Related papers: Fast data inversion for high-dimensional dynamical…
We show the skills of a data-driven low-dimensional linear model in predicting the spatio-temporal evolution of turbulent Rayleigh-B\'enard convection. The model is based on dynamic mode decomposition with delay-embedding, which provides a…
This paper presents an adaptive Kalman filter for a linear dynamic system perturbed by an additive disturbance. The objective is to estimate both of the state and the unknown disturbance concurrently, while learning the disturbance as a…
Large-scale recordings of neural activity are providing new opportunities to study neural population dynamics. A powerful method for analyzing such high-dimensional measurements is to deploy an algorithm to learn the low-dimensional latent…
We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in…
Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…
A set of N independent Gaussian linear time invariant systems is observed by M sensors whose task is to provide the best possible steady-state causal minimum mean square estimate of the state of the systems, in addition to minimizing a…
Gaussian process-based latent variable models are flexible and theoretically grounded tools for nonlinear dimension reduction, but generalizing to non-Gaussian data likelihoods within this nonlinear framework is statistically challenging.…
This work is about a slow-fast data assimilation system under non-Gaussian noisy fluctuations. Firstly, we show the existence of a random invariant manifold for a stochastic dynamical system with non-Gaussian noise and two-time scales.…
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…
This paper considers the Linear Minimum Variance recursive state estimation for the linear discrete time dynamic system with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is shown…
Modeling the joint distribution of extreme weather events in multiple locations is a challenging task with important applications. In this study, we use max-stable models to study extreme daily precipitation events in Switzerland. The…
Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…
This paper introduces a Factor Augmented Sparse Throughput (FAST) model that utilizes both latent factors and sparse idiosyncratic components for nonparametric regression. The FAST model bridges factor models on one end and sparse…
Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Recovering unobserved state variables is an important topic for the data assimilation of turbulent systems. In this article, an efficient continuous in time data…
Stabilization, disturbance rejection, and control of optical beams and optical spots are ubiquitous problems that are crucial for the development of optical systems for ground and space telescopes, free-space optical communication…
Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…
The development of physical simulators, called Ising machines, that sample from low energy states of the Ising Hamiltonian has the potential to drastically transform our ability to understand and control complex systems. However, most of…
We propose modeling raw functional data as a mixture of a smooth function and a highdimensional factor component. The conventional approach to retrieving the smooth function from the raw data is through various smoothing techniques.…
In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold…
In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to…