Related papers: Reachability of weakly nonlinear systems using Car…
A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of…
To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the behaviors of neural network systems will be crucial for…
Reachable sets for a dynamical system describe collections of system states that can be reached in finite time, subject to system dynamics. They can be used to guarantee goal satisfaction in controller design or to verify that unsafe…
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…
Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…
In this paper, we develop a class of high-order conservative methods for simulating non-equilibrium radiation diffusion problems. Numerically, this system poses significant challenges due to strong nonlinearity within the stiff source terms…
In this note, we consider the problem of choosing which nodes of a linear dynamical system should be actuated so that the state transfer from the system's initial condition to a given final state is possible. Assuming a standard complexity…
With the increasing use of ultrashort laser pulses and nanoscale-materials, one is regularly confronted to situations in which the properties of the media supporting propagation are not varying slowly with time (or space). Hence, the usual…
Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…
We propose a global convergent numerical method to reconstruct the initial condition of a nonlinear parabolic equation from the measurement of both Dirichlet and Neumann data on the boundary of a bounded domain. The first step in our method…
A system is Koopman super-linearizable if it admits a finite-dimensional embedding as a linear system. Super-linearization is used to leverage methods from linear systems theory to design controllers or observers for nonlinear systems. We…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…
This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…
In this note we consider the continuous Galerkin time stepping method of arbitrary order as a possible discretization scheme of nonlinear initial value problems. In addition, we develop and generalize a well known existing result for the…
This is a survey, which is a continuation of the previous survey of the author about applications of Carleman estimates to Inverse Problems, J. Inverse and Ill-Posed Problems, 21, 477-560, 2013. It is shown here that Tikhonov functionals…
Recently proposed quasi-classical DBAR-dressing method provides a systematic approach to study the weakly dispersive limit of integrable systems. We apply the quasi-classical DBAR-dressing method to describe dispersive corrections of any…