Related papers: PINNs Algorithmic Framework for Simulation of Nonl…

Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…

High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete…

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches…

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…

Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM…

Physics-informed neural networks (PINNs) offer a novel AI-driven framework for integrating physical laws directly into neural network models, facilitating the solution of complex multiphysics problems in materials engineering. This study…

Accurately and efficiently solving nonlinear differential equations is crucial for modeling dynamic behavior across science and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful solution that embeds physical…

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 recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique…

Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in…

Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to…

Physics-informed neural networks (PINNs) have recently emerged as a promising way to compute the solutions of partial differential equations (PDEs) using deep neural networks. However, despite their significant success in various fields, it…

Solving time-dependent Partial Differential Equations (PDEs) is one of the most critical problems in computational science. While Physics-Informed Neural Networks (PINNs) offer a promising framework for approximating PDE solutions, their…

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving inverse problems, especially in cases where no complete information about the system is known and scatter measurements are available. This is especially…

Physics-Informed Neural Networks (PINNs) have recently emerged as a promising alternative for solving partial differential equations, offering a mesh-free framework that incorporates physical laws directly into the learning process. In this…

We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical…

Physics-Informed Neural Networks (PINNs) have been recognized as a mesh-free alternative to solve partial differential equations where physics information is incorporated. However, in dealing with problems characterized by high stiffness or…

Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…

We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data. Unlike existing Bayesian PINN…