Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks

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 their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.Comment: 31 page

Controlling quantum many-body systems using reduced-order modelling

Quantum many-body control is among most challenging problems in quantum science, due to computational complexity of related underlying problems. We propose an efficient approach for solving a class of control problems for many-body quantum systems, where time-dependent controls are applied to a sufficiently small subsystem. The approach is based on a tensor-networks-based scheme to build a low-dimensional reduced-order model of the subsystem's non-Markovian dynamics. Simulating dynamics of such a reduced-order model, viewed as a ``digital twin" of the original subsystem, is significantly more efficient, which enables the use of gradient-based optimization toolbox in the control parameter space. We validate the proposed method by solving control problems for quantum spin chains. In particular, the approach automatically identifies sequences for exciting the quasiparticles and guiding their dynamics to recover and transmit information. Additionally, when disorder is induced and the system is in the many body localized phase, we find generalized spin-echo sequences for dynamics inversion, which show improved performance compared to standard ones. Our approach by design takes advantage of non-Markovian dynamics of a subsystem to make control protocols more efficient, and, under certain conditions can store information in the rest of the many-body system and subsequently retrieve it at a desired moment of time. We expect that our results will find direct applications in the study of many-body systems, in probing non-trivial quasiparticle properties, as well as in development control tools for quantum computing devices.Comment: 20 pages, 11 figure

Joint Radar and Communication Design: Applications, State-of-the-Art, and the Road Ahead

Sharing of the frequency bands between radar and communication systems has attracted substantial attention, as it can avoid under-utilization of otherwise permanently allocated spectral resources, thus improving efficiency. Further, there is increasing demand for radar and communication systems that share the hardware platform as well as the frequency band, as this not only decongests the spectrum, but also benefits both sensing and signaling operations via the full cooperation between both functionalities. Nevertheless, the success of spectrum and hardware sharing between radar and communication systems critically depends on high-quality joint radar and communication designs. In the first part of this paper, we overview the research progress in the areas of radar-communication coexistence and dual-functional radar-communication (DFRC) systems, with particular emphasis on application scenarios and technical approaches. In the second part, we propose a novel transceiver architecture and frame structure for a DFRC base station (BS) operating in the millimeter wave (mmWave) band, using the hybrid analog-digital (HAD) beamforming technique. We assume that the BS is serving a multi-antenna user equipment (UE) over a mmWave channel, and at the same time it actively detects targets. The targets also play the role of scatterers for the communication signal. In that framework, we propose a novel scheme for joint target search and communication channel estimation, which relies on omni-directional pilot signals generated by the HAD structure. Given a fully-digital communication precoder and a desired radar transmit beampattern, we propose to design the analog and digital precoders under non-convex constant-modulus (CM) and power constraints, such that the BS can formulate narrow beams towards all the targets, while pre-equalizing the impact of the communication channel. Furthermore, we design a HAD receiver that can simultaneously process signals from the UE and echo waves from the targets. By tracking the angular variation of the targets, we show that it is possible to recover the target echoes and mitigate the resulting interference to the UE signals, even when the radar and communication signals share the same signal-to-noise ratio (SNR). The feasibility and efficiency of the proposed approaches in realizing DFRC are verified via numerical simulations. Finally, the paper concludes with an overview of the open problems in the research field of communication and radar spectrum sharing (CRSS)