Related papers: A Computational Information Criterion for Particle…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost…
We consider a discrete time particle model for kinetic transport on the two dimensional integer lattice. The particle can move due to advection in the $x$-direction and due to dispersion. This happens when the particle is free, but it can…
The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects…
The rapid development of AI highlights the pressing need for sustainable energy, a critical global challenge for decades. Nuclear fusion, generally seen as an ultimate solution, has been the focus of intensive research for nearly a century,…
Verifying the performance of safety-critical, stochastic systems with complex noise distributions is difficult. We introduce a general procedure for the finite abstraction of nonlinear stochastic systems with non-standard (e.g., non-affine,…
This article presents an innovative approach for developing an efficient reduced-order model to study the dispersion of urban air pollutants. The need for real-time air quality monitoring has become increasingly important, given the rise in…
Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due to limited and noisy data, significant biological…
Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is…
We present a new transport-based approach to efficiently perform sequential Bayesian inference of static model parameters. The strategy is based on the extraction of conditional distribution from the joint distribution of parameters and…
In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
Claeskens and Hjort (2003) constructed the focused information criterion (FIC) and developed frequentist model averaging methods using maximum likelihood estimators assuming the observations to be independent and identically distributed.…
The robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached production-level accuracy. However, like classification models, segmentation models can be vulnerable to…
The movement of a particle described by Brownian motion is quantified by a single parameter, $D$, the diffusion constant. The estimation of $D$ from a discrete sequence of noisy observations is a fundamental problem in biological single…
Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of…
The problem of optimal motion planing and control is fundamental in robotics. However, this problem is intractable for continuous-time stochastic systems in general and the solution is difficult to approximate if non-instantaneous nonlinear…
Image classification is a well-studied task in computer vision, and yet it remains challenging under high-uncertainty conditions, such as when input images are corrupted or training data are limited. Conventional classification approaches…
In particle simulations, the weights of particles determine how many physical particles they represent. Adaptively adjusting these weights can greatly improve the efficiency of the simulation, without creating severe nonphysical artifacts.…
We address the problem of parameter estimation in models of systems biology from noisy observations. The models we consider are characterized by simultaneous deterministic nonlinear differential equations whose parameters are either taken…