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We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…

The robust distributed state estimation for a class of continuous-time linear time-invariant systems is achieved by a novel kernel-based distributed observer, which, for the first time, ensures fixed-time convergence properties. The…

Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the…

Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…

Despite extensive research, time series classification and forecasting on noisy data remain highly challenging. The main difficulties lie in finding suitable mathematical concepts to describe time series and effectively separate noise from…

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…

We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown flow map of the underlying system. It employs the idea of…

Most real world phenomena such as sunlight distribution under a forest canopy, minerals concentration, stock valuation, exhibit nonstationary dynamics i.e. phenomenon variation changes depending on the locality. Nonstationary dynamics pose…

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…

The theory of Koopman operators allows to deploy non-parametric machine learning algorithms to predict and analyze complex dynamical systems. Estimators such as principal component regression (PCR) or reduced rank regression (RRR) in kernel…

We propose a hybrid meta-learning framework for forecasting and anomaly detection in nonlinear dynamical systems characterized by nonstationary and stochastic behavior. The approach integrates a physics-inspired simulator that captures…

In the context of model-based control of industrial processes, it is a common practice to develop a data-driven linear dynamical model around a specified operating point. However, in applications involving wider operating conditions,…

Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…

This paper studies the classical problem of detecting the locations of signal occurrences in a one-dimensional noisy measurement. Assuming the signal occurrences do not overlap, we formulate the detection task as a constrained likelihood…

The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…

Despite the high performance of neural network-based time series forecasting methods, the inherent challenge in explaining their predictions has limited their applicability in certain application areas. Due to the difficulty in identifying…

Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…

A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…

Modern time series forecasting methods, such as Transformer and its variants, have shown strong ability in sequential data modeling. To achieve high performance, they usually rely on redundant or unexplainable structures to model complex…