Varying power-infeed from converter-based generation units introduces great uncertainty on system parameters such as inertia and damping. As a consequence, system operators face increasing challenges in performing dynamic security assessment and taking real-time control actions. Exploiting the widespread deployment of phasor measurement units (PMUs) and aiming at developing a fast dynamic state and parameter estimation tool, this paper investigates the performance of Physics-Informed Neural Networks (PINN) for discovering the frequency dynamics of future power systems. PINNs have the potential to address challenges such as the stronger non-linearities of low-inertia systems, increased measurement noise, and limited availability of data. The estimator is demonstrated in several test cases using a 4-bus system, and compared with state of the art algorithms, such as the Unscented Kalman Filter (UKF), to assess its performance.
We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical properties of soft tissue based on the full-field displacement measurements under quasi-static loading. In our model, we apply two independent neural networks, one for approximating the solution of the corresponding forward problem, and the other for approximating the unknown material parameter field. As a proof of concept, we validate our model on a prototypi…
The University of New South Wales（新南威尔士大学）；Massachusetts Institute of Technology（麻省理工学院）；University of British Columbia（不列颠哥伦比亚大学）；Sharif University of Technology（谢里夫理工大学）
We explore an application of the Physics Informed Neural Networks (PINNs) in conjunction with Airy stress functions and Fourier series to find optimal solutions to a few reference biharmonic problems of elasticity and elastic plate theory. Biharmonic relations are fourth-order partial differential equations (PDEs) that are challenging to solve using classical numerical methods, and have not been addressed using PINNs. Our work highlights a novel application of classical analytical methods to guide the construction of efficient neural networks with the minimal number of parameters that are very…
We explore the possibility to use physics-informed neural networks to drastically accelerate the solution of ordinary differential-algebraic equations that govern the power system dynamics. When it comes to transient stability assessment, the traditionally applied methods either carry a significant computational burden, require model simplifications, or use overly conservative surrogate models. Conventional neural networks can circumvent these limitations but are faced with high demand of high-quality training datasets, while they ignore the underlying governing equations. Physics-informed neu…
Understanding the thermal behavior of additive manufacturing (AM) processes is crucial for enhancing the quality control and enabling customized process design. Most purely physics-based computational models suffer from intensive computational costs and the need of calibrating unknown parameters, thus not suitable for online control and iterative design application. Data-driven models taking advantage of the latest developed computational tools can serve as a more efficient surrogate, but they are usually trained over a large amount of simulation data and often fail to effectively use small bu…
A Coupled Physics-Informed Neural Network for Greenhouse Climate State Reconstruction and Parameter Identification under Sparse Sensor Measurements
Centro de Modelamiento Matemático (CMM), University of Chile（智利大学数学建模中心）；College of Science, King Khalid University（哈立德国王大学理学院）；Presidency University（总统大学）
Technical University of Denmark（丹麦技术大学）；Center for Electric Power and Energy（电力与能源中心）
This paper introduces for the first time, to our knowledge, a framework for physics-informed neural networks in power system applications. Exploiting the underlying physical laws governing power systems, and inspired by recent developments in the field of machine learning, this paper proposes a neural network training procedure that can make use of the wide range of mathematical models describing power system behavior, both in steady-state and in dynamics. Physics-informed neural networks require substantially less training data and can result in simpler neural network structures, while achiev…
Data assimilation and parameter identification for water waves using the nonlinear Schrödinger equation and physics-informed neural networks
Hamburg University of Technology（汉堡工业大学）；TU Dortmund University（多特蒙德工业大学）；Technical University of Munich（慕尼黑工业大学）；German Aerospace Center（德国航空航天中心）；Imperial College London（伦敦帝国理工学院）；Technische Universität Berlin（柏林工业大学）
Partition of Unity Physics-Informed Neural Networks (POU-PINNs): An Unsupervised Framework for Physics-Informed Domain Decomposition and Mixtures of Experts
The University of Texas at El Paso（德克萨斯大学埃尔帕索分校）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；Clarkson University（克拉克森大学）；Texas A&M University in Kingsville（德克萨斯农工大学金斯维尔分校）
ETH Zürich（苏黎世联邦理工学院）；ETH AI Center（苏黎世联邦理工学院人工智能中心）
We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator learning. These bounds guarantee that PINNs and (physics-informed) DeepONets or FNOs will efficiently approximate the underlying solution or solution operator of generic partial differential equations (PDEs). Our framework utilizes existing neural network approximation results to obtain bounds on more involved learning architectures for PDEs. We illustrate …
The Physics-Informed Neural Network (PINN) approach is a new and promising way to solve partial differential equations using deep learning. The $L^2$ Physics-Informed Loss is the de-facto standard in training Physics-Informed Neural Networks. In this paper, we challenge this common practice by investigating the relationship between the loss function and the approximation quality of the learned solution. In particular, we leverage the concept of stability in the literature of partial differential equation to study the asymptotic behavior of the learned solution as the loss approaches zero. With…
This paper presents NSGA-PINN, a multi-objective optimization framework for effective training of Physics-Informed Neural Networks (PINNs). The proposed framework uses the Non-dominated Sorting Genetic Algorithm (NSGA-II) to enable traditional stochastic gradient optimization algorithms (e.g., ADAM) to escape local minima effectively. Additionally, the NSGA-II algorithm enables satisfying the initial and boundary conditions encoded into the loss function during physics-informed training precisely. We demonstrate the effectiveness of our framework by applying NSGA-PINN to several ordinary and p…
University of Twente（特文特大学）；Massachusetts Institute of Technology（麻省理工学院）
An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. An admissible displacement-stress solution pair is obtained from a mixed form of physics-informed neural networks, and the proposed error bound is formulated as the constitutive relation error defined by the solution pair. Such an error estimator provides an upper bound of the global error of neural network discretization. The bounding property, as well as the asymptotic behavior of the physics-informed neural network solutions, are studied in a demonstrating example.
PIDT: Physics-Informed Digital Twin for Optical Fiber Parameter Estimation
Dept. of Electrical Engineering, Chalmers Univ. of Technology, Sweden（电气工程系，瑞典查尔姆斯理工大学）；Dept. of Microtechnology and Nanoscience, Chalmers Univ. of Technology, Sweden（微电子与纳米科技系，瑞典查尔姆斯理工大学）
Brown University（布朗大学）；Xiamen University（厦门大学）；Dalian University of Technology（大连理工大学）
Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier-Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE. Moreover, solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer codes. Here, we review flow physics-informed learning, integrating seamlessly data and mathematical models, and implementing the…
We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier-Stokes equations with (extended) physics informed neural networks. We show that the underlying PDE residual can be made arbitrarily small for tanh neural networks with two hidden layers. Moreover, the total error can be estimated in terms of the training error, network size and number of quadrature points. The theory is illustrated with numerical experiments.
University of Nevada, Las Vegas（内华达大学拉斯维加斯分校）；University of Arkansas（阿肯色大学）；Lehigh University（里海大学）
In this paper, we show a physics-informed neural network solver for the time-dependent surface PDEs. Unlike the traditional numerical solver, no extension of PDE and mesh on the surface is needed. We show a simplified prior estimate of the surface differential operators so that PINN's loss value will be an indicator of the residue of the surface PDEs. Numerical experiments verify efficacy of our algorithm.
Bayesian Physics Informed Neural Networks (B-PINNs) have gained significant attention for inferring physical parameters and learning the forward solutions for problems based on partial differential equations. However, the overparameterized nature of neural networks poses a computational challenge for high-dimensional posterior inference. Existing inference approaches, such as particle-based or variance inference methods, are either computationally expensive for high-dimensional posterior inference or provide unsatisfactory uncertainty estimates. In this paper, we present a new efficient infere…
Technical University of Denmark（丹麦技术大学）；The Danish Hydrocarbon Research and Technology Centre（丹麦碳氢化合物研究与技术中心）
This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy harvesting. Specifically, we investigate how to extend the methodology of physics-informed neural networks to solve both the forward and inverse problems in relation to the nonlinear diffusivity and Biot's equations. We explore the accuracy of the physics-informed neural networks with different training example sizes and choices of hyperparameters. The impacts …
Conformal mapping based Physics-informed neural networks for designing neutral inclusions
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology（韩国科学技术院数学科学系）；Department of Artificial Intelligence, Chung-Ang University（Chung-Ang 大学人工智能系）
The objective of this paper is to investigate the ability of physics-informed neural networks to learn the magnetic field response as a function of design parameters in the context of a two-dimensional (2-D) magnetostatic problem. Our approach is as follows. First, we present a functional whose minimization is equivalent to solving parametric magnetostatic problems. Subsequently, we use a deep neural network (DNN) to represent the magnetic field as a function of space and parameters that describe geometric features and operating points. We train the DNN by minimizing the physics-informed funct…
Massachusetts Institute of Technology（麻省理工学院）；Sandia National Laboratories（桑迪亚国家实验室）
Physics-informed machine learning (PIML) has emerged as a promising new approach for simulating complex physical and biological systems that are governed by complex multiscale processes for which some data are also available. In some instances, the objective is to discover part of the hidden physics from the available data, and PIML has been shown to be particularly effective for such problems for which conventional methods may fail. Unlike commercial machine learning where training of deep neural networks requires big data, in PIML big data are not available. Instead, we can train such networ…
Identifying parameters in a system of nonlinear, ordinary differential equations is vital for designing a robust controller. However, if the system is stochastic in its nature or if only noisy measurements are available, standard optimization algorithms for system identification usually fail. We present a new approach that combines the recent advances in physics-informed neural networks and the well-known achievements of Kalman filters in order to find parameters in a continuous-time system with noisy measurements. In doing so, our approach allows estimating the parameters together with the me…
This paper introduces for the first time, to the best of our knowledge, the Bayesian Physics-Informed Neural Networks for applications in power systems. Bayesian Physics-Informed Neural Networks (BPINNs) combine the advantages of Physics-Informed Neural Networks (PINNs), being robust to noise and missing data, with Bayesian modeling, delivering a confidence measure for their output. Such a confidence measure can be very valuable for the operation of safety critical systems, such as power systems, as it offers a degree of trustworthiness for the neural network output. This paper applies the BPI…
In energy intensive industrial systems, an evaporative cooling process may introduce operational flexibility. Such flexibility refers to a systems ability to deviate from its scheduled energy consumption. Identifying the flexibility, and therefore, designing control that ensures efficient and reliable operation presents a great challenge due to the inherently complex dynamics of industrial systems. Recently, machine learning models have attracted attention for identifying flexibility, due to their ability to model complex nonlinear behavior. This research presents machine learning based method…
Control-Oriented System Identification: Classical, Learning, and Physics-Informed Approaches
Edwardson School of Industrial Engineering, Purdue University（普渡大学爱德华森工业工程学院）；Electrical and Computer Engineering, University of California San Diego（加州大学圣地亚哥分校电气与计算机工程）；Department of Computer Science, Rice University（莱斯大学计算机科学系）；University of Stuttgart, Institute for Systems Theory and Automatic Control（斯图加特大学系统理论与自动控制研究所）
