Related papers: On continuous variable quantum algorithms for orac…
The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such…
The probabilistic representation of weak solutions to a parabolic boundary value problem is established in the following framework. The boundary value problem consists of a second order parabolic equation defined on a time-varying Lipschitz…
We derive explicit solution representations for linear, dissipative, second-order Initial-Boundary Value Problems (IBVPs) with coefficients that are spatially varying, with linear, constant-coefficient, two-point boundary conditions. We…
We prove a Freidlin-Wentzell result for stochastic differential equations in infinite-dimensional Hilbert spaces perturbed by a cylindrical Wiener process. We do not assume the drift to be Lipschitz continuous, but only continuous with at…
In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference in each of these computational…
Quantum parallelism is the main feature of quantum computation. In 1985 D. Deutsch showed that a single quantum computation may be sufficient to state whether a two-valued function of a two-valued variable is constant or not. Though the…
We investigate structure-preserving finite element discretizations of the steady-state Stefan--Maxwell diffusion problem which governs diffusion within a phase consisting of multiple species. An approach inspired by augmented Lagrangian…
Uncertainty quantification (UQ) techniques are frequently used to ascertain output variability in systems with parametric uncertainty. Traditional algorithms for UQ are either system-agnostic and slow (such as Monte Carlo) or fast with…
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 present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework,…
We propose a new algorithm for computing validated bounds for the solutions to the first order variational equations associated to ODEs. These validated solutions are the kernel of numerics computer-assisted proofs in dynamical systems…
Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline…
This article focuses on the space-time isogeometric method for a linear time dependent fourth order problem. Using an auxiliary variable, first the problem is split into a system of two second order differential equations and then the…
This article considers linear processes with values in a separable Hilbert space exhibiting long-range dependence. The scaling limits for the sample autocovariance operators at different time lags are investigated in the topology of their…
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…
A fundamental challenge in neurosymbolic systems is applying continuous gradient-based optimization to discrete logical domains. While fuzzy relaxations provide differentiability, they often lack a formal structural alignment with classical…
We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit…
In this paper, we study the following variant of the junta learning problem. We are given oracle access to a Boolean function $f$ on $n$ variables that only depends on $k$ variables, and, when restricted to them, equals some predefined…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…