Starting Framework for Analog Numerical Analysis for Energy-Efficient Computing

Abstract

Abstract:The focus of this work is to develop a starting framework for analog numerical analysis and related algorithm questions. Digital computation is enabled by a framework developed over the last 80 years. Having an analog framework enables wider capability while giving the designer tools to make reasonable choices. Analog numerical analysis concerns computation on physical structures utilizing the real-valued representations of that physical system. This work starts the conversation of analog numerical analysis, including exploring the relevancy and need for this framework. A complexity framework based on computational strengths and weaknesses builds from addressing analog and digital numerical precision, as well as addresses analog and digital error propagation due to computation. The complimentary analog and digital computational techniques enable wider computational capabilities.

Analog Architecture Complexity Theory Empowering Ultra-Low Power Configurable Analog and Mixed Mode SoC Systems

“…Having a family of configurable analog devices grounds these discussions to practical implementations (Figure 28), rather than hypthosizing a theoretical machine. The areas of analog abstraction [9], numerical analysis [8], and now analog architectures become the foundation to consider these questions ( Figure 28). These issues around the real-valued computational models, and the computational implications ODE and PDE based computation, particularly to start formulations of an equivalent analog Turing machine model (Figure 28), as was hypothesized recently [2].…”

“…The broad potential of large-scale Field Programmable Analog Arrays (FPAA, e.g., [6], Figure 2) required an analog computation framework (Figure 1). Analog numerical analysis ( Figure 1) provides a first step [8] towards analog computation framework, and analog abstraction and its tool implementations ( Figure 1) provides another step [9]. .…”

“…This framework is essential for application-based system design using physical systems particularly given modern comfort with structured and automated digital design from code to working application. The tradeoff between analog and digital computation directly leads to the tradeoff between high-precision with poor numerics of digital computation versus the good numerics with lower precision of analog computation [8]. Physical computation may show improvements beyond just energy efficiency for digital computing machines [2].…”

“…Although the local coefficients are already computed for the FFT, computing the values locally results in equal or better metrics. If one computes these coefficients, one needs to be aware of the numerical error propagation [8] and code in ways to minimize those effects for the given precision. Storing the input and intermediate results requires memory access (e.g., O(N) for 1 processor), resulting in memory access complexity (e.g., ( √ N for 1 processor).…”

“…Physical dynamics effect analog computation and architecture complexity metrics, both in the coefficients and O( ). Ordinary Differential Equations (ODE) are the basic computations for analog computation, while typically being challenging for digital computation [8]. Partial Differential Equations (PDE) and numerical optimization analog solutions build upon ODE capabilities.…”