Related papers: Physics-integrated machine learning: embedding a n…

Fluid mechanics is a fundamental field in engineering and science. Solving the Navier-Stokes equation (NSE) is critical for understanding the behavior of fluids. However, the NSE is a complex partial differential equation that is difficult…

The integral equation approach to partial differential equations (PDEs) provides significant advantages in the numerical solution of the incompressible Navier-Stokes equations. In particular, the divergence-free condition and boundary…

Turbulence is ubiquitous in engineering and science, yet direct simulation is prohibitively expensive. The Reynolds-averaged Navier-Stokes (RANS) equations provide savings exceeding ten orders of magnitude but introduce unclosed terms (the…

Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…

Over the last few decades, existing Partial Differential Equation (PDE) solvers have demonstrated a tremendous success in solving complex, non-linear PDEs. Although accurate, these PDE solvers are computationally costly. With the advances…

Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs) by directly embedding them into the loss function. Despite their notable success, existing PINNs often exhibit training…

The predictive accuracy of the Navier-Stokes equations is known to degrade at the limits of the continuum assumption, thereby necessitating expensive and often highly approximate solutions to the Boltzmann equation. While tractable in one…

One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…

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,…

Deep learning paradigms, such as PINNs and neural operators, have significantly advanced the solving of PDEs. However, they often struggle to capture the continuous integral nature of physical systems, relying either on pointwise residuals…

This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier-Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize…

Meshfree particle methods, such as Smoothed Particle Hydrodynamics (SPH) and the Moving Particle Semi-Implicit (MPS) method, are widely used to simulate complex free-surface and multiphase flows. A key challenge in these methods is the…

We introduce \emph{Dynamical Physics-Modeled Neural Networks} (DynPMNNs), a continuous-time deep learning architecture in which each hidden layer is defined as the solution of an ordinary differential equation. Unlike classical feed-forward…

Physics-Informed Neural Networks have emerged as a promising methodology for solving PDEs, gaining significant attention in computer science and various physics-related fields. Despite being demonstrated the ability to incorporate the…

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…

We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for…

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…

Physics-informed neural networks (PINNs) provide a mesh-free framework for solving partial differential equations by embedding governing physics into neural-network training. Recent studies have shown that parameterized PINNs can learn…

We present a machine learning-based framework for blending data-driven turbulent closures in the Reynolds-Averaged Navier-Stokes (RANS) equations, aimed at improving their generalizability across diverse flow regimes. Specialized models…

This work aims to incorporate basic calibrations of Reynolds-averaged Navier-Stokes (RANS) models as part of machine learning (ML) frameworks. The ML frameworks considered are tensor-basis neural network (TBNN), physics-informed machine…