Related papers: On the randomized Euler algorithm under inexact in…
Variational quantum algorithms have been one of the most intensively studied applications for near-term quantum computing applications. The noisy intermediate-scale quantum (NISQ) regime, where small enough algorithms can be run…
The use of numerical simulation for prediction of characteristics of chaotic dynamical systems inherently involves unpredictable processes. In this work, we develop a model for the expected error in the simulation of ergodic, chaotic ODE…
Neuronal responses are conspicuously variable. We focus on one particular aspect of that variability: the precision of action potential timing. We show that for common models of noisy spike generation, elementary considerations imply that…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…
It is well known that the Euler method for a random ordinary differential equation $\mathrm{d}X_t/\mathrm{d}t = f(t, X_t, Y_t)$ driven by a stochastic process $\{Y_t\}_t$ with $\theta$-H\"older sample paths is estimated to be of strong…
This paper is devoted to order-one explicit approximations of random periodic solutions to multiplicative noise driven stochastic differential equations (SDEs) with non-globally Lipschitz coefficients. The existence of the random periodic…
The recently proposed statistical finite element (statFEM) approach synthesises measurement data with finite element models and allows for making predictions about the unknown true system response. We provide a probabilistic error analysis…
In this work we investigate the phenomenon of pathwise non-uniqueness for the stochastic incompressible Euler equations with a passive tracer on the whole Euclidean space. The stochastic perturbations are interpreted as a transport noise…
We present a new stochastic differential equation model for the spontaneous emission noise and carrier noise in semiconductor lasers. The correlations between these two types of noise have often been neglected in recent studies of the…
Randomized compiling reduces the effects of errors on quantum computers by tailoring arbitrary Markovian errors into stochastic Pauli noise. Here we prove that randomized compiling also tailors non-Markovian errors into local stochastic…
The purpose of this work is twofold. First, we construct probabilistically strong solutions to the three-dimensional Euler equations perturbed by additive noise that are $\mathbb{P}$-almost surely continuous in time, H\"older in space, and…
This work proposes a learning-based statistical refinement method for improving the denoising results of a given denoiser without knowing the precise noise distribution or accessing clean images or calibration data. While there are many…
Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…
In this paper, we consider robust system identification under sparse outliers and random noises. In our problem, system parameters are observed through a Toeplitz matrix. All observations are subject to random noises and a few are corrupted…
Stiff ordinary differential equations (ODEs) are common in many science and engineering fields, but standard neural ODE approaches struggle to accurately learn these stiff systems, posing a significant barrier to widespread adoption of…
Reliability analysis aims at estimating the failure probability of an engineering system. It often requires multiple runs of a limit-state function, which usually relies on computationally intensive simulations. Traditionally, these…
Timeseries generated from a dynamical source can often be modeled as sample paths of a stochastic differential equation (SDE). The timeseries thus reflects the motion of a particle which flows along the direction provided by a drift /…
We study a controlled version of the Bayesian sequential testing problem for the drift of a Wiener process, in which the observer exercises discretion over the signal intensity. This control incurs a running cost that reflects the resource…
Stochastic differential equations with noisy memory are often impossible to solve analytically. Therefore, we derive a numerical Euler-Maruyama scheme for such equations and prove that the mean-square error of this scheme is of order…
We provide existence and uniqueness of global (and local) mild solutions for a general class of semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures under local Lipschitz and linear…