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Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition and empirical interpolation rely on linear approximation…
This paper studies sparse density estimation via $\ell_1$ penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
Semantic occupancy has emerged as a powerful representation in world models for its ability to capture rich spatial semantics. However, most existing occupancy world models rely on static and fixed embeddings or grids, which inherently…
Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…
We consider the scenario where the parameters of a probabilistic model are expected to vary over time. We construct a novel prior distribution that promotes sparsity and adapts the strength of correlation between parameters at successive…
Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…
Infectious disease spread is a multi-scale process composed of within-host (biological) and between-host (social) drivers and disentangling them from each other is a central challenge in epidemiology. Here, we introduce VIBES, a multi-scale…
The Bayesian analysis of infectious disease surveillance data from multiple locations typically involves building and fitting a spatio-temporal model of how the disease spreads in the structured population. Here we present new generally…
We develop a stochastic epidemic model progressing over dynamic networks, where infection rates are heterogeneous and may vary with individual-level covariates. The joint dynamics are modeled as a continuous-time Markov chain such that…
We develop a feedback control method for networked epidemic spreading processes. In contrast to most prior works which consider mean field, open-loop control schemes, the present work develops a novel framework for feedback control of…
Infectious disease outbreaks recapitulate biology: they emerge from the multi-level interaction of hosts, pathogens, and their shared environment. As a result, predicting when, where, and how far diseases will spread requires a complex…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
Infectious diseases that incorporate pre-symptomatic transmission are challenging to monitor, model, predict and contain. We address this scenario by studying a variant of a stochastic susceptible-exposed-infected-recovered model on…
Among various spatio-temporal prediction tasks, epidemic forecasting plays a critical role in public health management. Recent studies have demonstrated the strong potential of spatio-temporal graph neural networks (STGNNs) in extracting…
In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…
We approach the development of models and control strategies of susceptible-infected-susceptible (SIS) epidemic processes from the perspective of marked temporal point processes and stochastic optimal control of stochastic differential…
Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…
Compartmental epidemic models have been widely used for predicting the course of epidemics, from estimating the basic reproduction number to guiding intervention policies. Studies commonly acknowledge these models' assumptions but less…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…