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The paper is devoted to the study of the backward behavior of solutions of the initial boundary value problem for the chevron pattern equations under homogeneous Dirichlet’s boundary conditions. We prove that, as t → ∞, the asymptotic behavior of ...

We develop an optimal control framework that enables to determine the most-beneficial ways of investing in technology and directing capital within an economy. Our developed framework features three main novelties: the optimization of a cross–...${}_{}\mathrm{}$${}^{}\mathrm{}$${}_{}{}^{}$${}_{}{}^{}$

Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural networks, ...

• We propose BsPINNs, a binary structured neural network framework addressing PINNs' limits with rapidly changing solutions.
• BsPINNs partition the network into channels with partially independent parameters, enabling decomposition into ...

The aim of this note is to construct a neural network for which the linear finite element approximation of a simple one dimensional boundary value problem is a minimum of the cost function to find out if the neural network is able to reproduce ...

The application of Artificial Neural Networks (ANNs) has been extensively investigated for fluid dynamic problems. A specific form of ANNs are Physics-Informed Neural Networks (PINNs). They incorporate physical laws in the training and have ...

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• PINNs improved the ANN prediction accuracy for the potential flow cases in this work.
• Random distribution of training data lead to a higher prediction accuracy of ANNs.
• A Sequence-to-sequence method enabled temporal interpolation ...

Control of mixed-autonomy traffic where Human-driven Vehicles (HVs) and Autonomous Vehicles (AVs) coexist on the road has gained increasing attention over the recent decades. This paper addresses the boundary stabilization problem for mixed ...

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 lack ...

• Limitations of auto-differentiation hinder its accuracy to compute physical gradients.
• Foreign numerical operators can be used to compute the physical gradients.
• A model enriched with physical invariances knowledge can manage ...

We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented up to ...

• A novel physics-informed convolutional neural network f-PICNN for PDEs without any labelled data.
• Nonlinear convolutional units (NCUs).
• Memory mechanism (numerical results show it can considerably speed up the convergence).
• ...

The physics and interdisciplinary problems in science and engineering are mainly described as partial differential equations (PDEs). Recently, a novel method using physics-informed neural networks (PINNs) to solve PDEs by employing deep neural ...

A novel framework is proposed that utilizes symbolic regression via genetic programming to identify free-form partial differential equations from scarce and noisy data. The framework successfully identified ground truth models for four synthetic ...

• Symbolic regression identifies partial differential equations from scarce and noisy data.
• Framework successfully identified ground truth models of four synthetic systems.
• Framework identifies partial differential equation models ...

We consider the solution to the biharmonic equation in mixed form discretized by the Hybrid High-Order (HHO) methods. The two resulting second-order elliptic problems can be decoupled via the introduction of a new unknown, corresponding to the ...

In this paper, the boundary control problem for a class of flexible riser control systems with input quantization and boundary position constraints is studied. Since quantization errors can adversely affect the performance of the control system, ...

In this study, we investigate how the updating of weights during forward operation and the computation of gradients during backpropagation impact the optimization process, training procedure, and overall performance of the neural network, ...

• SQR-SkipResNet, inspired by highway networks, ensures stability and convergence.
• Plain NN's instability due to weight norm fluctuations hampers convergence.
• Deeper networks' impact on accuracy varies with problem complexity.
• ...

In this paper, we investigate the method of solving partial differential equations (PDEs) using artificial neural network (ANN) structures, which have been actively applied in artificial intelligence models. The ANN model for solving PDEs offers ...

The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to a series of computational techniques for numerical solutions. Although numerous latest advances are accomplished in developing neural operators, a ...

• We propose a new neural operator model for partial differential equation (PDE) solving and realize an effective linear prediction of non-linear dynamics via Koopman operator.
• Our approach achieves robust and accurate modeling of the ...

A novel mesh-free kernel method is presented for solving function interpolation problems and partial differential equations (PDEs). Despite the simplicity and accuracy of the radial basis function (RBF) method, two main difficulties have been ...

In exterior calculus on smooth manifolds, the exterior derivative and wedge products are natural with respect to smooth maps between manifolds, that is, these operations commute with pullback. In discrete exterior calculus (DEC), simplicial ...

Randomized Neural Networks (RNNs) are a variety of neural networks in which the hidden-layer parameters are fixed to randomly assigned values, and the output-layer parameters are obtained by solving a linear system through least squares. This ...

The following work presents a new method to solve Poisson’s equation and, more generally, sparse linear systems using graph neural networks. We propose a supervised approach to solve the discretized representation of Poisson’s equation at every ...

Physics-informed neural networks (PINNs) provide a means of obtaining approximate solutions of partial differential equations and systems through the minimisation of an objective function which includes the evaluation of a residual function at a ...