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Physics-informed neural networks (PINNs) have been widely utilized for solving a range of partial differential equations (PDEs) in various scientific and engineering disciplines. This paper presents a Fourier heuristic-enhanced PINN (termed…
Approximating solutions of ordinary and partial differential equations constitutes a significant challenge. Based on functional expressions that inherently depend on neural networks, neural forms are specifically designed to precisely…
Deep neural networks work well at approximating complicated functions when provided with data and trained by gradient descent methods. At the same time, there is a vast amount of existing functions that programmatically solve different…
In previous studies, we introduced a neural network framework based on symmetric differential equations, along with one of its training methods. In this article, we present another training approach for this neural network. This method…
We present a simple and effective method for representing periodic functions and enforcing exactly the periodic boundary conditions for solving differential equations with deep neural networks (DNN). The method stems from some simple…
Semi-gradient Q-learning is applied in many fields, but due to the absence of an explicit loss function, studying its dynamics and implicit bias in the parameter space is challenging. This paper introduces the Fokker--Planck equation and…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
The holonomic gradient method gives an algorithm to efficiently and accurately evaluate normalizing constants and their derivatives. We apply the holonomic gradient method in the case of the conditional Poisson or multinomial distribution…
This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…
We propose an iterative method for nonlinear semidefinite programs with box constraints. The search direction in the proposed method utilizes the distance from the current point to the boundary of a feasible set. The computation of the…
Traditional Monte Carlo integration using uniform random sampling exhibits degraded efficiency in low-regularity or high-dimensional problems. We propose a novel deep learning framework based on deterministic number-theoretic sampling…
While model selection is a well-studied topic in parametric and nonparametric regression or density estimation, selection of possibly high-dimensional nuisance parameters in semiparametric problems is far less developed. In this paper, we…
This article introduces an iterative method for solving nonsingular non-Hermitian positive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two non-Hermitian positive…
We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase…
This paper introduces a deep learning system based on a quantum neural network for the binary classification of points of a specific geometric pattern (Two-Moons Classification problem) on a plane. We believe that the use of hybrid deep…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
Physics-informed neural networks (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…
Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions. Independent variables are fed into the input layer, and the output is considered as solution's value.…
In this paper, we introduce cell-average based neural network (CANN) method to solve high-dimensional parabolic partial differential equations. The method is based on the integral or weak formulation of partial differential equations. A…
The article proposes a Caputo fractional conjugate gradient (CFCG) method for unconstrained optimization problems which is applicable to smooth as well as non-smooth problmes. The proposed method uses a non-adaptive version of the Caputo…