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Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the…
Spatial-temporal forecasting plays an important role in many real-world applications, such as traffic forecasting, air pollutant forecasting, crowd-flow forecasting, and so on. State-of-the-art spatial-temporal forecasting models take…
Missing data in spatiotemporal systems presents a significant challenge for modern applications, ranging from environmental monitoring to urban traffic management. The integrity of spatiotemporal data often deteriorates due to hardware…
Cloth manipulation is challenging due to its highly complex dynamics, near-infinite degrees of freedom, and frequent self-occlusions, which complicate both state estimation and dynamics modeling. Inspired by recent advances in generative…
We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…
Simulations of large-scale plasma systems are typically based on a fluid approximation approach. These models construct a moment-based system of equations that approximate the particle-based physics as a fluid, but as a result lack the…
We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…
Numerical climate model simulations run at high spatial and temporal resolutions generate massive quantities of data. As our computing capabilities continue to increase, storing all of the data is not sustainable, and thus it is important…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…
The FKPP equation with a variable growth rate and advection by an incompressible velocity field is considered as a model for plankton dispersed by ocean currents. If the average growth rate is negative then the model has a…
This paper gives an overview of parameter estimation and system identification for quantum input-output systems by continuous observation of the output field. We present recent results on the quantum Fisher information of the output with…
Despite rapid progress in live-imaging techniques, many complex biophysical and biochemical systems remain only partially observable, thus posing the challenge to identify valid theoretical models and estimate their parameters from an…
Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
A fundamental problem in collaborative sensing lies in providing an accurate prediction of critical events (e.g., hazardous environmental condition, urban abnormalities, economic trends). However, due to the resource constraints,…
We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they…
We present a method for providing statistical guarantees on runtime safety and goal reachability for integrated planning and control of a class of systems with unknown nonlinear stochastic underactuated dynamics. Specifically, given a…
A new energy-based stochastic extension of the Schrodinger equation for which the wave function collapses after the passage of a finite amount of time is proposed. An exact closed-form solution to the dynamical equation, valid for all…