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Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
Observations in various applications are frequently represented as a time series of multidimensional arrays, called tensor time series, preserving the inherent multidimensional structure. In this paper, we present a factor model approach,…
In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain dynamical systems modeling complex interactions. In such…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
As tensor-valued data become increasingly common in time series analysis, there is a growing need for flexible and interpretable models that can handle high-dimensional predictors and responses across multiple modes. We propose a unified…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…
Higher-order data with high dimensionality is of immense importance in many areas of machine learning, computer vision, and video analytics. Multidimensional arrays (commonly referred to as tensors) are used for arranging higher-order data…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
This paper proposes a supervised dimension reduction methodology for tensor data which has two advantages over most image-based prognostic models. First, the model does not require tensor data to be complete which expands its application to…
Link prediction in dynamic networks remains a fundamental challenge in network science, requiring the inference of potential interactions and their evolving strengths through spatiotemporal pattern analysis. Traditional static network…
We investigate various data-driven methods to enhance projection-based model reduction techniques with the aim of capturing bifurcating solutions. To show the effectiveness of the data-driven enhancements, we focus on the incompressible…
Boolean automata networks, genetic regulation networks, and metabolic networks are just a few examples of biological modelling by discrete dynamical systems (DDS). A major issue in modelling is the verification of the model against the…
Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…
Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…
Feedback control synthesis for nonlinear, parameter-dependent fluid flow control problems is considered. The optimal feedback law requires the solution of the Hamilton-Jacobi-Bellman (HJB) PDE suffering the curse of dimensionality. This is…
Hyper spectral imaging is a remote sensing technology, providing variety of applications such as material identification, space object identification, planetary exploitation etc. It deals with capturing continuum of images of the earth…
Power amplifiers (PAs) are essential components in wireless communication systems, and the design of their behavioral models has been an important research topic for many years. The widely used generalized memory polynomial (GMP) model…
A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step.…