Related papers: Reconstructing Nonlinear Dynamical Systems from Mu…

This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…

A body of recent work in modeling neural activity focuses on recovering low-dimensional latent features that capture the statistical structure of large-scale neural populations. Most such approaches have focused on linear generative models,…

In this paper, a machine learning-based simulation framework of general-purpose multibody dynamics is introduced. The aim of the framework is to generate a well-trained meta-model of multibody dynamics (MBD) systems. To this end, deep…

Time series data is prevalent in a wide variety of real-world applications and it calls for trustworthy and explainable models for people to understand and fully trust decisions made by AI solutions. We consider the problem of building…

Dynamical systems (DS) theory is fundamental for many areas of science and engineering. It can provide deep insights into the behavior of systems evolving in time, as typically described by differential or recursive equations. A common…

Deep Learning (DL) models can be used to tackle time series analysis tasks with great success. However, the performance of DL models can degenerate rapidly if the data are not appropriately normalized. This issue is even more apparent when…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

Learning shared structure across environments facilitates rapid learning and adaptive behavior in neural systems. This has been widely demonstrated and applied in machine learning to train models that are capable of generalizing to novel…

Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…

The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Time series data, defined by equally spaced points over time, is essential in fields like medicine, telecommunications, and energy. Analyzing it involves tasks such as classification, clustering, prototyping, and regression. Classification…

This paper considers learning the hidden causal network of a linear networked dynamical system (NDS) from the time series data at some of its nodes -- partial observability. The dynamics of the NDS are driven by colored noise that generates…

This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…

Multi-modal biomedical time series (MBTS) data offers a holistic view of the physiological state, holding significant importance in various bio-medical applications. Owing to inherent noise and distribution gaps across different modalities,…

Purpose: To develop a deep learning method on a nonlinear manifold to explore the temporal redundancy of dynamic signals to reconstruct cardiac MRI data from highly undersampled measurements. Methods: Cardiac MR image reconstruction is…