A Damping-Tunable Snap System: From Dissipative Hyperchaos to Conservative Chaos

A hyperjerk system described by a single fourth-order ordinary differential equation of the form x⃜=f(x⃛,x¨,x˙,x) has been referred to as a snap system. A damping-tunable snap system, capable of an adjustable attractor dimension (DL) ranging from dissipative hyperchaos (DL<4) to conservative chaos (DL=4), is presented for the first time, in particular not only in a snap system, but also in a four-dimensional (4D) system. Such an attractor dimension is adjustable by nonlinear damping of a relatively simple quadratic function of the form Ax2, easily tunable by a single parameter A. The proposed snap system is practically implemented and verified by the reconfigurable circuits of field programmable analog arrays (FPAAs).

Enabling Training of Neural Networks on Noisy Hardware

Deep neural networks (DNNs) are typically trained using the conventional stochastic gradient descent (SGD) algorithm. However, SGD performs poorly when applied to train networks on non-ideal analog hardware composed of resistive device arrays with non-symmetric conductance modulation characteristics. Recently we proposed a new algorithm, the Tiki-Taka algorithm, that overcomes this stringent symmetry requirement. Here we build on top of Tiki-Taka and describe a more robust algorithm that further relaxes other stringent hardware requirements. This more robust second version of the Tiki-Taka algorithm (referred to as TTv2) 1. decreases the number of device conductance states requirement from 1000s of states to only 10s of states, 2. increases the noise tolerance to the device conductance modulations by about 100x, and 3. increases the noise tolerance to the matrix-vector multiplication performed by the analog arrays by about 10x. Empirical simulation results show that TTv2 can train various neural networks close to their ideal accuracy even at extremely noisy hardware settings. TTv2 achieves these capabilities by complementing the original Tiki-Taka algorithm with lightweight and low computational complexity digital filtering operations performed outside the analog arrays. Therefore, the implementation cost of TTv2 compared to SGD and Tiki-Taka is minimal, and it maintains the usual power and speed benefits of using analog hardware for training workloads. Here we also show how to extract the neural network from the analog hardware once the training is complete for further model deployment. Similar to Bayesian model averaging, we form analog hardware compatible averages over the neural network weights derived from TTv2 iterates. This model average then can be transferred to another analog or digital hardware with notable improvements in test accuracy, transcending the trained model itself. In short, we describe an end-to-end training and model extraction technique for extremely noisy crossbar-based analog hardware that can be used to accelerate DNN training workloads and match the performance of full-precision SGD.

FPAA Implementations of Fractional-Order Chaotic Systems

In this paper, fractional-order chaotic systems in an analog-based platform are realized using field programmable analog arrays (FPAA) hardware. With the help of this work, we aim to increase the complexity of chaotic systems. Approximated transfer functions in frequency domain are obtained by analyzing different values of fractional-order integrator with the Charef approximation method. In this study, fractional-order numerical calculation of Rssler and Sprott type-H chaotic systems is carried out. MATLAB Simulink model for chaotic systems that satisfy the conditions of chaos in the boundaries of fractional order value is schematically presented. Moreover, CAM designs and analysis that facilitate the realization of fractional-order transfer functions in FPAA platforms are introduced. The analog-based FPAA experimental and numerical outcomes for fractional order chaotic systems are demonstrated. The comparison of the results obtained in the numerical analysis and simulation study with the experimental results is given. This study confirms that the unpredictability of the chaos carrier signals realized by digital-based can be increased with analog-based FPAA hardware and fractional-order structures so as to provide safer transfer of information signals.

Pragmatic Implementation of the Front-End of an N-bit/V ADC based on FPGA and FPAA

Reconfigurability has made it possible, among other benefits, to replace traditional discrete components with chips, whose internal components can be programmed in this case FPAAs (Field Programmable Analog Arrays). This paper presents a design and implementation of FPAA of the analog front end dedicated to a new ADC architecture called “N-bit/V”. After validation of the algorithm in simulation, the experimentation results show that the obtained reconfigurable circuit can replace the traditional discrete components-based circuits.

Analog Accelerator for Simulation and Diagnostics

We propose a new method for solving Initial Value Problems (IVPs). Our method is based on analog computing and has the potential to almost eliminate traditional switching time in digital computing. The approach can be used to simulate large systems longer, faster, and with higher accuracy. Many algorithms for Model-Based Diagnosis use numerical integration to simulate physical systems. The numerical integration process is often either computationally expensive or imprecise. We propose a new method, based on Field-Programmable Analog Arrays (FPAAs) that has the potential to overcome many practical problems. We envision a software/hardware framework for solving systems of simultaneous Ordinary Differential Equations (ODEs) in fraction of the time of traditional numerical algorithms. In this paper we describe the solving of an IVP with the help of an Analog Computing Unit (ACU). To do this we build a special calculus based on operational amplifiers (op-amps) with local feedback. We discuss the implementation of the ACU on an Integrated Circuit (IC). We analyze the working if the IC and simulate the dynamic Lotka-Volterra system with the de-facto standard tool for electrical simulation: Spice.