Related papers: Accelerating Multiscale Simulation of Complex Geom…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
The Position Based Fluids (PBF) method is a state-of-the-art approach for fluid simulations in the context of real-time applications like games. It uses an iterative solver concept that tries to maintain a constant fluid density…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…
High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…
We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a…
Achieving strongly symmetric stress approximations for linear elasticity problems in high-contrast media poses a significant computational challenge. Conventional methods often struggle with prohibitively high computational costs due to…
We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…
Following the seminal work of Nesterov, accelerated optimization methods have been used to powerfully boost the performance of first-order, gradient-based parameter estimation in scenarios where second-order optimization strategies are…
Molecular simulations of the forced unfolding and refolding of biomolecules or molecular complexes allow to gain important kinetic, structural and thermodynamic information about the folding process and the underlying energy landscape. In…
Accurately and efficiently estimating system performance under uncertainty is paramount in power system planning and operation. Monte Carlo simulation is often used for this purpose, but convergence may be slow, especially when detailed…
Quantifying uncertainties in physical or engineering systems often requires a large number of simulations of the underlying computer models that are computationally intensive. Emulators or surrogate models are often used to accelerate the…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
An overview is given over the recently developed and now widely used Monte Carlo algorithms with reduced or eliminated critical slowing down. The basic techniques are overrelaxation, cluster algorithms and multigrid methods. With these…
As a key component of power system production simulation, load forecasting is critical for the stable operation of power systems. Machine learning methods prevail in this field. However, the limited training data can be a challenge. This…
Model-based iterative reconstruction plays a key role in solving inverse problems. However, the associated minimization problems are generally large-scale, nonsmooth, and sometimes even nonconvex, which present challenges in designing…
Machine learning-based weather forecasting models now surpass state-of-the-art numerical weather prediction systems, but training and operating these models at high spatial resolution remains computationally expensive. We present a modular…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
In this paper, we present a multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…
This work develops a multivariate extension of the Fixed Rank Kriging (FRK) framework for spatial prediction in settings where multiple spatial processes may provide complementary information. The goal is to preserve the computational…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…