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Reservoir computing is applied to model the large-scale evolution and the resulting low-order turbulence statistics of a two-dimensional turbulent Rayleigh-B\'{e}nard convection flow at a Rayleigh number ${\rm Ra}=10^7$ and a Prandtl number…
In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature. Existing solver-based acceleration methods often face significant image quality…
We are interested in the numerical solution of large systems of hyperbolic conservation laws or systems in which the characteristic decomposition is expensive to compute. Solving such equations using finite volumes or Discontinuous Galerkin…
Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine…
In reservoir simulation, solution of the coupled systems of nonlinear algebraic equations that are associated with fully-implicit (backward Euler) discretization is challenging. Having a robust and efficient nonlinear solver is necessary in…
This paper addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multitasking. First, an approximating reservoir model is presented…
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…
In computational fluid dynamics, there is an inevitable trade off between accuracy and computational cost. In this work, a novel multi-fidelity deep generative model is introduced for the surrogate modeling of high-fidelity turbulent flow…
We present an efficient solver for massively-parallel direct numerical simulations of incompressible turbulent flows. The method uses a second-order, finite-volume pressure-correction scheme, where the pressure Poisson equation is solved…
Topology optimization problems usually feature multiple local minimizers. To guarantee convergence to local minimizers that perform best globally or to find local solutions that are desirable for practical applications due to easy…
The paper presents a strategy to construct an incremental Singular Value Decomposition (SVD) for time-evolving, spatially 3D discrete data sets. A low memory access procedure for reducing and deploying the snapshot data is presented.…
In this paper, we observe an interesting phenomenon for a hybridizable discontinuous Galerkin (HDG) method for eigenvalue problems. Specifically, using the same finite element method, we may achieve both upper and lower eigenvalue bounds…
Reservoir computing (RC) is attracting attention as a machine-learning technique for edge computing. In time-series classification tasks, the number of features obtained using a reservoir depends on the length of the input series.…
The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant…
A multi-scale framework was recently proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent, where we…
Hydrodynamical simulations are the most accurate way to model structure formation in the universe, but they often involve a large number of astrophysical parameters modeling subgrid physics, in addition to cosmological parameters. This…
In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…