Related papers: Principal dynamical components
Time-invariant linear dynamical system arises in many real-world applications,and its usefulness is widely acknowledged. A practical limitation with this model is that its latent dimension that has a large impact on the model capability…
We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…
We consider the sparse principal component analysis for high-dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish the oracle inequalities for…
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…
In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in…
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…
Finite-dimensional dissipative dynamical systems with multiple time-scales are obtained when modeling chemical reaction kinetics with ordinary differential equations. Such stiff systems are computationally hard to solve and therefore,…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean…
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…
We address the challenge of dimension reduction in the discrete-time optimal control problem which is solved repeatedly online within the framework of model predictive control. Our study demonstrates that a reduced-order approach, aimed at…
This paper studies a dynamic real-time optimization in the context of model-based time-optimal operation of batch processes under parametric model mismatch. In order to tackle the model-mismatch issue, a receding-horizon policy is usually…
Time series forecasting models are becoming increasingly prevalent due to their critical role in decision-making across various domains. However, most existing approaches represent the coupled temporal patterns, often neglecting the…
In applications involving ordinal predictors, common approaches to reduce dimensionality are either extensions of unsupervised techniques such as principal component analysis, or variable selection procedures that rely on modeling the…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
Multivariate imputation by chained equations (MICE) is one of the most popular approaches to address missing values in a data set. This approach requires specifying a univariate imputation model for every variable under imputation. The…
Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and…