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Time series forecasting is prevalent in various real-world applications. Despite the promising results of deep learning models in time series forecasting, especially the Recurrent Neural Networks (RNNs), the explanations of time series…

Neural populations exhibit latent dynamical structures that drive time-evolving spiking activities, motivating the search for models that capture both intrinsic network dynamics and external unobserved influences. In this work, we introduce…

The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in…

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…

Neuromechanics aims to understand the link between an animal's neural activity and its physical behaviors. Recent advances in experimental and machine learning techniques enable simultaneous recordings of neural and locomotion dynamics over…

Modeling dynamical systems and unraveling their underlying causal relationships is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and…

A core problem in machine learning is to learn expressive latent variables for model prediction on complex data that involves multiple sub-components in a flexible and interpretable fashion. Here, we develop an approach that improves…

In recent years, there has been renewed interest in developing methods for skeleton-based human action recognition. A skeleton sequence can be naturally represented as a high-order tensor time series. In this paper, we model and analyze…

We investigate the use of discrete and continuous versions of physics-informed neural network methods for learning unknown dynamics or constitutive relations of a dynamical system. For the case of unknown dynamics, we represent all the…

Distributed deep learning systems (DDLS) train deep neural network models by utilizing the distributed resources of a cluster. Developers of DDLS are required to make many decisions to process their particular workloads in their chosen…

Neuroscience is experiencing a data revolution in which many hundreds or thousands of neurons are recorded simultaneously. Currently, there is little consensus on how such data should be analyzed. Here we introduce LFADS (Latent Factor…

A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…

Symbolic systems are powerful frameworks for modeling cognitive processes as they encapsulate the rules and relationships fundamental to many aspects of human reasoning and behavior. Central to these models are systematicity,…

Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time…

Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale transportation system. Existing methods aim to reconstruct STTD using low-dimensional models. However, they are limited to data-specific…

A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie…

Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system…

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…