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The Wave Based Method (WBM) is a Trefftz method for the simulation of wave problems in vibroacoustics. Like other Trefftz methods, it employs a non-standard discretisation basis consisting of solutions of the partial differential equation…

Accurate calculation of the motion of a compact object in a background spacetime induced by a supermassive black hole is required for the future detection of such binary systems by the gravitational-wave detector LISA. Reaching the desired…

A matrix model of an asymptotically free theory with a bound state is solved using a perturbative similarity renormalization group for hamiltonians. An effective hamiltonian with a small width, calculated including the first three terms in…

We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a…

Regularization is a popular technique to solve the overfitting problem of machine learning algorithms. Most regularization technique relies on parameter selection of the regularization coefficient. Plug-in method and cross-validation…

The variational perturbation theory for wave functions, which has been shown to work well for bound states of the anharmonic oscillator, is applied to resonance states of the anharmonic oscillator with negative coupling constant. We obtain…

We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…

In this paper, we address the problem of approximating solutions of ill-posed problems using mollification. We quickly review existing mollification regularization methods and provide two new approximate solutions to a general ill-posed…

In this paper we prove the convergence of solutions to discrete models for binary waveguide arrays toward those of their formal continuum limit, for which we also show the existence of localized standing waves. This work rigorously…

The generalized perturbative approach is an all purpose variant of Stein's method used to obtain rates of normal approximation. Originally developed for functions of independent random variables this method is here extended to functions of…

In this paper, a general class of regularized $M$-estimators of scatter matrix are proposed which are suitable also for low or insufficient sample support (small $n$ and large $p$) problems. The considered class constitutes a natural…

In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…

We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…

We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…

We derive the Whitham equations from the water waves equations in the shallow water regime using two different methods, thus obtaining a direct and rigorous link between these two models. The first one is based on the construction of…

Given an inverse problem with a normalizing flow prior, we wish to estimate the distribution of the underlying signal conditioned on the observations. We approach this problem as a task of conditional inference on the pre-trained…

One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score matching estimation" is presented here on…

We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient…