Daniel J. Gauthier

Wendson A. S. Barbosa, Daniel J. Gauthier

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 $10^3-10^4$ times faster for training process and training data set $\sim 10^2$ 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 $\sim$10.

Daniel J. Gauthier, Ingo Fischer, André Röhm

Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and hence smaller training data sets than competing approaches. Recently, a simpler formulation, known as next-generation reservoir computing, removes many algorithm metaparameters and identifies a well-performing traditional reservoir computer, thus simplifying training even further. Here, we study a particularly challenging problem of learning a dynamical system that has both disparate time scales and multiple co-existing dynamical states (attractors). We compare the next-generation and traditional reservoir computer using metrics quantifying the geometry of the ground-truth and forecasted attractors. For the studied four-dimensional system, the next-generation reservoir computing approach uses $\sim 1.7 \times$ less training data, requires $10^3 \times$ shorter `warm up' time, has fewer metaparameters, and has an $\sim 100\times$ higher accuracy in predicting the co-existing attractor characteristics in comparison to a traditional reservoir computer. Furthermore, we demonstrate that it predicts the basin of attraction with high accuracy. This work lends further support to the superior learning ability of this new machine learning algorithm for dynamical systems.

Robert M. Kent, Wendson A. S. Barbosa, Daniel J. Gauthier

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 10 data points for training, can control the system to a desired trajectory in a single iteration, and is robust to noise and modeling error.

Robert M. Kent, Wendson A. S. Barbosa, Daniel J. Gauthier

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. Here, we show that a nonlinear controller based on next-generation reservoir computing can tackle a difficult control problem: controlling a chaotic system to an arbitrary time-dependent state. The model is accurate, yet it is small enough to be evaluated on a field-programmable gate array typically found in embedded devices. Furthermore, the model only requires 25.0 $\pm$ 7.0 nJ per evaluation, well below other algorithms, even without systematic power optimization. Our work represents the first step in deploying efficient machine learning algorithms to the computing "edge."

Robert M. Kent, Linipun Phuttitarn, Chaithanya Naik Mude et al.

Quantum computers require high-fidelity measurement of many qubits to achieve a quantum advantage. Traditional approaches suffer from readout crosstalk for a neutral-atom quantum processor with a tightly spaced array. Although classical machine learning algorithms based on convolutional neural networks can improve fidelity, they are computationally expensive, making it difficult to scale them to large qubit counts. We present two simpler and scalable machine learning algorithms that realize matched filters for the readout problem. One is a local model that focuses on a single qubit, and the other uses information from neighboring qubits in the array to prevent crosstalk among the qubits. We demonstrate error reductions of up to 32% and 43% for the site and array models, respectively, compared to a conventional Gaussian threshold approach. Additionally, our array model uses two orders of magnitude fewer trainable parameters and four orders of magnitude fewer multiplications and nonlinear function evaluations than a recent convolutional neural network approach, with only a minor (3.5%) increase in error across different readout times. Another strength of our approach is its physical interpretability: the learned filter can be visualized to provide insights into experimental imperfections. We also show that a convolutional neural network model for improved can be pruned to have 70x and 4000x fewer parameters, respectively, while maintaining similar errors. Our work shows that simple machine learning approaches can achieve high-fidelity qubit measurements while remaining scalable to systems with larger qubit counts.

C. J. Wright, N. Biederman, B. Gyovai et al.

Machine learning was applied to create a digital twin of a numerical simulation of a single-scroll jet engine. A similar model based on the insights gained from this numerical study was used to create a digital twin of a JetCat P100-RX jet engine using only experimental data. Engine data was collected from a custom sensor system measuring parameters such as thrust, exhaust gas temperature, shaft speed, weather conditions, etc. Data was gathered while the engine was placed under different test conditions by controlling shaft speed. The machine learning model was generated (trained) using a next-generation reservoir computer, a best-in-class machine learning algorithm for dynamical systems. Once the model was trained, it was used to predict behavior it had never seen with an accuracy of better than 1.8% when compared to the testing data.

André Röhm, Daniel J. Gauthier, Ingo Fischer

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, as well as 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 co-existing attractors, here a 4-dimensional extension of the well-known Lorenz chaotic system. We demonstrate that a reservoir computer can infer entirely unexplored parts of the phase space: a properly trained reservoir computer can predict the existence of attractors that were never approached during training and therefore are labelled as unseen. We provide examples where attractor inference is achieved after training solely on a single noisy trajectory.

Graham E. Rowlands, Minh-Hai Nguyen, Guilhem J. Ribeill et al.

The rapidity and low power consumption of superconducting electronics makes them an ideal substrate for physical reservoir computing, which commandeers the computational power inherent to the evolution of a dynamical system for the purposes of performing machine learning tasks. We focus on a subset of superconducting circuits that exhibit soliton-like dynamics in simple transmission line geometries. With numerical simulations we demonstrate the effectiveness of these circuits in performing higher-order parity calculations and channel equalization at rates approaching 100 Gb/s. The availability of a proven superconducting logic scheme considerably simplifies the path to a fully integrated reservoir computing platform and makes superconducting reservoirs an enticing substrate for high rate signal processing applications.

Daniel Canaday, Andrew Pomerance, Daniel J Gauthier

We propose and demonstrate a nonlinear control method that can be applied to unknown, complex systems where the controller is based on a type of artificial neural network known as a reservoir computer. In contrast to many modern neural-network-based control techniques, which are robust to system uncertainties but require a model nonetheless, our technique requires no prior knowledge of the system and is thus model-free. Further, our approach does not require an initial system identification step, resulting in a relatively simple and efficient learning process. Reservoir computers are well-suited to the control problem because they require small training data sets and remarkably low training times. By iteratively training and adding layers of reservoir computers to the controller, a precise and efficient control law is identified quickly. With examples on both numerical and high-speed experimental systems, we demonstrate that our approach is capable of controlling highly complex dynamical systems that display deterministic chaos to nontrivial target trajectories.

Noeloikeau Charlot, Daniel Canaday, Andrew Pomerance et al.

We introduce a Physically Unclonable Function (PUF) based on an ultra-fast chaotic network known as a Hybrid Boolean Network (HBN) implemented on a field programmable gate array. The network, consisting of $N$ coupled asynchronous logic gates displaying dynamics on the sub-nanosecond time scale, acts as a `digital fingerprint' by amplifying small manufacturing variations during a period of transient chaos. In contrast to other PUF designs, we use both $N$-bits per challenge and obtain $N$-bits per response by considering challenges to be initial states of the $N$-node network and responses to be states captured during the subsequent chaotic transient. We find that the presence of chaos amplifies the frozen-in randomness due to manufacturing differences and that the extractable entropy is approximately $50\%$ of the maximum of $N2^{N}$ bits. We obtain PUF uniqueness and reliability metrics $μ_{inter}$ = 0.40$\pm$0.01 and $μ_{intra}$ = 0.05$\pm$0.00, respectively, for an $N=256$ network. These metrics correspond to an expected Hamming distance of 102.4 bits per response. Moreover, a simple cherry-picking scheme that discards noisy bits yields $μ_{intra} < 0.01$ while still retaining $\sim200$ bits/response (corresponding to a Hamming distance of $\sim80$ bits/response). In addition to characterizing the uniqueness and reliability, we demonstrate super-exponential scaling in the entropy up to $N=512$ and demonstrate that PUFmeter, a recent PUF analysis tool, is unable to model our PUF. Finally, we characterize the temperature variation of the HBN-PUF and propose future improvements.