The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power systems. Physics-Informed Neural Networks (PINNs) have recently emerged as a promising solution for drastically accelerating computations of non-linear dynamical systems. This work investigates the applicability of these methods for power system dynamics, focusing on the dynamic response to load disturbances. Comparing the prediction of PINNs to the solution of conventional solvers, we find that PINNs can be 10 to 1000 times faster than conventional solvers. At the same time, we find them to be sufficiently accurate and numerically stable even for large time steps. To facilitate a deeper understanding, this paper also present a new regularisation of Neural Network (NN) training by introducing a gradient-based term in the loss function. The resulting NNs, which we call dtNNs, help us deliver a comprehensive analysis about the strengths and weaknesses of the NN based approaches, how incorporating knowledge of the underlying physics affects NN performance, and how this compares with conventional solvers for power system dynamics.
In this paper, we introduce SciANN, a Python package for scientific computing and physics-informed deep learning using artificial neural networks. SciANN uses the widely used deep-learning packages Tensorflow and Keras to build deep neural networks and optimization models, thus inheriting many of Keras's functionalities, such as batch optimization and model reuse for transfer learning. SciANN is designed to abstract neural network construction for scientific computations and solution and discovery of partial differential equations (PDE) using the physics-informed neural networks (PINN) archite…
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…
SPINONet: Scalable Spiking Physics-informed Neural Operator for Computational Mechanics Applications
Department of Applied Mechanics（应用力学系）；Indian Institute of Technology Delhi（德里印度理工学院）；Institute of Structural Mechanics and Dynamics in Aerospace Engineering（航空航天工程中的结构力学与动力学研究所）；Faculty of Aerospace Engineering and Geodesy（航空航天工程与大地测量学系）；University of Stuttgart（斯图加特大学）；Experimental Hepatobiliary Surgery Group（肝胆外科实验小组）；Department of Hepatobiliary Surgery and Visceral Transplantation（肝胆外科与内脏移植部）；University of Leipzig Medical Center（莱比锡大学医学中心）；Department of Civil and Systems Engineering（土木与系统工程系）；Johns Hopkins University（约翰霍普金斯大学）；Data Science and AI Institute（数据科学与人工智能研究所）；Yardi School of Artificial Intelligence (YScAI)（Yardi人工智能学院（YScAI））
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…
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…
Defense Innovation Institute, Chinese Academy of Military Science（中国人民解放军军事科学院国防科技创新研究院）；Human Resource Center（人力资源中心）
Learning solutions of partial differential equations (PDEs) with Physics-Informed Neural Networks (PINNs) is an attractive alternative approach to traditional solvers due to its flexibility and ease of incorporating observed data. Despite the success of PINNs in accurately solving a wide variety of PDEs, the method still requires improvements in terms of computational efficiency. One possible improvement idea is to optimize the generation of training point sets. Residual-based adaptive sampling and quasi-uniform sampling approaches have been each applied to improve the training effects of PINN…
The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural network, the network learns global features corresponding to low-frequency components while high-frequency components are approximated at a much slower rate. For a class of equations in which the solution contains a wide range of scales, the network training process can suffer from slow convergence and low accuracy due to its inability to capture the high-fre…
Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks
Tsinghua University（清华大学）；Bauhaus-Universität Weimar（魏玛包豪斯大学）；CNPC Engineering Technology RD Company Limited（中国石油集团工程技术研究院有限公司）；Queensland University of Technology（昆士兰科技大学）；Leibniz University Hannover（汉诺威莱布尼茨大学）
Cost-Informed Learning for Aggregating Building HVAC Flexibility
State Key Laboratory of Advanced Electromagnetic Technology, Huazhong University of Science and Technology（华中科技大学先进电磁技术国家重点实验室）；Thayer School of Engineering, Dartmouth College（达特茅斯学院塔克工程学院）；HyperStrong Technology Co., Ltd.（HyperStrong科技有限公司）
Mass Conservation on Rails -- Rethinking Physics-Informed Learning of Ice Flow Vector Fields
School of Computer Science（计算机科学学院）；The University of Sydney（悉尼大学）；Human Technology Institute（人机技术研究所）；University of Technology Sydney（技术大学悉尼分校）；NVIDIA（NVIDIA公司）
The calibration of solid constitutive models with full-field experimental data is a long-standing challenge, especially in materials which undergo large deformation. In this paper, we propose a physics-informed deep-learning framework for the discovery of constitutive model parameterizations given full-field displacement data and global force-displacement data. Contrary to the majority of recent literature in this field, we work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. The approach presented in…
A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks
Université de Toulouse（图卢兹大学）；INP-ENSEEIHT（国立图卢兹应用科学学院-国立高等电子、电工、计算机、水力与电信学院）；IRIT（图卢兹计算机研究所）；CERFACS（欧洲科学计算高级研究中心）；BRLi（BRLi公司）；Université de Lyon（里昂大学）；INRIA（法国国家信息与自动化研究所）；ENSL（里昂高等师范学院）；UCBL（里昂第一大学）；CNRS（法国国家科学研究中心）；University of Namur（那慕尔大学）
With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently emerged and succeeded in various forward and inverse PDE problems thanks to their excellent properties, such as flexibility, mesh-free solutions, and unsupervised training. However, their slower convergence speed and relatively inaccurate solutions often limit their broader applicability in many science and engineering domains. This paper proposes a new kind of data-driven PDEs so…
Physics-Informed Neural Network Surrogate Models for River Stage Prediction
Graz Technical University of Technology（格拉茨技术大学）；University of New Orleans（新奥尔良大学）；US Army Corps of Engineers（美国陆军工程兵团）；Naval Research Laboratory（海军研究实验室）
Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical methods is how they approximate the physical fields of interest. Physics-informed deep learning is a novel approach recently developed for modeling PDE solutions and shows promise to solve computational mechanics problems without using any labeled data. The philosophy behind it is to approximate the quantity of interest (e.g., PDE solution variables) by a deep neu…
A scaled TW-PINN: A physics-informed neural network for traveling wave solutions of reaction-diffusion equations with general coefficients
Department of Mathematics \& POSTECH MINDS (Mathematical Institute for Data Science), Pohang University of Science；Graduate School of Artificial Intelligence \& POSTECH MINDS (Mathematical Institute for Data Science), Pohang University of Science
Scale-PINN: Learning Efficient Physics-Informed Neural Networks Through Sequential Correction
Institute of High Performance Computing（高性能计算研究所）；Centre for Frontier AI Research（前沿人工智能研究中心）；School of Mechanical Engineering（机械工程学院）；College of Computing and Data Science（计算与数据科学学院）
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…
In many computational problems in engineering and science, function or model differentiation is essential, but also integration is needed. An important class of computational problems include so-called integro-differential equations which include both integrals and derivatives of a function. In another example, stochastic differential equations can be written in terms of a partial differential equation of a probability density function of the stochastic variable. To learn characteristics of the stochastic variable based on the density function, specific integral transforms, namely moments, of …
Simulating Three-dimensional Turbulence with Physics-informed Neural Networks
Institution for Foundation of Data Science, Yale University（数据科学基础研究所，耶鲁大学）；Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania（机械工程与应用力学系，宾夕法尼亚大学）；Sibley School of Mechanical and Aerospace Engineering, Cornell University（机械与航空航天工程学院，康奈尔大学）；Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory（先进计算、数学和数据部门，太平洋西北国家实验室）
Magnetic resonance velocimetry (MRV) is a non-invasive experimental technique widely used in medicine and engineering to measure the velocity field of a fluid. These measurements are dense but have a low signal-to-noise ratio (SNR). The measurements can be de-noised by imposing physical constraints on the flow, which are encapsulated in governing equations for mass and momentum. Previous studies have required the shape of the boundary (for example, a blood vessel) to be known a priori. This, however, requires a set of additional measurements, which can be expensive to obtain. In this paper, we…
University of Cambridge（剑桥大学）；Heriot-Watt University（赫瑞-瓦特大学）；Maxwell Institute for Mathematical Sciences（麦克斯韦数学科学研究所）
Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be approximated numerically. The finite element method, for instance, is a usual standard methodology to do so. The recent success of deep neural networks at various approximation tasks has motivated their use in the numerical solution of PDEs. These so-called physics-informed neural networks and their variants have shown to be able to successfully approximate a …
Northeastern University（东北大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Lawrence Berkeley Lab（劳伦斯伯克利实验室）
While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim to predict turbulent flow by learning its highly nonlinear dynamics from spatiotemporal velocity fields of large-scale fluid flow simulations of relevance to turbulence modeling and climate modeling. We adopt a hybrid approach by marrying two well-established turbulent flow simulation techniques with deep learning. Specifically, we introduce trainable spect…
