Related papers: Neural network based approach for solving problems…

Neural networks constrained by the physical laws emerged as an alternate numerical tool. In this paper, the governing equation that represents the propagation of sound inside a one-dimensional duct carrying a heterogeneous medium is…

The study of sound propagation in a uniform duct having a mean flow has many applications, such as in the design of gas turbines, heating, ventilation and air conditioning ducts, automotive intake and exhaust systems, and in the modeling of…

Physics-informed neural networks offered an alternate way to solve several differential equations that govern complicated physics. However, their success in predicting the acoustic field is limited by the vanishing-gradient problem that…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…

We present a novel neural network architecture for the efficient prediction of sound fields in two and three dimensions. The network is designed to automatically satisfy the Helmholtz equation, ensuring that the outputs are physically…

The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…

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…

Recently deep learning and machine learning approaches have been widely employed for various applications in acoustics. Nonetheless, in the area of sound field processing and reconstruction classic methods based on the solutions of wave…

State-of-the-art performance for many edge applications is achieved by deep neural networks (DNNs). Often, these DNNs are location- and time-sensitive, and must be delivered over a wireless channel rapidly and efficiently. In this paper, we…

Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…

In this paper, neural network approximation methods are developed for elliptic partial differential equations with multi-frequency solutions. Neural network work approximation methods have advantages over classical approaches in that they…

In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not…

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…

We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the boundary (or initial) conditions…

Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…

Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…

Sound field reconstruction refers to the problem of estimating the acoustic pressure field over an arbitrary region of space, using only a limited set of measurements. Physics-informed neural networks have been adopted to solve the problem…

Many phenomena in physics, including light, water waves, and sound, are described by wave equations. Given their coefficients, wave equations can be solved to high accuracy, but the presence of the wavelength scale often leads to large…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…