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The study deals with the parallelization of 2D and 3D finite element based Navier-Stokes codes using direct solvers. Development of sparse direct solvers using multifrontal solvers has significantly reduced the computational time of direct…

This work presents a deep learning-based framework for the solution of partial differential equations on complex computational domains described with computer-aided design tools. To account for the underlying distribution of the training…

Geometrically parametrized Partial Differential Equations are nowadays widely used in many different fields as, for example, shape optimization processes or patient specific surgery studies. The focus of this work is on some advances for…

The incompressible magnetohydrodynamic (MHD) equations are fundamental in many scientific and engineering applications. However, their strong nonlinearity and dual divergence-free constraints make them highly challenging for conventional…

In this paper a new high order semi-implicit discontinuous Galerkin method (SI-DG) is presented for the solution of the incompressible Navier-Stokes equations on staggered space-time adaptive Cartesian grids (AMR) in two and three…

Conventional fluid simulations can be time consuming and energy intensive. We researched the viability of a neural network for simulating incompressible fluids in a randomized obstacle-heavy environment, as an alternative to the numerical…

In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital (AD) beamforming can be used to attain a high directional gain without requiring a dedicated radio frequency (RF) chain for each antenna element, which…

Numerical simulators are essential tools in the study of natural fluid-systems, but their performance often limits application in practice. Recent machine-learning approaches have demonstrated their ability to accelerate spatio-temporal…

High-order accurate discontinuous Galerkin (DG) methods have emerged as powerful tools for solving partial differential equations such as the compressible Navier-Stokes equations due to their excellent dispersion-dissipation properties and…

Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…

Meshfree solution schemes for the incompressible Navier--Stokes equations are usually based on algorithms commonly used in finite volume methods, such as projection methods, SIMPLE and PISO algorithms. However, drawbacks of these algorithms…

In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…

Natural gradient descent (NGD) provided deep insights and powerful tools to deep neural networks. However the computation of Fisher information matrix becomes more and more difficult as the network structure turns large and complex. This…

In this work we prove that weak solutions constructed by a variational multiscale method are suitable in the sense of Scheffer. In order to prove this result, we consider a subgrid model that enforces orthogonality between subgrid and…

Neural networks have been used to solve different types of large data related problems in many different fields.This project takes a novel approach to solving the Navier-Stokes Equations for turbulence by training a neural network using…

Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…

The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary…

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…

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer…

This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…