Related papers: On Learning Discrete-Time Fractional-Order Dynamic…

In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e.g., exclusively through proper orthogonal decomposition (POD) - when applied to nonlinear…

Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…

We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with…

Decomposing multivariate time series with certain basic dynamics is crucial for understanding, predicting and controlling nonlinear spatiotemporally dynamic systems such as the brain. Dynamic mode decomposition (DMD) is a method for…

Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by…

Unlike conventional data such as natural images, audio and speech, raw multi-channel Electroencephalogram (EEG) data are difficult to interpret. Modern deep neural networks have shown promising results in EEG studies, however finding robust…

Simulating the long-term dynamics of multi-scale and multi-physics systems poses a significant challenge in understanding complex phenomena across science and engineering. The complexity arises from the intricate interactions between scales…

Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to…

The goal of fine-grained action recognition is to successfully discriminate between action categories with subtle differences. To tackle this, we derive inspiration from the human visual system which contains specialized regions in the…

We present a novel approach to learn the formulae characterising the emergent behaviour of a dynamical system from system observations. At a high level, the approach starts by devising a statistical dynamical model of the system which…

Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…

Building machine learning models using EEG recorded outside of the laboratory setting requires methods robust to noisy data and randomly missing channels. This need is particularly great when working with sparse EEG montages (1-6 channels),…

Learning dynamical systems properties from data provides important insights that help us understand such systems and mitigate undesired outcomes. In this work, we propose a framework for learning spatio-temporal (ST) properties as formal…

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and…

This paper investigates the finite-time stability (FTS) of nonlinear conformable fractional-order delayed impulsive systems (CFODISs). Using the conformable fractional-order (CFO) derivative framework, we derive a novel FTS result by…

Recently, researchers have begun to experiment with deep learning-based methods for detecting major depressive disor-der (MDD) using electroencephalogram (EEG) signals in search of a more objective means of diagnosis. However, exist-ing…

Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have…

Time domain simulations of electromagnetic problems are highly valuable in engineering applications, as they allow for the analysis of transient behavior and broadband responses. These simulations utilize time stepping schemes, where each…

Deep learning applies hierarchical layers of hidden variables to construct nonlinear high dimensional predictors. Our goal is to develop and train deep learning architectures for spatio-temporal modeling. Training a deep architecture is…