Related papers: Sparse Grids based Adaptive Noise Reduction strate…
In this paper, we propose a novel normalized subband adaptive filter algorithm suited for sparse scenarios, which combines the proportionate and sparsity-aware mechanisms. The proposed algorithm is derived based on the proximal…
Due to the high computational load of modern numerical simulation, there is a demand for approaches that would reduce the size of discrete problems while keeping the accuracy reasonable. In this work, we present an original algorithm to…
Quantifying uncertainty in predictive simulations for real-world problems is of paramount importance - and far from trivial, mainly due to the large number of stochastic parameters and significant computational requirements. Adaptive sparse…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
Modeling multi-scale collisionless magnetized processes constitutes an important numerical challenge. By treating electrons as a fluid and ions kinetically, the so-called hybrid Particle-In-Cell (PIC) codes represent a promising…
We give algorithms for designing near-optimal sparse controllers using policy gradient with applications to control of systems corrupted by multiplicative noise, which is increasingly important in emerging complex dynamical networks.…
The particle-in-cell (PIC) method is a well-established and widely used kinetic plasma modelling approach that provides a hybrid Lagrangian-Eulerian approach to solve the plasma kinetic equation. Despite its power in capturing details of…
First-principles particle-in-cell (PIC) simulation is a powerful tool for understanding plasma behavior, but this power often comes at great computational expense. Artificially reducing the ion/electron mass ratio is a time-honored practice…
Particle-in-cell (PIC) simulations are essential for studying kinetic plasma processes, but they often suffer from statistical noise, especially in plasmas with fast flows. We have also found that the typical central difference scheme used…
In this paper, we propose a sparsity-promoting feedback control design for stochastic linear systems with multiplicative noise. The objective is to identify a sparse control architecture that optimizes the closed-loop performance while…
Sparse grids based on Lagrange polynomials have become one of the staple methods for approximating functions that are high-dimensional and expensive to evaluate, in the context e.g. of PDE-based parametric design exploration. They are…
Modeling inviscid compressible flows with shocks and vortex dominated dynamics remains challenging for particle grid methods due to moving discontinuities, cell crossing noise, and quadrature degradation under strong deformation. Building…
The sparse pseudo-input Gaussian process (SPGP) is a new approximation method for speeding up GP regression in the case of a large number of data points N. The approximation is controlled by the gradient optimization of a small set of M…
Classical simulation of many-body quantum systems remains economical only when wavefunction amplitudes stay localized in the working basis. Fixed-basis sparse-state simulators scale memory as $\mathcal{O}(k)$ by keeping the largest…
High-dimensional interpolation problems appear in various applications of uncertainty quantification, stochastic optimization and machine learning. Such problems are computationally expensive and request the use of adaptive grid generation…
We propose a sparse grid stochastic collocation method for long-time simulations of stochastic differential equations (SDEs) driven by white noise. The method uses pre-determined sparse quadrature rules for the forcing term and constructs…
A novel adaptive technique for electromagnetic Particle In Cell (PIC) plasma simulations is presented here. Two main issues are identified in designing adaptive techniques for PIC simulation: first, the choice of the size of the particle…
Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
An electrostatic, implicit particle-in-cell (PIC) model for collisionless, fully magnetized, paraxial plasma expansions in a magnetic nozzle is introduced with exact charge, energy, and magnetic moment conservation properties. The approach…