Related papers: Artificial Neural Network Approach for Solving Fra…
This paper discusses a new method to solve definite integrals using artificial neural networks. The objective is to build a neural network that would be a novel alternative to pre-established numerical methods and with the help of a…
Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE residual as the loss function. This strategy is called "physics-informed neural networks" (PINNs), but it currently cannot produce high-accuracy…
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…
In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of dimensionality. Specifically, we introduce a concept which we…
The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself. In residual networks, instead of having a discrete sequence of hidden layers, the…
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…
In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…
NeuroEvolution (NE) methods are known for applying Evolutionary Computation to the optimisation of Artificial Neural Networks(ANNs). Despite aiding non-expert users to design and train ANNs, the vast majority of NE approaches disregard the…
We compare the Finite Element Method (FEM) simulation of a standard Partial Differential Equation thermal problem of a plate with a hole with a Neural Network (NN) simulation. The largest deviation from the true solution obtained from FEM…
Many real-world dynamical systems are associated with first integrals (a.k.a. invariant quantities), which are quantities that remain unchanged over time. The discovery and understanding of first integrals are fundamental and important…
A Feed Forward Error Back Propagation Artificial Neural Network(ANN) algorithm is developed for electron/positron identification in a wide momentum region (10 - 300 GeV/c). The method was proposed for the Transition Radiation Detector of…
Distributed optimization is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned problems and face stability-versus-speed tradeoffs. We introduce fractional…
Randomized neural networks (RaNNs) are attractive for partial differential equations (PDEs) because they replace expensive end-to-end training with a linear least-squares solve over randomized hidden features. Their practical performance,…
This study presents the conditional neural fields for reduced-order modeling (CNF-ROM) framework to approximate solutions of parametrized partial differential equations (PDEs). The approach combines a parametric neural ODE (PNODE) for…
In this paper, an innovative Physical Model-driven Neural Network (PMNN) method is proposed to solve time-fractional differential equations. It establishes a temporal iteration scheme based on physical model-driven neural networks which…
We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…
Enhancing the robustness and accuracy of time series forecasting models is an active area of research. Recently, Artificial Neural Networks (ANNs) have found extensive applications in many practical forecasting problems. However, the…
Although various linear log-distance path loss models have been developed, advanced models are requiring to more accurately and flexibly represent the path loss for complex environments such as the urban area. This letter proposes an…
Artificial neural networks (ANNs) are at the core of most Deep learning (DL) algorithms that successfully tackle complex problems like image recognition, autonomous driving, and natural language processing. However, unlike biological brains…
ADCME is a novel computational framework to solve inverse problems involving physical simulations and deep neural networks (DNNs). This paper benchmarks its capability to learn spatially-varying physical fields using DNNs. We demonstrate…