Related papers: Numerical Stability of the Nystr\"om Method
A time discretization method is called strongly stable, if the norm of its numerical solution is nonincreasing. It is known that, even for linear semi-negative problems, many explicit Runge--Kutta (RK) methods fail to preserve this…
Using vanilla NeuralODEs to model large and/or complex systems often fails due two reasons: Stability and convergence. NeuralODEs are capable of describing stable as well as instable dynamic systems. Selecting an appropriate numerical…
Neural networks (NNs) can achieved high performance in various fields such as computer vision, and natural language processing. However, deploying NNs in resource-constrained safety-critical systems has challenges due to uncertainty in the…
A scheme for stabilizing stochastic approximation iterates by adaptively scaling the step sizes is proposed and analyzed. This scheme leads to the same limiting differential equation as the original scheme and therefore has the same…
This paper addresses the problem of estimating the positions of points from distance measurements corrupted by sparse outliers. Specifically, we consider a setting with two types of nodes: anchor nodes, for which exact distances to each…
A method for enhancing the stability and robustness of explicit schemes in computational fluid dynamics is presented. The method is based in reformulating explicit schemes in matrix form, which cane modified gradually into semi or…
The shock instability problem commonly arises in flow simulations involving strong shocks, particularly when employing high-order schemes, limiting their applications in hypersonic flow simulations. This study focuses on exploring the…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
The increased integration of intermittent and decentralised forms of power production has eroded the stability margins of power grids and made it more challenging to ensure reliable and secure power transmission. Reliable grid operation…
STOchastic Recursive Momentum (STORM)-based algorithms have been widely developed to solve one to $K$-level ($K \geq 3$) stochastic optimization problems. Specifically, they use estimators to mitigate the biased gradient issue and achieve…
Stably inverting a dynamic system model is the foundation of numerous servo designs. Existing inversion techniques have provided accurate model approximations that are often highly effective in feedforward controls. However, when the…
In the first part of this work, we develop a novel scheme for solving nonparametric regression problems. That is the approximation of possibly low regular and noised functions from the knowledge of their approximate values given at some…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
When the target of statistical inference is chosen in a data-driven manner, the guarantees provided by classical theories vanish. We propose a solution to the problem of inference after selection by building on the framework of algorithmic…
The Brunovsky canonical form provides sparse structural representations that are beneficial for computational optimal control, yet existing methods fail to compute it reliably. We propose a technique that produces Brunovsky transformations…
In this paper, we explore the stability of an inverted pendulum under a generalized parametric excitation described by a superposition of $N$ cosines with different amplitudes and frequencies, based on a simple stability condition that does…
We develop a Nitsche-based formulation for a general class of stabilized finite element methods for the Stokes problem posed on a pair of overlapping, non-matching meshes. By ex- tending the least-squares stabilization to the overlap…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
Low-order virtual element methods (VEM) compute a consistent finite-strain contribution through polynomial projections and rely on stabilization to control the unresolved modes in the projector kernel. In current hyperelastic VEM practice,…