On the analog computer solution of first-order partial differential equations

Little, W.D.; Soudack, A. C.

doi:10.1016/s0378-4754(65)80035-0

Cited by 6 publications

(2 citation statements)

References 2 publications

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“…We have seen how the Antikythera Mechanism was an early attempt using analog computing, and this line of engineering has been pursued over centuries. For example in 1836 a way was proposed to solve differential equations using a thread wrapped around a cylinder (Coriolis, 1836), and more recently using analog computers (Hartree, 1940;Little and Soudack, 1965;Barrios et al, 2019). Finally, after simulations of the behavior of the neuronal networks hardware was created that implemented analog computing into microprocessors (Wijekoon and Dudek, 2012;Martel et al, 2020).…”

Section: Analog and Digital Computingmentioning

confidence: 99%

From Analog to Digital Computing: Is Homo sapiens’ Brain on Its Way to Become a Turing Machine?

Danchin

Fenton

2022

Front. Ecol. Evol.

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The abstract basis of modern computation is the formal description of a finite state machine, the Universal Turing Machine, based on manipulation of integers and logic symbols. In this contribution to the discourse on the computer-brain analogy, we discuss the extent to which analog computing, as performed by the mammalian brain, is like and unlike the digital computing of Universal Turing Machines. We begin with ordinary reality being a permanent dialog between continuous and discontinuous worlds. So it is with computing, which can be analog or digital, and is often mixed. The theory behind computers is essentially digital, but efficient simulations of phenomena can be performed by analog devices; indeed, any physical calculation requires implementation in the physical world and is therefore analog to some extent, despite being based on abstract logic and arithmetic. The mammalian brain, comprised of neuronal networks, functions as an analog device and has given rise to artificial neural networks that are implemented as digital algorithms but function as analog models would. Analog constructs compute with the implementation of a variety of feedback and feedforward loops. In contrast, digital algorithms allow the implementation of recursive processes that enable them to generate unparalleled emergent properties. We briefly illustrate how the cortical organization of neurons can integrate signals and make predictions analogically. While we conclude that brains are not digital computers, we speculate on the recent implementation of human writing in the brain as a possible digital path that slowly evolves the brain into a genuine (slow) Turing machine.

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Section: Analog and Digital Computingmentioning

confidence: 99%

From Analog to Digital Computing: Is Homo sapiens’ Brain on Its Way to Become a Turing Machine?

Danchin

Fenton

2022

Front. Ecol. Evol.

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“…However, FPGAs only accelerate the numerical algorithms, do not provide a different computing model. Finally, there is significant effort in exploring ASICs and non-CMOS devices to accelerate specific dynamical systems, for example, simple first/second order equations, oscillatory networks, and spiking systems [25,29,[31][32][33]41]. The ASIC-based approach provides high energy-efficiency, but lack the capability of solving different types of dynamical systems in a single platform.…”

Section: Introductionmentioning

confidence: 99%

A Programmable Hardware Accelerator for Simulating Dynamical Systems

Kung

Long

Kim

et al. 2017

SIGARCH Comput. Archit. News

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The fast and energy-efficient simulation of dynamical systems defined by coupled ordinary/partial differential equations has emerged as an important problem. The accelerated simulation of coupled ODE/PDE is critical for analysis of physical systems as well as computing with dynamical systems. This paper presents a fast and programmable accelerator for simulating dynamical systems. The computing model of the proposed platform is based on multilayer cellular nonlinear network (CeNN) augmented with nonlinear function evaluation engines. The platform can be programmed to accelerate wide classes of ODEs/PDEs by modulating the connectivity within the multilayer CeNN engine. An innovative hardware architecture including data reuse, memory hierarchy, and near-memory processing is designed to accelerate the augmented multilayer CeNN. A dataflow model is presented which is supported by optimized memory hierarchy for efficient function evaluation. The proposed solver is designed and synthesized in 15nm technology for the hardware analysis. The performance is evaluated and compared to GPU nodes when solving wide classes of differential equations and the power consumption is analyzed to show orders of magnitude improvement in energy efficiency.

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A hybrid method for the solution of first order partial differential equations arising in non-linear estimation

El-Zorkany

Balasubramanian

1976

Mathematics and Computers in Simulation

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On the analog computer solution of first-order partial differential equations

Cited by 6 publications

References 2 publications

From Analog to Digital Computing: Is Homo sapiens’ Brain on Its Way to Become a Turing Machine?

From Analog to Digital Computing: Is Homo sapiens’ Brain on Its Way to Become a Turing Machine?

A Programmable Hardware Accelerator for Simulating Dynamical Systems

A hybrid method for the solution of first order partial differential equations arising in non-linear estimation

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