Related papers: A Local Macroscopic Conservative (LoMaC) low rank …
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
The Vlasov-Fokker-Planck equation describes the evolution of the probability density of the position and velocity of particles under the influence of external confinement, interaction, friction, and stochastic force. It is well-known that…
This paper explores Tadmor's minimum entropy principle for the relativistic hydrodynamics (RHD) equations and incorporates this principle into the design of robust high-order discontinuous Galerkin (DG) and finite volume schemes for RHD on…
Recovery of low-rank matrices from a small number of linear measurements is now well-known to be possible under various model assumptions on the measurements. Such results demonstrate robustness and are backed with provable theoretical…
The low-rank tensor completion (LRTC) problem aims to reconstruct a tensor from partial sample information, which has attracted significant interest in a wide range of practical applications such as image processing and computer vision.…
The low-variance direct simulation Monte Carlo (LVDSMC) is a powerful method to simulate low-speed rarefied gas flows. However, in the near-continuum flow regime, due to limitations on the time step and spatial cell size, it takes plenty of…
We propose a novel reformulation of the Vlasov-Amp{\`e}re equations for plasmas. This reformulation exposes discrete symmetries to achieve simultaneous conservation of mass, momentum, and energy; preservation of Gauss's law involution;…
This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…
Consider the Vlasov-Poisson-Landau system with Coulomb potential in the weakly collisional regime on a $3$-torus, i.e. $$\begin{aligned} \partial_t F(t,x,v) + v_i \partial_{x_i} F(t,x,v) + E_i(t,x) \partial_{v_i} F(t,x,v) = \nu…
We introduce a `virtual-move' Monte Carlo (VMMC) algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an…
We extend the recently-developed explicit, energy-conserving particle-in-cell (PIC) scheme of [1] to the relativistic Vlasov-Maxwell system. As in the non-relativistic case, the method is built on an optimization problem that is…
A novel Lattice Boltzmann Method applicable to compressible fluid flows is developed. This method is based on replacing the governing equations by a relaxation system and the interpretation of the diagonal form of the relaxation system as a…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
Efficient fine-tuning plays a fundamental role in modern large models, with low-rank adaptation emerging as a particularly promising approach. However, the existing variants of LoRA are hampered by limited expressiveness, a tendency to…
We present a windowed technique to learn parsimonious time-varying autoregressive models from multivariate timeseries. This unsupervised method uncovers interpretable spatiotemporal structure in data via non-smooth and non-convex…
With increasing size of large language models (LLMs), full-parameter fine-tuning imposes substantial memory demands. To alleviate this, we propose a novel memory-efficient training paradigm called Momentum Low-rank compression (MLorc). The…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…
This paper studies the Vlasov-Monge-Ampere system (VMA), a fully non-linear version of the Vlasov-Poisson system (VP) where the (real) Monge-Ampere equation substitutes for the usual Poisson equation. This system can be derived as a…
We introduce a novel, model-independent method for the efficient simulation of low-entropy systems, whose dynamics can be accurately described with a limited number of states. Our method leverages the time-dependent variational principle to…