Related papers: Physics-Informed Graphical Neural Network for Para…
The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…
This paper presents a novel approach for accelerating n-body simulations by integrating a physics-informed graph neural networks (GNN) with traditional numerical methods. Our method implements a leapfrog-based simulation engine to generate…
Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…
Solving power flow (PF) equations is the basis of power flow analysis, which is important in determining the best operation of existing systems, performing security analysis, etc. However, PF equations can be out-of-date or even unavailable…
Distributed renewable generation, elastic loads, and purposeful manipulation of meter readings challenge the monitoring and control of today's power systems (PS). In this context, to maintain a comprehensive view of the system in real time,…
Traffic state estimation (TSE) bifurcates into two categories, model-driven and data-driven (e.g., machine learning, ML), while each suffers from either deficient physics or small data. To mitigate these limitations, recent studies…
Power grids play a very important role in delivering electrical energy to homes, industries and other places that require it. Because of this increased demand they are facing a great challenge of voltage variations. This happens due to…
Optimal Power Flow (OPF) is a very traditional research area within the power systems field that seeks for the optimal operation point of electric power plants, and which needs to be solved every few minutes in real-world scenarios.…
I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…
Incorporating inductive biases into ML models is an active area of ML research, especially when ML models are applied to data about the physical world. Equivariant Graph Neural Networks (GNNs) have recently become a popular method for…
Graph Neural Networks (GNNs) have deeply modified the landscape of numerical simulations by demonstrating strong capabilities in approximating solutions of physical systems. However, their ability to extrapolate beyond their training domain…
Power grids are critical infrastructures of paramount importance to modern society and, therefore, engineered to operate under diverse conditions and failures. The ongoing energy transition poses new challenges for the decision-makers and…
Graph neural networks (GNNs) have been shown to be astonishingly capable models for molecular property prediction, particularly as surrogates for expensive density functional theory calculations of relaxed energy for novel material…
Traffic state estimation (TSE) fundamentally involves solving high-dimensional spatiotemporal partial differential equations (PDEs) governing traffic flow dynamics from limited, noisy measurements. While Physics-Informed Neural Networks…
Graph neural networks (GNNs) are among the most powerful tools in deep learning. They routinely solve complex problems on unstructured networks, such as node classification, graph classification, or link prediction, with high accuracy.…
Physics-guided neural networks (PGNN) is an effective tool that combines the benefits of data-driven modeling with the interpretability and generalization of underlying physical information. However, for a classical PGNN, the penalization…
Reinforcement learning is well known for its ability to model sequential tasks and learn latent data patterns adaptively. Deep learning models have been widely explored and adopted in regression and classification tasks. However, deep…
Solving partial differential equations (PDEs) is an important yet challenging task in fluid mechanics. In this study, we embed an improved Fourier series into neural networks and propose a physics-informed Fourier basis neural network…
This paper introduces a framework for combining scientific knowledge of physics-based models with neural networks to advance scientific discovery. This framework, termed physics-guided neural networks (PGNN), leverages the output of…