Related papers: Discretize first, filter next: learning divergence…
In this paper we propose a strategy to approximate incompressible hydrostatic free surface Euler and Navier-Stokes models. The main advantage of the proposed models is that the water depth is a dynamical variable of the system and hence the…
We examine and benchmark the emerging idea of applying the large-eddy simulation (LES) formalism to unconventionally coarse grids where RANS would be considered more appropriate at first glance. We distinguish this idea from…
A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier-Stokes equations in three-dimensional domains. This scheme, based on an incremental pressure projection method, decouples each component of…
Deep neural networks (DNNs) have been shown to over-fit a dataset when being trained with noisy labels for a long enough time. To overcome this problem, we present a simple and effective method self-ensemble label filtering (SELF) to…
The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations --…
We study a finite-element based space-time discretisation for the 2D stochastic Navier-Stokes equations in a bounded domain supplemented with no-slip boundary conditions. We prove optimal convergence rates in the energy norm with respect to…
Numerous models for supervised and reinforcement learning benefit from combinations of discrete and continuous model components. End-to-end learnable discrete-continuous models are compositional, tend to generalize better, and are more…
Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
This paper focuses on investigating the learning operators for identifying weak solutions to the Navier-Stokes equations. Our objective is to establish a connection between the initial data as input and the weak solution as output. To…
Deep neural networks (DNNs) have significantly advanced machine learning, with model depth playing a central role in their successes. The dynamical system modeling approach has recently emerged as a powerful framework, offering new…
Consider the transient incompressible Navier-Stokes flow at high Reynolds numbers. A high-order H(div)-conforming FEM with pointwise divergence-free dis- crete velocities is applied to implicit large-eddy-simulation in two limit cases: i)…
Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The…
We present a structure-preserving Eulerian algorithm for solving $L^2$-gradient flows and a structure-preserving Lagrangian algorithm for solving generalized diffusions. Both algorithms employ neural networks as tools for spatial…
Large-eddy simulations of incompressible Newtonian fluid flows with approximate deconvolution models based on the van Cittert method are reported. The Legendre spectral element method is used for the spatial discretization to solve the…
We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…
Many simulated complex systems that support persistent self-organizing patterns, i.e. gliders, have a 'state-plus-update' paradigm. This approach can be found in computational models of physics, continuous and neural cellular automata,…
Generalization of deep neural networks remains one of the main open problems in machine learning. Previous theoretical works focused on deriving tight bounds of model complexity, while empirical works revealed that neural networks exhibit…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
Deep neural networks struggle to continually learn multiple sequential tasks due to catastrophic forgetting of previously learned tasks. Rehearsal-based methods which explicitly store previous task samples in the buffer and interleave them…
In speech deepfake detection, one of the critical aspects is developing detectors able to generalize on unseen data and distinguish fake signals across different datasets. Common approaches to this challenge involve incorporating diverse…