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Physics-informed neural networks (PINN) is a machine learning (ML)-based method to solve partial differential equations that has gained great popularity due to the fast development of ML libraries in the last few years. The…

For multi-scale problems, the conventional physics-informed neural networks (PINNs) face some challenges in obtaining available predictions. In this paper, based on PINNs, we propose a practical deep learning framework for multi-scale…

Physics-informed neural networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks.…

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,…

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…

In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…

Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…

We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…

The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community last years. Physics Informed Neural Networks (PINNs) is one of this methods and represent a…

Deep learning based approaches like Physics-informed neural networks (PINNs) and DeepONets have shown promise on solving PDE constrained optimization (PDECO) problems. However, existing methods are insufficient to handle those PDE…

Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by…

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…

In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…

We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

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…