Related papers: Neural network representation of the probability d…

The standard approaches to neural network implementation yield powerful function approximation capabilities but are limited in their abilities to learn meta representations and reason probabilistic uncertainties in their predictions.…

Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…

Solving partial differential equations (PDEs) is the canonical approach for understanding the behavior of physical systems. However, large scale solutions of PDEs using state of the art discretization techniques remains an expensive…

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 However, PF equations can be out-of-date or even unavailable…

A physics-informed neural network (PINN), which has been recently proposed by Raissi et al [J. Comp. Phys. 378, pp. 686-707 (2019)], is applied to the partial differential equation (PDE) of liquid film flows. The PDE considered is the time…

Probabilistic power flow (PPF) analysis is critical to power system operation and planning. PPF aims at obtaining probabilistic descriptions of the state of the system with stochastic power injections (e.g., renewable power generation and…

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

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…

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving partial differential equations (PDEs) involving fluid mechanics. However, the method has so far succeeded only in inviscid flows and incompressible viscous…

In modern federated learning, one of the main challenges is to account for inherent heterogeneity and the diverse nature of data distributions for different clients. This problem is often addressed by introducing personalization of the…

Neural networks (NNs) are employed to predict equations of state from a given isotropic pair potential using the virial expansion of the pressure. The NNs are trained with data from molecular dynamics simulations of monoatomic gases and…

The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary…

Feature propagation in Deep Neural Networks (DNNs) can be associated to nonlinear discrete dynamical systems. The novelty, in this paper, lies in letting the discretization parameter (time step-size) vary from layer to layer, which needs to…

In this paper, we study the partial differential equation models of neural networks. Neural network can be viewed as a map from a simple base model to a complicate function. Based on solid analysis, we show that this map can be formulated…

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…

The success of deep learning techniques over the last decades has opened up a new avenue of research for weather forecasting. Here, we take the novel approach of using a neural network to predict full probability density functions at each…

We propose an approach to solving partial differential equations (PDEs) using a set of neural networks which we call Neural Basis Functions (NBF). This NBF framework is a novel variation of the POD DeepONet operator learning approach where…

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…

Density functional theory is one of the most efficient and widely used computational methods of quantum mechanics, especially in fields such as solid state physics and quantum chemistry. From the theoretical perspecive, its central object…