Data-driven learning is rapidly evolving and places a new perspective on realizing state-space dynamical systems. However, dynamical systems derived from nonlinear ordinary differential equations (ODEs) suffer from limitations in computational efficiency. Thus, this paper stems from data-driven learning to advance states of dynamical systems utilizing a structured neural network (StNN). The proposed learning technique also seeks to identify an optimal, low-complexity operator to solve dynamical systems, the so-called Hankel operator, derived from time-delay measurements. Thus, we utilize the StNN based on the Hankel operator to solve dynamical systems as an alternative to existing data-driven techniques. We show that the proposed StNN reduces the number of parameters and computational complexity compared with the conventional neural networks and also with the classical data-driven techniques, such as Sparse Identification of Nonlinear Dynamics (SINDy) and Hankel Alternative view of Koopman (HAVOK), which is commonly known as delay-Dynamic Mode Decomposition(DMD) or Hankel-DMD. More specifically, we present numerical simulations to solve dynamical systems utilizing the StNN based on the Hankel operator beginning from the fundamental Lotka-Volterra model, where we compare the StNN with the LEarning Across Dynamical Systems (LEADS), and extend our analysis to highly nonlinear and chaotic Lorenz systems, comparing the StNN with conventional neural networks, SINDy, and HAVOK. Hence, we show that the proposed StNN paves the way for realizing state-space dynamical systems with a low-complexity learning algorithm, enabling prediction and understanding of future states.

--True-time-delay (TTD) beamformers can produce wideband, squint-free beams in both analog and digital signal domains, unlike frequency-dependent FFT beams. Our previous work showed that TTD beamformers can be efficiently realized using the elements of delay V andermonde matrix (DVM), answering the longstanding beam-squint problem. Thus, building on our work on classical algorithms based on DVM, we propose neural network (NN) architecture to realize wideband multi-beam beamformers using structure-imposed weight matrices and submatrices. The structure and sparsity of the weight matrices and submatrices are shown to reduce the space and computational complexities of the NN greatly. L) complexity, where M is the number of nodes in each layer of the network, p is the number of submatrices per layer, and M >> p . We will show numerical simulations in the 24 GHz to 32 GHz range to demonstrate the numerical feasibility of realizing wideband multi-beam beamformers using the proposed neural architecture. We also show the complexity reduction of the proposed NN and compare that with fully connected NNs, to show the efficiency of the proposed architecture without sacrificing accuracy. The accuracy of the proposed NN architecture was shown using the mean squared error, which is based on an objective function of the weight matrices and beamformed signals of antenna arrays, while also normalizing nodes. The proposed NN architecture shows a low-complexity NN realizing wideband multi-beam beamformers in real-time for low-complexity intelligent systems. H. Aluvihare is with the Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, FL, 32703 USA email:aluvihah@my.erau.edu S. Sivasankar is with the Department of Electrical and Computer Engineering, Florida International University, Miami, FL, 33174 USA email:ssiva011@fiu.edu X. Li is with the Department of Mathematics & Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA e-mail: xli@fit.edu

Tensorial neural networks (TNNs) combine the successes of multilinear algebra with those of deep learning to enable extremely efficient reduced-order models of high-dimensional problems. Here, I describe a deep neural network architecture that fuses multiple TNNs into a larger network, intended to solve a broader class of problems than a single TNN. I evaluate this architecture, referred to as a "stacked tensorial neural network" (STNN), on a parametric PDE with three independent variables and three parameters. The three parameters correspond to one PDE coefficient and two quantities describing the domain geometry. The STNN provides an accurate reduced-order description of the solution manifold over a wide range of parameters. There is also evidence of meaningful generalization to parameter values outside its training data. Finally, while the STNN architecture is relatively simple and problem agnostic, it can be regularized to incorporate problem-specific features like symmetries and physical modeling assumptions.

Traffic flow forecasting is a crucial task in urban computing. The challenge arises as traffic flows often exhibit intrinsic and latent spatio-temporal correlations that cannot be identified by extracting the spatial and temporal patterns of traffic data separately. We argue that such correlations are universal and play a pivotal role in traffic flow. We put forward spacetime interval learning as a paradigm to explicitly capture these correlations through a unified analysis of both spatial and temporal features. Unlike the state-of-the-art methods, which are restricted to a particular road network, we model the universal spatio-temporal correlations that are transferable from cities to cities. To this end, we propose a new spacetime interval learning framework that constructs a local-spacetime context of a traffic sensor comprising the data from its neighbors within close time points. Based on this idea, we introduce spacetime neural network (STNN), which employs novel spacetime convolution and attention mechanism to learn the universal spatio-temporal correlations. The proposed STNN captures local traffic patterns, which does not depend on a specific network structure. As a result, a trained STNN model can be applied on any unseen traffic networks. We evaluate the proposed STNN on two public real-world traffic datasets and a simulated dataset on dynamic networks. The experiment results show that STNN not only improves prediction accuracy by 15% over state-of-the-art methods, but is also effective in handling the case when the traffic network undergoes dynamic changes as well as the superior generalization capability.

We established a Spatio-Temporal Neural Network, namely STNN, to forecast the spread of the coronavirus COVID-19 outbreak worldwide in 2020. The basic structure of STNN is similar to the Recurrent Neural Network (RNN) incorporating with not only temporal data but also spatial features. Two improved STNN architectures, namely the STNN with Augmented Spatial States (STNN-A) and the STNN with Input Gate (STNN-I), are proposed, which ensure more predictability and flexibility. STNN and its variants can be trained using Stochastic Gradient Descent (SGD) algorithm and its improved variants (e.g., Adam, AdaGrad and RMSProp). Our STNN models are compared with several classical epidemic prediction models, including the fully-connected neural network (BPNN), and the recurrent neural network (RNN), the classical curve fitting models, as well as the SEIR dynamical system model. Numerical simulations demonstrate that STNN models outperform many others by providing more accurate fitting and prediction, and by handling both spatial and temporal data.