Related papers: Weak approximations for Wiener functionals
This paper presents a close form solution in Reproducing Kernel Hilbert Space (RKHS) for the famed Wiener filter, which we called the functional Wiener filter(FWF). Instead of using the Wiener-Hopf factorization theory, here we define a new…
This paper presents an algorithm for applying the high-order recombination method, originally introduced by Lyons and Litterer in ``High-order recombination and an application to cubature on Wiener space'' (Ann. Appl. Probab.…
In this article we apply a discrete action principle for the Vlasov--Maxwell equations in a structure-preserving particle-field discretization framework. In this framework the finite-dimensional electromagnetic potentials and fields are…
We present a variant of accelerated gradient descent algorithms, adapted from Nesterov's optimal first-order methods, for weakly-quasi-convex and weakly-quasi-strongly-convex functions. We show that by tweaking the so-called estimate…
An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A…
In this paper, several weak Orlicz-Hardy martingale spaces associated with concave functions are introduced, and some weak atomic decomposition theorems for them are established. With the help of weak atomic decompositions, a sufficient…
There is tremendous potential in using neural networks to optimize numerical methods. In this paper, we introduce and analyse a framework for the neural optimization of discrete weak formulations, suitable for finite element methods. The…
We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\^o calculus, such…
In this paper, we construct a simple and robust two-point finite volume discretization applicable to isotropic linearized elasticity, valid in also in the incompressible Stokes' limit. The discretization is based only on co-located,…
We present a semiclassical trace formula for the canonical partition function of arbitrary one-dimensional systems. The approximation is obtained via the stationary exponent method applied to the phase-space integration of the density…
We consider the dynamics of an elastic continuum under large deformation but small strain. Such systems can be described by the equations of geometrically nonlinear elastodynamics in combination with the St. Venant-Kirchhoff material law.…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
In this paper we discuss weak convergence of continuous-time Markov chains to a non-symmetric pure jump process. We approach this problem using Dirichlet forms as well as semimartingales. As an application, we discuss how to approximate a…
This letter proposes a fast identification algorithm for Wiener-Hammerstein systems. The computational cost of separating the front and the back linear time invariant block dynamics is significantly improved by using discrete optimization.…
We develop a convergence theory for non-monotone approximation schemes for fully nonlinear parabolic partial differential equations. Modern computational methods such as kernel-based collocation, spectral methods, physics-informed neural…
The dynamic damage model in viscoelastic materials in Kelvin-Voigt rheology is discretised by a scheme which is coupled, suppresses spurious numerical attenuation during vibrations, and has a variational structure with a convex potential…
In this paper, we consider a class of structured nonsmooth optimization problems over an embedded submanifold of a Euclidean space, where the first part of the objective is the sum of a difference-of-convex (DC) function and a smooth…
A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…
In many applications that involve the inference of an unknown smooth function, the inference of its derivatives will often be just as important as that of the function itself. To make joint inferences of the function and its derivatives, a…