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The mean square displacement and instantaneous diffusion coefficient for different configurations of charged particles in stochastic motion are calculated by numerically solving the associated equations of motion. The method is suitable for…

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…

There have been increasing reports that the diffusion coefficient of macromolecules depends on time and fluctuates randomly. Here, a novel method to elucidate the fluctuating diffusivity from trajectory data is developed. The time-averaged…

We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead,…

This paper addresses the problem of estimating the modes of an observed non-stationary mixture signal in the presence of an arbitrary distributed noise. A novel Bayesian model is introduced to estimate the model parameters from the…

We consider a multiplicative deconvolution problem, in which the density $f$ or the survival function $S^X$ of a strictly positive random variable $X$ is estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y =…

We present a sampling-free approach for computing the epistemic uncertainty of a neural network. Epistemic uncertainty is an important quantity for the deployment of deep neural networks in safety-critical applications, since it represents…

Deep learning-based object pose estimators are often unreliable and overconfident especially when the input image is outside the training domain, for instance, with sim2real transfer. Efficient and robust uncertainty quantification (UQ) in…

Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…

Modeling the Point Spread Function (PSF) of wide-field surveys is vital for many astrophysical applications and cosmological probes including weak gravitational lensing. The PSF smears the image of any recorded object and therefore needs to…

In this work, we propose using the mixture density network (MDN) to estimate cosmological parameters. We test the MDN method by constraining parameters of the $\Lambda$CDM and $w$CDM models using Type Ia supernovae and the power spectra of…

Functional uncertainty quantification (FunUQ) was recently proposed to quantify uncertainties in models and simulations that originate from input functions, as opposed to parameters. This paper extends FunUQ to quantify uncertainties…

We investigate the dynamics of individual colloidal particles in a one-dimensional periodic potential using the intermediate scattering function (ISF) as a key observable. We elaborate a theoretical framework and derive formally exact…

We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo…

The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD)…

Galaxy imaging surveys observe a vast number of objects that are affected by the instrument's Point Spread Function (PSF). Weak lensing missions, in particular, aim at measuring the shape of galaxies, and PSF effects represent an important…

Diffusion models typically inject isotropic Gaussian noise, disregarding structure in the data. Motivated by the way quantum squeezed states redistribute uncertainty according to the Heisenberg uncertainty principle, we introduce Squeezed…

Inertial microfluidic devices (IMDs) offer low-cost, high-throughput alternative techniques for many traditional particle- (or cell-) manipulation tasks, but simulating them requires being able to predict particle migration, and thus…

The mean free paths of low-energy electrons in liquid water are of fundamental importance for modelling radiation damage and many related physico-chemical processes. Neither theoretical predictions nor experimental estimations have so far…

The Davies-Fulling model describes the scattering of a massless field by a moving mirror in 1+1 dimensions. When the mirror travels under uniform acceleration, one encounters severe problems which are due to the infinite blue shift effects…