32], where partial/ordinary differential equation (P/ODE) functions explicitly regularize NN training. While this technique is relatively new, it has quickly attracted thousands of followup extensions and associated publications [33].…”

Section: Model Training and Physics-based Regularizationmentioning

confidence: 99%

Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems

Stiasny¹,

Chevalier²,

Nellikkath³

et al. 2022

Preprint

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Deep decarbonization of the energy sector will require massive penetration of stochastic renewable energy resources and an enormous amount of grid asset coordination; this represents a challenging paradigm for the power system operators who are tasked with maintaining grid stability and security in the face of such changes. With its ability to learn from complex datasets and provide predictive solutions on fast timescales, machine learning (ML) is well-posed to help overcome these challenges as power systems transform in the coming decades. In this work, we outline five key challenges (dataset generation, data pre-processing, model training, model assessment, and model embedding) associated with building trustworthy ML models which learn from physics-based simulation data. We then demonstrate how linking together individual modules, each of which overcomes a respective challenge, at sequential stages in the machine learning pipeline can help enhance the overall performance of the training process. In particular, we implement methods that connect different elements of the learning pipeline through feedback, thus "closing the loop" between model training, performance assessments, and re-training. We demonstrate the effectiveness of this framework, its constituent modules, and its feedback connections by learning the N-1 small-signal stability margin associated with a detailed model of a proposed North Sea Wind Power Hub system.

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Section: Model Training and Physics-based Regularizationmentioning

confidence: 99%

Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems

Stiasny¹,

Chevalier²,

Nellikkath³

et al. 2022

Preprint

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“…the main idea behind the PINN is that the governing equation is used, rather than the labeled solution, in the loss function to keep the neural network solution approaching the strong solution of PDEs. PINNs have been successfully used in solving a large number of nonlinear PDEs, including Burgers, Schröinger, Navier-Stokes, Allen-Cahn, high-speed flows, etc [20,37,25,5].…”

Section: Introductionmentioning

confidence: 99%

A weighted first-order formulation for solving anisotropic diffusion equations with deep neural networks

Xie¹,

Zhai²,

Liu³

et al. 2022

Preprint

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In this paper, a new weighted first-order formulation is proposed for solving the anisotropic diffusion equations with deep neural networks. For many numerical schemes, the accurate approximation of anisotropic heat flux is crucial for the overall accuracy. In this work, the heat flux is firstly decomposed into two components along the two eigenvectors of the diffusion tensor, thus the anisotropic heat flux approximation is converted into the approximation of two isotropic components. Moreover, to handle the possible jump of the diffusion tensor across the interface, the weighted first-order formulation is obtained by multiplying this first-order formulation by a weighted function. By the decaying property of the weighted function, the weighted first-order formulation is always well-defined in the pointwise way. Finally, the weighted first-order formulation is solved with deep neural network approximation. Compared to the neural network approximation with the original second-order elliptic formulation, the proposed method can significantly improve the accuracy, especially for the discontinuous anisotropic diffusion problems.

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“…Raissi, et al (2019) introduced the concept of incorporating governing PDEs in the loss function of a deep neural network to solve both forward and inverse problems. Since then, PINN has been used for solving various scientific problems in several domains (Cuomo, Di Cola, Giampaolo, Rozza, Raissi, & Piccialli, 2022) including fluid flow (Cai, Mao, Wang, Yin & Karniadakis, 2022) and heat transfer (Cai, Wang, Wang, Perdikaris & Karniadakis, 2021). A few limitations of the PINNs have been recently highlighted by Cuomo et al (2022) in their review.…”

Section: Introductionmentioning

confidence: 99%

“…Since then, PINN has been used for solving various scientific problems in several domains (Cuomo, Di Cola, Giampaolo, Rozza, Raissi, & Piccialli, 2022) including fluid flow (Cai, Mao, Wang, Yin & Karniadakis, 2022) and heat transfer (Cai, Wang, Wang, Perdikaris & Karniadakis, 2021). A few limitations of the PINNs have been recently highlighted by Cuomo et al (2022) in their review. Even though the inference time for PINN models is considerably low, high training time and significant convergence difficulties in complex scenarios limit their implementation in real life applications .…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Moseley, Markham, and Nissen-Meyer (2021) proposed the domain decomposition approach to solve large multiscale problems. Another limitation of current PINN techniques is that they fail to generalize over dynamically changing boundary conditions (Cuomo et al 2022) (2021) has presented use of transfer learning with pre-trained neural network for one-shot inference for linear system of both ordinary and partial differential equations. In the present work, we apply some of these concepts to develop a PINN model for real-time health monitoring of an industrial APH.…”

Section: Introductionmentioning

confidence: 99%

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Physics Informed Neural Network for Health Monitoring of an Air Preheater

Jadhav

Deodhar²,

Gupta³

et al. 2022

PHME_CONF

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Air Preheater (APH) is a regenerative heat exchanger employed in thermal power plants to save fuel by improving their thermal efficiency. Monitoring the health of APH vis-a-vis its fouling is critical because fouling often results in forced outages of the power plant, incurring huge revenue losses. APH fouling is a complex thermo-chemical phenomenon governed by flue gas composition, operating temperatures, fuel type and ambient conditions. Absence of sensors within the APH make it difficult to estimate the level of fouling and its progression even for an experienced operator. Attempts to estimate APH fouling in real-time via modeling are scarce. Here we present a physics-informed neural network (PINN) that tracks the health of an APH by real-time estimation of fouling conditions within the APH as a function of real-time sensor measurements. To account for multi-fluid operation in a multi-sector design of APH, the domain is decomposed into several sub-domains. PINN is applied to each sub-domain and the overall solution is ensured by applying continuity conditions at the sub-domain interfaces. The model predicts the interior temperatures and fouling zones within the APH using external sensor measurements such as air temperature and gas composition. The model predictions are consistent with physics and yet computationally efficient in run-time. The model does not need sensor data but can be improved further by accommodating available sensor data. The real-time predictions by the model improve operator’s visibility in fouling. The predictions can be used further for estimating the remaining useful cycle life of the APH, thereby avoiding forced outages. The model can easily be integrated with the digital twin of an APH for its predictive maintenance.

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Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next

Cited by 30 publications

References 119 publications

Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems

Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems

A weighted first-order formulation for solving anisotropic diffusion equations with deep neural networks

Physics Informed Neural Network for Health Monitoring of an Air Preheater

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