Related papers: On the stability of robust dynamical low-rank appr…
The robustness of dynamical systems against external perturbations is crucial in engineering; however, it is often overlooked for the lack of methods for rapidly computing it. This paper proposes a novel algorithm for estimating the…
In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant.…
In this work, we design and analyze a Discrete de Rham (DDR) scheme for a contact mechanics problem involving fractures along which a model of Tresca friction is considered. Our approach is based on a mixed formulation involving a…
We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…
This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time"…
An efficient technique based on low-rank separated approximations is proposed for computation of three-dimensional integrals arising in the energy deposition model that describes ion-atomic collisions. Direct tensor-product quadrature…
Electrical grids are now much more complex due to the rapid integration of distributed generation and alternative energy sources, which makes forecasting grid stability with optimized control a crucial task for operators. Traditional…
We consider a phase-field fracture propagation model, which consists of two (nonlinear) coupled partial differential equations. The first equation describes the displacement evolution, and the second is a smoothed indicator variable,…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
The Intelligent Driver Model is studied and several drawbacks with respect to driving simulators are defined. We present two modifications of the IDM. The first one gives any predefined distance to the leading vehicle in a steady state. The…
The primary challenge in solving kinetic equations, such as the Vlasov equation, is the high-dimensional phase space. In this context, dynamical low-rank approximations have emerged as a promising way to reduce the high computational cost…
In this paper, discrete linear quadratic regulator (DLQR) and iterative linear quadratic regulator (ILQR) methods based on high-order Runge-Kutta (RK) discretization are proposed for solving linear and nonlinear quadratic optimal control…
Low-rank inducing unitarily invariant norms have been introduced to convexify problems with low-rank/sparsity constraint. They are the convex envelope of a unitary invariant norm and the indicator function of an upper bounding rank…
Multibody dynamics simulators are an important tool in many fields, including learning and control for robotics. However, many existing dynamics simulators suffer from inaccuracies when dealing with constrained mechanical systems due to…
From serving a cup of coffee to positioning mechanical parts during assembly, stable object placement is a crucial skill for future robots. It becomes particularly challenging under geometric uncertainties, e.g., when the object pose or…
This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously adapt low-rank weights in time to rapidly predict the…
In this work, we introduce a novel low-rank structure tailored for solving the inverse scattering problem. The particular low-rank structure is given by the generalized prolate spheroidal wave functions, computed stably and accurately via a…
This paper investigates the tilt stability of local minimizers for nonlinear programs under the relaxed constant rank constraint qualification in finite dimensions. By employing a neighborhood primal-dual approach and extending calculus…
In a previous work we developed a convex infinite dimensional linear programming (LP) approach to approximating the region of attraction (ROA) of polynomial dynamical systems subject to compact basic semialgebraic state constraints. Finite…
Traveltime tomography is a very effective tool to reconstruct acoustic, seismic or electromagnetic wave speed distribution. To infer the velocity image of the medium from the measurements of first arrivals is a typical example of ill-posed…