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A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension…
We propose the use of Deterministic Generalized Asynchronous Random Boolean Networks [Gershenson, 2002] as models of contextual deterministic discrete dynamical systems. We show that changes in the context have drastic effects on the global…
Adaptive time series forecasting is essential for prediction under regime changes. Several classical methods assume linear Gaussian state space model (LGSSM) with variances constant in time. However, there are many real-world processes that…
Deep learning has emerged as a compelling framework for scientific and engineering computing, motivating growing interest in neural network-based solvers for partial differential equations (PDEs). Within this landscape, network…
We study a deterministic dynamics with two time scales in a continuous state attractor network. To the usual (fast) relaxation dynamics towards point attractors (``patterns'') we add a slow coupling dynamics that makes the visited patterns…
Ride-hailing system requires efficient management of dynamic demand and supply to ensure optimal service delivery, pricing strategies, and operational efficiency. Designing spatio-temporal forecasting models separately in a task-wise and…
Continual Learning (CL) refers to a learning setup where data is non stationary and the model has to learn without forgetting existing knowledge. The study of CL for sequential patterns revolves around trained recurrent networks. In this…
We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in…
Evolutionary Strategies (ES) are a popular family of black-box zeroth-order optimization algorithms which rely on search distributions to efficiently optimize a large variety of objective functions. This paper investigates the potential…
Extreme event are sudden large-amplitude changes in the state or observables of chaotic nonlinear systems, which characterize many scientific phenomena. Because of their violent nature, extreme events typically have adverse consequences,…
A discrete-time conditional Gaussian Koopman network (CGKN) is developed in this work to learn surrogate models that can perform efficient state forecast and data assimilation (DA) for high-dimensional complex dynamical systems, e.g.,…
A novel State-Space Neural Network with Ordered variance (SSNNO) is presented in which the state variables are ordered in decreasing variance. A systematic way of model order reduction with SSNNO is proposed, which leads to a Reduced order…
Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in…
Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of…
Accurate spatio-temporal prediction is crucial for the sustainable development of smart cities. However, current approaches often struggle to capture important spatio-temporal relationships, particularly overlooking global relations among…
We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…
Graph-based next-step prediction models have recently been very successful in modeling complex high-dimensional physical systems on irregular meshes. However, due to their short temporal attention span, these models suffer from error…
This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…
This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes…
This paper presents a transfer learning method in speech emotion recognition based on a Time-Delay Neural Network (TDNN) architecture. A major challenge in the current speech-based emotion detection research is data scarcity. The proposed…