Related papers: Improving the accuracy of the Newmark method throu…
Precision matrix estimation is a fundamental topic in multivariate statistics and modern machine learning. This paper proposes an adversarially perturbed precision matrix estimation framework, motivated by recent developments in adversarial…
Backward error (BE) analysis emerges as a powerful tool for assessing the backward stability and strong backward stability of numerical algorithms. In this paper, we explore structured BEs for a class of double saddle point problems…
The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an optimal rate convergence analysis and error estimate for finite…
Explicit time-marching schemes are popular for solving time-dependent partial differential equations; one of the biggest challenges these methods suffer is increasing the critical time-marching step size that guarantees numerical stability.…
This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…
This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. The proposed methods are based on a specific subset of explicit one-step…
An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (a…
This paper addresses the problem of state and parameter estimation for a class of second-order systems with single output. A new filtered transformation is proposed for the system via dynamic vector and matrix. In this method, the dynamics…
Advanced optimization algorithms such as Newton method and AdaGrad benefit from second order derivative or second order statistics to achieve better descent directions and faster convergence rates. At their heart, such algorithms need to…
The backpropagation algorithm for calculating gradients has been widely used in computation of weights for deep neural networks (DNNs). This method requires derivatives of objective functions and has some difficulties finding appropriate…
This paper investigates a time-stepping procedure of the Newmark type for dynamic analyses of viscoelastic structures characterized by a generalized Maxwell model. We depart from a scheme developed for a three-parameter model by Hatada et…
In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional $\theta$-scheme, we reduce truncation errors by taking $\theta$ carefully for every subinterval…
Optimization techniques play a crucial role in estimating parameters and state information for nonlinear systems. However, some critical aspects of these problems have received little attention in previous research. In this paper, we…
We propose a cheaper version of \textit{a posteriori} error estimator from arXiv:1707.00057 for the linear second-order wave equation discretized by the Newmark scheme in time and by the finite element method in space. The new estimator…
The stability of integrators dealing with high order Differential Algebraic Equations (DAEs) is a major issue. The usual procedures give rise to instabilities that are not predicted by the usual linear analysis, rendering the common checks…
A neural networks (NN) compensator is designed for systems with multi-segment piecewise-linear nonlinearities. The compensator uses the back stepping technique with NN for inverting the multi-segment piecewise-linear nonlinearities in the…
We study the numerical anisotropy existent in compact difference schemes as applied to hyperbolic partial differential equations, and propose an approach to reduce this error and to improve the stability restrictions based on a previous…
We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…
We investigate the stochastic modified equation which plays an important role in the stochastic backward error analysis for explaining the mathematical mechanism of a numerical method. The contribution of this paper is threefold. First, we…
We show that deep learning algorithms can be deployed to study bifurcations of particle trajectories. We demonstrate this for two physical systems, the unperturbed Duffing equation and charged particles in magnetic reversal by using the AI…