Related papers: Structure Preservation for the Deep Neural Network…
We derive a new margin-based regularization formulation, termed multi-margin regularization (MMR), for deep neural networks (DNNs). The MMR is inspired by principles that were applied in margin analysis of shallow linear classifiers, e.g.,…
Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…
Information loss in numerical physics simulations can arise from various sources when solving discretized partial differential equations. In particular, errors related to numerical precision ("sub-precision errors") can accumulate in the…
Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Yet despite their efficiency, computations remain expensive…
We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent…
Within the domain of Computational Fluid Dynamics, Direct Numerical Simulation (DNS) is used to obtain highly accurate numerical solutions for fluid flows. However, this approach for numerically solving the Navier-Stokes equations is…
Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
Computational Fluid Dynamics (CFD) simulation by the numerical solution of the Navier-Stokes equations is an essential tool in a wide range of applications from engineering design to climate modeling. However, the computational cost and…
We propose a deep neural network (DNN) based least distance (LD) estimator (DNN-LD) for a multivariate regression problem, addressing the limitations of the conventional methods. Due to the flexibility of a DNN structure, both linear and…
Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational…
Discrete dislocation dynamics (DDD) is a widely employed computational method to study plasticity at the mesoscale that connects the motion of dislocation lines to the macroscopic response of crystalline materials. However, the…
Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and…
In this paper we present a numerical approach to solve the Navier-Stokes equations on moving domains with second-order accuracy. The space discretization is based on the ghost-point method, which falls under the category of unfitted…
Semi-Lagrangian (SL) schemes are highly efficient for simulating transport equations and are widely used across various applications. Despite their success, designing genuinely multi-dimensional and conservative SL schemes remains a…
In component shape optimization, the component properties are often evaluated by computationally expensive simulations. Such optimization becomes unfeasible when it is focused on a global search requiring thousands of simulations to be…
The ubiquity of fluids in the physical world explains the need to accurately simulate their dynamics for many scientific and engineering applications. Traditionally, well established but resource intensive CFD solvers provide such…
Adjoint-based optimization methods are attractive for aerodynamic shape design primarily due to their computational costs being independent of the dimensionality of the input space and their ability to generate high-fidelity gradients that…
In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…