Related papers: Hybrid quantum physics-informed neural networks fo…

Computing dynamical distributions in quantum many-body systems represents one of the paradigmatic open problems in theoretical condensed matter physics. Despite the existence of different techniques both in real-time and frequency space,…

A novel hybrid deep neural network architecture is designed to capture the spatial-temporal features of unsteady flows around moving boundaries directly from high-dimensional unsteady flow fields data. The hybrid deep neural network is…

Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…

Accurately predicting fluid dynamics and evolution has been a long-standing challenge in physical sciences. Conventional deep learning methods often rely on the nonlinear modeling capabilities of neural networks to establish mappings…

In this paper we introduce a novel Neural Networks-based approach for approximating solutions to the (2D) incompressible Navier--Stokes equations, which is an extension of so called Deep Random Vortex Methods (DRVM), that does not require…

Kinetic approaches, i.e., methods based on the lattice Boltzmann equations, have long been recognized as an appealing alternative for solving incompressible Navier-Stokes equations in computational fluid dynamics. However, such approaches…

Despite the significant breakthrough of neural networks in the last few years, their spreading in the field of computational fluid dynamics is very recent, and many applications remain to explore. In this paper, we explore the drag…

The steady incompressible Navier--Stokes equations pose significant computational challenges due to their nonlinear convective terms and pressure--velocity coupling. Physics-informed neural networks (PINNs) provide a mesh-free framework for…

Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our…

The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…

In this work, we detail the GPU-porting of an in-house pseudo-spectral solver tailored towards large-scale simulations of interface-resolved simulation of drop- and bubble-laden turbulent flows. The code relies on direct numerical…

Modeling of fluid flows requires corresponding adequate and effective approaches that would account for multiscale nature of the considered physics. Despite the tremendous growth of computational power in the past decades, modeling of fluid…

Estimating the geometric and volumetric properties of transparent deformable liquids is challenging due to optical complexities and dynamic surface deformations induced by container movements. Autonomous robots performing precise liquid…

The permeability of complex porous materials can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as…

Achievement of solutions in Navier-Stokes equation is one of challenging quests, especially for its closure problem. For achievement of particular solutions, there are variety of numerical simulations including Direct Numerical Simulation…

This paper presents an innovative framework for analyzing the regularity of solutions to the stochastic Navier-Stokes equations by integrating Sobolev-Besov hybrid spaces with fractional operators and quantum-inspired dynamics. We propose…

Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…

Physics-informed neural networks have emerged as a coherent framework for building predictive models that combine statistical patterns with domain knowledge. The underlying notion is to enrich the optimization loss function with known…

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…

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…