Related papers: SPADE4: Sparsity and Delay Embedding based Forecas…

This article concerns the predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. We develop a novel approach based on supervised dimension reduction for such data in order to…

Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…

We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the…

Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…

Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit…

Recently developed techniques to acquire high-quality human mobility data allow large-scale simulations of the spread of infectious diseases with high spatial and temporal resolution.Analysis of such data has revealed the oversimplification…

We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…

A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model…

Global transport and communication networks enable information, ideas and infectious diseases now to spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like…

We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…

Accurate epidemic forecasting plays a vital role for governments in developing effective prevention measures for suppressing epidemics. Most of the present spatio-temporal models cannot provide a general framework for stable, and accurate…

Complex systems in physics, chemistry, and biology that evolve over time with inherent randomness are typically described by stochastic differential equations (SDEs). A fundamental challenge in science and engineering is to determine the…

To forecast the time dynamics of an epidemic, we propose a discrete stochastic model that unifies and generalizes previous approaches to the subject. Viewing a given population of individuals or groups of individuals with given health state…

Compartmental models of epidemics are widely used to forecast the effects of communicable diseases such as COVID-19 and to guide policy. Although it has long been known that such processes take place on social networks, the assumption of…

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

Delay-coordinate embedding is a powerful, time-tested mathematical framework for reconstructing the dynamics of a system from a series of scalar observations. Most of the associated theory and heuristics are overly stringent for real-world…

In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…

Epidemic spreading of infectious diseases is ubiquitous and has often considerable impact on public health and economic wealth. The large variability in spatio-temporal patterns of epidemics prohibits simple interventions and demands for a…

We study epidemic arrival times in meta-population disease models through the lens of front propagation into unstable states. We demonstrate that several features of invasion fronts in the PDE context are also relevant to the network case.…

A model based on a thermodynamic approach is proposed for predicting the dynamics of communicable epidemics in a city, when the epidemic is governed by controlling efforts of multiple scales so that an entropy is associated with the system.…