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Higher order schemes for stochastic partial differential equations that do not possess commutative noise require the simulation of iterated stochastic integrals. In this work, we propose a derivative-free Milstein type scheme to approximate…

Space-time varying media enable unprecedented control over electromagnetic waves, yet most existing studies assume idealized, nondispersive materials and thus fail to capture the intrinsic frequency dispersion of realistic platforms. Here,…

This Point spread function (PSF) plays a crucial role in many computational imaging applications, such as shape from focus/defocus, depth estimation, and fluorescence microscopy. However, the mathematical model of the defocus process is…

In machine learning, likelihood-free inference refers to the task of performing an analysis driven by data instead of an analytical expression. We discuss the application of Neural Spline Flows, a neural density estimation algorithm, to the…

Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…

Deep learning is gaining increasing popularity for spatiotemporal forecasting. However, prior works have mostly focused on point estimates without quantifying the uncertainty of the predictions. In high stakes domains, being able to…

Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples…

We propose a novel meshless method to achieve super resolution from scattered data obtained from sparse, randomly positioned sensors such as the particle tracers of particle tracking velocimetry. The method combines K Nearest Neighbor…

Machine-learning models of atomic-scale interactions achieve the accuracy of the quantum mechanical calculations on which they are trained, but at a dramatically lower computational cost. Their predictions can be made trustworthy by…

To solve the obscureness in measurement brought about from the weak ergodicity breaking appeared in anomalous diffusions we have suggested the time-averaged mean squared displacement (MSD) $\bar{\delta^2 (\tau)}_\tau$ with a integral…

High-dimensional data are often assumed to lie on lower-dimensional manifolds. We study how to construct diffusion processes on this data manifold using only point cloud samples and without access to charts, projections, or other geometric…

First principles approaches have revolutionized our ability in using computers to predict, explore and design materials. A major advantage commonly associated with these approaches is that they are fully parameter free. However, numerically…

Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…

$\alpha$-stable distributions are utilised as models for heavy-tailed noise in many areas of statistics, finance and signal processing engineering. However, in general, neither univariate nor multivariate $\alpha$-stable models admit closed…

Inverse scattering problems, such as those in electromagnetic imaging using phaseless data (PD-ISPs), involve imaging objects using phaseless measurements of wave scattering. Such inverse problems can be highly non-linear and ill-posed…

Diffusion models have emerged as one of the most promising frameworks for deep generative modeling. In this work, we explore the potential of non-uniform diffusion models. We show that non-uniform diffusion leads to multi-scale diffusion…

This paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field…

Diffusion models have achieved great success in image synthesis through iterative noise estimation using deep neural networks. However, the slow inference, high memory consumption, and computation intensity of the noise estimation model…

Model-form uncertainty (MFU) in assumptions made during physics-based model development is widely considered a significant source of uncertainty; however, there are limited approaches that can quantify MFU in predictions extrapolating…

Wide-area synchrophasor ambient measurements provide a valuable data source for real-time oscillation mode monitoring and analysis. This paper introduces a novel method for identifying inter-area oscillation modes using wide-area ambient…