Related papers: Data-driven model order reduction for T-Product-Ba…

Data-driven inference of the generative dynamics underlying a set of observed time series is of growing interest in machine learning and the natural sciences. In neuroscience, such methods promise to alleviate the need to handcraft models…

This paper presents a technique for reduced-order Markov modeling for compact representation of time-series data. In this work, symbolic dynamics-based tools have been used to infer an approximate generative Markov model. The time-series…

We propose two kinds of model order reduction methods for discrete time-delay systems with inhomogeneous initial conditions. The peculiar properties of discrete Walsh functions are directly utilized to compute the Walsh coefficients of the…

Directional motion towards a specified destination is a common occurrence in physical processes and human societal activities. Utilizing this prior information can significantly improve the control and predictive performance of system…

The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…

Database engines have historically absorbed many of the innovations in data processing, adding features to process graph data, XML, object oriented, and text among many others. In this paper, we make the case that it is time to do the same…

Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…

Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models. With a lot of hype and industrial demand in this field, it is not always clear how much progress…

Data-driven material models have many advantages over classical numerical approaches, such as the direct utilization of experimental data and the possibility to improve performance of predictions when additional data is available. One…

In this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining…

Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order…

Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in…

Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling…

Reduced Order Modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control.…

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…

In this paper, we tackle the challenge of predicting stock movements in financial markets by introducing Higher Order Transformers, a novel architecture designed for processing multivariate time-series data. We extend the self-attention…

For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper…

Accurate models of mechanical system dynamics are often critical for model-based control and reinforcement learning. Fully data-driven dynamics models promise to ease the process of modeling and analysis, but require considerable amounts of…

Unlike 2D raster images, there is no single dominant representation for 3D visual data processing. Different formats like point clouds, meshes, or implicit functions each have their strengths and weaknesses. Still, grid representations such…