Related papers: An Efficient Wavelet-based Physics Informed Residu…
Reconstruction of fine-scale information from sparse data is relevant to many practical fluid dynamic applications where the sensing is typically sparse. Fluid flows in an ideal sense are manifestations of nonlinear multiscale PDE dynamical…
Mesh generation is essential for accurate and efficient computational fluid dynamics simulations. To resolve critical features in the flow, adaptive mesh refinement (AMR) is routinely employed in certain regions of the computational domain,…
We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…
Physics-informed neural networks (PINNs) effectively embed physical principles into machine learning, but often struggle with complex or alternating geometries. We propose a novel method for integrating geometric transformations within…
In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology,…
In this study, we employ physics-informed neural networks (PINNs) to solve forward and inverse problems via the Boltzmann-BGK formulation (PINN-BGK), enabling PINNs to model flows in both the continuum and rarefied regimes. In particular,…
The block-based coding structure in the hybrid video coding framework inevitably introduces compression artifacts such as blocking, ringing, etc. To compensate for those artifacts, extensive filtering techniques were proposed in the loop of…
Solving the two-dimensional shallow water equations is a fundamental problem in flood simulation technology. In recent years, physics-informed neural networks (PINNs) have emerged as a novel methodology for addressing this problem. Given…
Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…
Physics-informed Neural Network (PINN) faces significant challenges when approximating solutions to conservation laws, particularly in ensuring conservation and accurately resolving discontinuities. To address these limitations, we propose…
The computation of the seismic wavefield by solving the Helmholtz equation is crucial to many practical applications, e.g., full waveform inversion. Physics-informed neural networks (PINNs) provide functional wavefield solutions represented…
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…
This study benchmarks hybrid quantum physics-informed neural network (HQPINN) to model high-speed flows, compared against classical physics-informed neural networks (PINNs) and fully quantum neural networks (QNNs). The HQPINN architecture…
We leverage Physics-Informed Neural Networks (PINNs) to learn solution functions of parametric Navier-Stokes Equations (NSE). Our proposed approach results in a feasible optimization problem setup that bypasses PINNs' limitations in…
This paper employs physics-informed neural networks (PINNs) to solve Fisher's equation, a fundamental reaction-diffusion system with both simplicity and significance. The focus is on investigating Fisher's equation under conditions of large…
Physics-informed neural networks (PINNs) are employed to solve the classical compressible flow problem in a converging-diverging nozzle. This problem represents a typical example described by the Euler equations, thorough understanding of…
Physics-informed neural network (PINN) is a powerful emerging method for studying forward-inverse problems of partial differential equations (PDEs), even from limited sample data. Variable coefficient PDEs, which model real-world phenomena,…
We study the convergence of gradient flow for the training of deep neural networks. If Residual Neural Networks are a popular example of very deep architectures, their training constitutes a challenging optimization problem due notably to…
In this article, we propose a novel Stabilized Physics Informed Neural Networks method (SPINNs) for solving wave equations. In general, this method not only demonstrates theoretical convergence but also exhibits higher efficiency compared…
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,…