Controlling chaos using edge computing hardware.

Machine learning provides a data-driven approach for creating a digital twin of a system - a digital model used to predict the system behavior. Having an accurate digital twin can drive many applications, such as controlling autonomous systems. Often, the size, weight, and power consumption of the digital twin or related controller must be minimized, ideally realized on embedded computing hardware that can operate without a cloud-computing connection.

Controlling chaotic maps using next-generation reservoir computing.

In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the controller in a series of control tasks for the chaotic Hénon map, including controlling the system between unstable fixed points, stabilizing the system to higher order periodic orbits, and to an arbitrary desired state. We show that our controller succeeds in these tasks, requires only ten data points for training, can control the system to a desired trajectory in a single iteration, and is robust to noise and modeling error.

Perspectives on adaptive dynamical systems.

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems.

Learning spatiotemporal chaos using next-generation reservoir computing.

Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture that, when combined with a next-generation reservoir computer, displays state-of-the-art performance with a computational time - times faster for training process and training data set ∼ times smaller than other machine learning algorithms. We also take advantage of the translational symmetry of the model to further reduce the computational cost and training data, each by a factor of ∼10.

Symmetry-aware reservoir computing.

We demonstrate that matching the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increases its processing power. We apply our method to the parity task, a challenging benchmark problem that highlights inversion and permutation symmetries, and to a chaotic system inference task that presents an inversion symmetry rule. For the parity task, our symmetry-aware RC obtains zero error using an exponentially reduced neural network and training data, greatly speeding up the time to result and outperforming artificial neural networks.

Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing.

Reservoir computers are powerful tools for chaotic time series prediction. They can be trained to approximate phase space flows and can thus both predict future values to a high accuracy and reconstruct the general properties of a chaotic attractor without requiring a model. In this work, we show that the ability to learn the dynamics of a complex system can be extended to systems with multiple co-existing attractors, here a four-dimensional extension of the well-known Lorenz chaotic system.

Next generation reservoir computing.

Reservoir computing is a best-in-class machine learning algorithm for processing information generated by dynamical systems using observed time-series data. Importantly, it requires very small training data sets, uses linear optimization, and thus requires minimal computing resources. However, the algorithm uses randomly sampled matrices to define the underlying recurrent neural network and has a multitude of metaparameters that must be optimized.

Qubit-Based Clock Synchronization for QKD Systems Using a Bayesian Approach.

Quantum key distribution (QKD) systems provide a method for two users to exchange a provably secure key. Synchronizing the users' clocks is an essential step before a secure key can be distilled. Qubit-based synchronization protocols directly use the transmitted quantum states to achieve synchronization and thus avoid the need for additional classical synchronization hardware.

Forecasting chaotic systems with very low connectivity reservoir computers.

We explore the hyperparameter space of reservoir computers used for forecasting of the chaotic Lorenz '63 attractor with Bayesian optimization. We use a new measure of reservoir performance, designed to emphasize learning the global climate of the forecasted system rather than short-term prediction. We find that optimizing over this measure more quickly excludes reservoirs that fail to reproduce the climate.

Rapid time series prediction with a hardware-based reservoir computer.

Reservoir computing is a neural network approach for processing time-dependent signals that has seen rapid development in recent years. Physical implementations of the technique using optical reservoirs have demonstrated remarkable accuracy and processing speed at benchmark tasks. However, these approaches require an electronic output layer to maintain high performance, which limits their use in tasks such as time-series prediction, where the output is fed back into the reservoir.

Bounding the outcome of a two-photon interference measurement using weak coherent states.

The interference of two photons at a beam splitter is at the core of many quantum photonic technologies, such as quantum key distribution or linear-optics quantum computing. Observing high-visibility interference is challenging because of the difficulty of realizing indistinguishable single-photon sources. Here, we perform a two-photon interference experiment using phase-randomized weak coherent states with different mean photon numbers.

Scalable cryogenic readout circuit for a superconducting nanowire single-photon detector system.

The superconducting nanowire single-photon detector (SNSPD) is a leading technology for quantum information science applications using photons, and is finding increasing uses in photon-starved classical imaging applications. Critical detector characteristics, such as timing resolution (jitter), reset time, and maximum count rate, are heavily influenced by the readout electronics that sense and amplify the photon detection signal. We describe a readout circuit for SNSPDs using commercial off-the-shelf amplifiers operating at cryogenic temperatures.

Provably secure and high-rate quantum key distribution with time-bin qudits.

The security of conventional cryptography systems is threatened in the forthcoming era of quantum computers. Quantum key distribution (QKD) features fundamentally proven security and offers a promising option for quantum-proof cryptography solution. Although prototype QKD systems over optical fiber have been demonstrated over the years, the key generation rates remain several orders of magnitude lower than current classical communication systems.

Advanced active quenching circuit for ultra-fast quantum cryptography.

Commercial photon-counting modules based on actively quenched solid-state avalanche photodiode sensors are used in a wide variety of applications. Manufacturers characterize their detectors by specifying a small set of parameters, such as detection efficiency, dead time, dark counts rate, afterpulsing probability and single-photon arrival-time resolution (jitter). However, they usually do not specify the range of conditions over which these parameters are constant or present a sufficient description of the characterization process.

Transient dynamics and their control in time-delay autonomous Boolean ring networks.

Biochemical systems with switch-like interactions, such as gene regulatory networks, are well modeled by autonomous Boolean networks. Specifically, the topology and logic of gene interactions can be described by systems of continuous piecewise-linear differential equations, enabling analytical predictions of the dynamics of specific networks. However, most models do not account for time delays along links associated with spatial transport, mRNA transcription, and translation.

Super-transient scaling in time-delay autonomous Boolean network motifs.

Autonomous Boolean networks are commonly used to model the dynamics of gene regulatory networks and allow for the prediction of stable dynamical attractors. However, most models do not account for time delays along the network links and noise, which are crucial features of real biological systems. Concentrating on two paradigmatic motifs, the toggle switch and the repressilator, we develop an experimental testbed that explicitly includes both inter-node time delays and noise using digital logic elements on field-programmable gate arrays.

Forced synchronization of autonomous dynamical Boolean networks.

We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal.

Coupling scales for modelling heavy metal vaporization from municipal solid waste incineration in a fluid bed by CFD.

Municipal Solid Waste Incineration (MSWI) in fluidized bed is a very interesting technology mainly due to high combustion efficiency, great flexibility for treating several types of waste fuels and reduction in pollutants emitted with the flue gas. However, there is a great concern with respect to the fate of heavy metals (HM) contained in MSW and their environmental impact. In this study, a coupled two-scale CFD model was developed for MSWI in a bubbling fluidized bed.

Reservoir computing with a single time-delay autonomous Boolean node.

We demonstrate reservoir computing with a physical system using a single autonomous Boolean logic element with time-delay feedback. The system generates a chaotic transient with a window of consistency lasting between 30 and 300 ns, which we show is sufficient for reservoir computing. We then characterize the dependence of computational performance on system parameters to find the best operating point of the reservoir.

The effect of temperature and heating rate on char properties obtained from solar pyrolysis of beech wood.

Char samples were produced from pyrolysis in a lab-scale solar reactor. The pyrolysis of beech wood was carried out at temperatures ranging from 600 to 2000°C, with heating rates from 5 to 450°C/s. CHNS, scanning electron microscopy analysis, X-ray diffractometry, Brunauer-Emmett-Teller adsorption were employed to investigate the effect of temperature and heating rate on char composition and structure.

Multirhythmicity in an optoelectronic oscillator with large delay.

An optoelectronic oscillator exhibiting a large delay in its feedback loop is studied both experimentally and theoretically. We show that multiple square-wave oscillations may coexist for the same values of the parameters (multirhythmicity). Depending on the sign of the phase shift, these regimes admit either periods close to an integer fraction of the delay or periods close to an odd integer fraction of twice the delay.

Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators.

We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists.

Giant all-optical tunable group velocity dispersion in an optical fiber.

We realize a strongly dispersive material with large tunable group velocity dispersion (GVD) in a commercially-available photonic crystal fiber. Specifically, we pump the fiber with a two-frequency pump field that induces an absorbing resonance adjacent to an amplifying resonance via the stimulated Brillouin processes. We demonstrate all-optical control of the GVD by measuring the linear frequency chirp impressed on a 28-nanosecond-duration optical pulse by the medium and find that it is tunable over the range ± 7.