Related papers: Generalizations of Mat\'ern's hard-core point proc…

An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n$. This paper focuses on methods…

We consider a stochastic spatial point process with births and deaths on $\mathbb{R}^d$, with the hard-core property that at any time the balls of radius half of any two points do not overlap. We give explicit construction of the process.…

Understanding degradation is crucial for ensuring the longevity and performance of materials, systems, and organisms. To illustrate the similarities across applications, this article provides a review of data-based method in materials…

Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…

While the traditional formulation of machine learning tasks is in terms of performance on average, in practice we are often interested in how well a trained model performs on rare or difficult data points at test time. To achieve more…

Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods. A PDMP is…

Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations…

Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…

In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We…

We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator.…

With the rise of deep learning, there has been renewed interest within the process industries to utilize data on large-scale nonlinear sensing and control problems. We identify key statistical and machine learning techniques that have seen…

Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless…

Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…

Adhesion is a fundamental phenomenon that plays a role in many engineering and biological applications. This paper concerns the use of machine learning to characterize the effective adhesive properties when a thin film is peeled from a…

Deep neural networks (DNNs) offer significant flexibility and robust performance. This makes them ideal for building not only system models but also advanced neural network controllers (NNCs). However, their high complexity and…

Gaussian processes are an effective model class for learning unknown functions, particularly in settings where accurately representing predictive uncertainty is of key importance. Motivated by applications in the physical sciences, the…

Machine learning methods for solving the equations of dynamical mean-field theory are developed. The method is demonstrated on the three dimensional Hubbard model. The key technical issues are defining a mapping of an input function to an…

This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…

Shot noise processes are used in applied probability to model a variety of physical systems in, for example, teletraffic theory, insurance and risk theory and in the engineering sciences. In this work we prove a large deviation principle…

Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain…