相关论文: Curriculum Learning-Driven PIELMs for Fluid Flow S…

Active flow control remains a significant challenge due to the high-dimensional, nonlinear nature of fluid dynamics. Quantum machine learning may prove effective in addressing these issues, given that quantum computing possesses superiority…

Recent works have explored the potential of machine learning as data-driven turbulence closures for RANS and LES techniques. Beyond these advances, the high expressivity and agility of physics-informed neural networks (PINNs) make them…

In this paper, we propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs). From a perspective of physical simulation, we redefine the problem of approximating the gradient flow utilizing…

Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete…

In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…

Physics-Informed Neural Networks (PINNs) have emerged as a promising machine learning approach for solving partial differential equations (PDEs). However, PINNs face significant challenges in balancing multi-objective losses, as multiple…

Despite their ubiquity throughout science and engineering, only a handful of partial differential equations (PDEs) have analytical, or closed-form solutions. This motivates a vast amount of classical work on numerical simulation of PDEs and…

In recent years, there have been a surge in applications of neural networks (NNs) in physical sciences. Although various algorithmic advances have been proposed, there are, thus far, limited number of studies that assess the…

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…

We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud based neural network to capture…

Compressible flow problems are characterized by highly nonlinear, implicit, and often transcendental governing equations. In undergraduate gas dynamics education, solving these equations traditionally relies on iterative numerical methods…

Physics-informed machine learning (PIML) is emerging as a potentially transformative paradigm for modeling complex biomedical systems by integrating parameterized physical laws with data-driven methods. Here, we review three main classes of…

The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the…

Deriving governing equations of complex physical systems based on first principles can be quite challenging when there are certain unknown terms and hidden physical mechanisms in the systems. In this work, we apply a deep learning…

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…

Fluid dynamics computations for tube-like geometries are important for biomedical evaluation of vascular and airway fluid dynamics. Physics-Informed Neural Networks (PINNs) have recently emerged as a good alternative to traditional…

Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively…

A primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs). This paper aims…

We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…

Vortex flows are ubiquitous in both natural processes and engineering applications, including phenomena such as typhoons, water currents, and aerospace fluid dynamics. The vortex particle method, a computational approach grounded in vortex…