Related papers: Time-Uniform Error Bound for Temporal Coarse Grain…

We propose a discrete time discrete space Markov chain approximation with a Brownian bridge correction for computing curvilinear boundary crossing probabilities of a general diffusion process on a finite time interval. For broad classes of…

Score-based generative models (SGMs) aim at estimating a target data distribution by learning score functions using only noise-perturbed samples from the target.Recent literature has focused extensively on assessing the error between the…

Gradient-domain machine learning (GDML) is an accurate and efficient approach to learn a molecular potential and associated force field based on the kernel ridge regression algorithm. Here, we demonstrate its application to learn an…

We obtain optimal Gaussian concentration bounds (GCBs) for stochastic chains of unbounded memory (SCUMs) on countable alphabets. These stochastic processes are also known as "chains with complete connections" or "$g$-measures". We consider…

The theory of open quantum system is one of the most essential tools for the development of quantum technologies. Furthermore, the Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) Master Equation plays a key role as it is the most…

We present an error analysis for the discontinuous Galerkin method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation. Under some mild assumptions, we show that the DG method converges uniformly…

Gaussian processes (GPs) and Gaussian random fields (GRFs) are essential for modelling spatially varying stochastic phenomena. Yet, the efficient generation of corresponding realisations on high-resolution grids remains challenging,…

A common tool in the practice of Markov Chain Monte Carlo is to use approximating transition kernels to speed up computation when the desired kernel is slow to evaluate or intractable. A limited set of quantitative tools exist to assess the…

We present a new approximation technique for quantum field theory. The standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In a…

Quantum Krylov subspace diagonalization (QKSD) is an emerging method used in place of quantum phase estimation in the early fault-tolerant era, where limited quantum circuit depth is available. In contrast to the classical Krylov subspace…

We provide novel information-theoretic generalization bounds for stochastic gradient Langevin dynamics (SGLD) under the assumptions of smoothness and dissipativity, which are widely used in sampling and non-convex optimization studies. Our…

Approximating the solution of the nonlinear filtering problem with Gaussian mixtures has been a very popular method since the 1970s. However, the vast majority of such approximations are introduced in an ad-hoc manner without theoretical…

To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…

Standard quantum error correction (QEC) models typically assume discrete, Markovian noise, obscuring the continuous quantum nature of physical environments. In this manuscript, we investigate the fundamental limits of an actively corrected…

We derive conditional a priori error estimates of a wide class of finite volume and Runge-Kutta discontinuous Galerkin methods with abstract limiting for hyperbolic systems of conservation laws in 1D via the verification of weak consistency…

Stabilizing autonomous linear time delay systems, particularly when addressing an unlimited number of pointwise and distributed delays (DDs) under dissipative constraints, poses a significant challenge. Existing solutions are often hindered…

We study pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observations of the driving Brownian motion. We prove lower error…

Fault tolerance is widely regarded as indispensable for achieving scalable and reliable quantum computing. However, the spacetime overhead required for fault-tolerant quantum computating remains prohibitively large. A critical challenge…

Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…

The long-time evolution of extreme mass-ratio inspiral systems requires minimal phase and dispersion errors to accurately compute far-field waveforms, while high accuracy is essential near the smaller black hole (modeled as a Dirac delta…