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This paper presents a comprehensive review of the design of experiments used in the surrogate models. In particular, this study demonstrates the necessity of the design of experiment schemes for the Physics-Informed Neural Network (PINN),…

Machine Learning · Statistics 2022-02-15 Sourav Das , Solomon Tesfamariam

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…

Machine Learning · Computer Science 2022-04-06 Jeremy Yu , Lu Lu , Xuhui Meng , George Em Karniadakis

Physics-informed neural networks (PINNs) is an emerging category of neural networks which can be trained to solve supervised learning tasks while taking into consideration given laws of physics described by general nonlinear partial…

Cryptography and Security · Computer Science 2026-04-07 Solon Falas , Charalambos Konstantinou , Maria K. Michael

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…

Machine Learning · Computer Science 2024-01-17 Abdul Hannan Mustajab , Hao Lyu , Zarghaam Rizvi , Frank Wuttke

The concepts and techniques of physics-informed neural networks (PINNs) is studied and limitations are identified to make it efficient to approximate dynamical equations. Potential working research domains are explored for increasing the…

Computational Physics · Physics 2023-01-13 Siddharth Rout

Recently, deep reinforcement learning (DRL)-based approach has shown promisein solving complex decision and control problems in power engineering domain.In this paper, we present an in-depth analysis of DRL-based voltage control fromaspects…

Artificial Intelligence · Computer Science 2020-12-25 Xiren Zhou , Siqi Wang , Ruisheng Diao , Desong Bian , Jiahui Duan , Di Shi

Physics-Informed Neural Networks have shown unique utility in parameterising the solution of a well-defined partial differential equation using automatic differentiation and residual losses. Though they provide theoretical guarantees of…

Machine Learning · Computer Science 2022-05-17 Vignesh Gopakumar , Stanislas Pamela , Debasmita Samaddar

Renewable energy resources (RERs) have been increasingly integrated into large-scale distributed power systems. Considering uncertainties and voltage fluctuation issues introduced by RERs, in this paper, we propose a deep reinforcement…

Machine Learning · Computer Science 2022-08-08 Jinhao Li , Ruichang Zhang , Hao Wang , Zhi Liu , Hongyang Lai , Yanru Zhang

High-performance scientific simulations, important for comprehension of complex systems, encounter computational challenges especially when exploring extensive parameter spaces. There has been an increasing interest in developing deep…

Machine Learning · Computer Science 2024-07-15 Pradeep Bajracharya , Javier Quetzalcóatl Toledo-Marín , Geoffrey Fox , Shantenu Jha , Linwei Wang

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…

Machine Learning · Computer Science 2022-11-02 Raphaël Pellegrin , Blake Bullwinkel , Marios Mattheakis , Pavlos Protopapas

Deep learning for distribution grid optimization can be advocated as a promising solution for near-optimal yet timely inverter dispatch. The principle is to train a deep neural network (DNN) to predict the solutions of an optimal power flow…

Optimization and Control · Mathematics 2020-07-09 Manish K. Singh , Sarthak Gupta , Vassilis Kekatos , Guido Cavraro , Andrey Bernstein

An adjoint formulation leveraging a physics-informed neural network (PINN) is employed to advance the density moment of a runaway electron (RE) distribution forward in time. A distinguishing feature of this approach is that once the adjoint…

Plasma Physics · Physics 2024-12-18 Christopher J. McDevitt , Jonathan Arnaud , Xian-Zhu Tang

Stirred tanks are vital in chemical and biotechnological processes, particularly as bioreactors. Although computational fluid dynamics (CFD) is widely used to model the flow in stirred tanks, its high computational cost$-$especially in…

Computational Engineering, Finance, and Science · Computer Science 2025-07-21 Veronika Trávníková , Eric von Lieres , Marek Behr

Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints. Their practical effectiveness however can be…

Machine Learning · Computer Science 2023-08-17 Sifan Wang , Shyam Sankaran , Hanwen Wang , Paris Perdikaris

Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at…

Computational Engineering, Finance, and Science · Computer Science 2024-08-23 Saakaar Bhatnagar , Andrew Comerford , Araz Banaeizadeh

The increasing integration of renewable energy sources (RESs) is transforming traditional power grid networks, which require new approaches for managing decentralized energy production and consumption. Microgrids (MGs) provide a promising…

Machine Learning · Computer Science 2025-11-19 Davide Salaorni , Federico Bianchi , Francesco Trovò , Marcello Restelli

Training a deep neural network to maximize a target objective has become the standard recipe for successful machine learning over the last decade. These networks can be optimized with supervised learning, if the target objective is…

Machine Learning · Computer Science 2025-05-12 Bernhard Jaeger , Andreas Geiger

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

Machine Learning · Computer Science 2022-12-16 Jian Cheng Wong , Chinchun Ooi , Abhishek Gupta , Yew-Soon Ong

This paper presents a Reinforcement Learning (RL) based energy market for a prosumer dominated microgrid. The proposed market model facilitates a real-time and demanddependent dynamic pricing environment, which reduces grid costs and…

Systems and Control · Electrical Eng. & Systems 2020-09-24 Arman Ghasemi , Amin Shojaeighadikolaei , Kailani Jones , Morteza Hashemi , Alexandru G. Bardas , Reza Ahmadi

For multi-scale problems, the conventional physics-informed neural networks (PINNs) face some challenges in obtaining available predictions. In this paper, based on PINNs, we propose a practical deep learning framework for multi-scale…

Machine Learning · Computer Science 2024-12-18 Yong Wang , Yanzhong Yao , Jiawei Guo , Zhiming Gao