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Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

Despite their ubiquity, the rich physics present in a plasma sheath has inhibited the development of a generally applicable description of this critical region. The present study utilizes a physics-informed neural network (PINN) to evaluate…

Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral…

In this paper, Physics Informed Neural Network (PINN) is explored in order to obtain flow predictions near the wall region accurately with measurements (or sampling points) away from the wall. Often, in fluid mechanics experiments, it is…

Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren…

Though PINNs (physics-informed neural networks) are now deemed as a complement to traditional CFD (computational fluid dynamics) solvers rather than a replacement, their ability to solve the Navier-Stokes equations without given data is…

Fluid flows are governed by the nonlinear Navier-Stokes equations, which can manifest multiscale dynamics even from predictable initial conditions. Predicting such phenomena remains a formidable challenge in scientific machine learning,…

Physics-informed neural networks (PINNs), owing to their mesh-free nature, offer a powerful approach for solving high-dimensional partial differential equations (PDEs) in complex geometries, including irregular domains. This capability…

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…

Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier-Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms,…

Physics-Informed Neural Networks (PINNs) offer a powerful paradigm for flow reconstruction, seamlessly integrating sparse velocity measurements with the governing Navier-Stokes equations to recover complete velocity and latent pressure…

Presently, there is a steady state approach in Computational fluid dynamics (CFD) to obtain a steady solution directly from the steady state governing equations. Whereas, for obtaining a time-periodic flow solution, the present unsteady…

We report a new approach to flow field tomography that uses the Navier-Stokes and advection-diffusion equations to regularize reconstructions. Tomography is increasingly employed to infer 2D or 3D fluid flow and combustion structures from a…

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) have recently emerged as a promising alternative for extracting unknown quantities from experimental data. Despite this potential, much of the recent literature has relied on sparse, high-fidelity…

Neural surrogates and operator networks for solving partial differential equation (PDE) problems have attracted significant research interest in recent years. However, most existing approaches are limited in their ability to generalize…

We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than…

In aerodynamic design, the use of Computational Fluid Dynamics (CFD) tools has long relied on Reynolds-Averaged Navier-Stokes (RANS) and Unsteady RANS (URANS) turbulence models. However, these methods face limitations in predicting…

Advancements in computational fluid mechanics have largely relied on Newtonian frameworks, particularly through the direct simulation of Navier-Stokes equations. In this work, we propose an alternative computational framework that employs…

Artificial intelligence has revolutionized optical device design, overcoming the efficiency bottlenecks of traditional methods. For holographic metasurfaces, conventional iterative algorithms suffer from time-consuming iterations and…