Conventional von Neumann computers have difficulty in solving complex and ill-posed real-world problems. However, living organisms often face such problems in real life, and must quickly obtain suitable solutions through physical, dynamical, and collective computations involving vast assemblies of neurons. These highly parallel computations through high-dimensional dynamics (computation through dynamics) are completely different from the numerical computations on von Neumann computers (computation through algorithms). In this paper, we explore a novel computational mechanism with high-dimensional physical chaotic neuro-dynamics. We physically constructed two hardware prototypes using analog chaotic-neuron integrated circuits. These systems combine analog computations with chaotic neuro-dynamics and digital computation through algorithms. We used quadratic assignment problems (QAPs) as benchmarks. The first prototype utilizes an analog chaotic neural network with 800-dimensional dynamics. An external algorithm constructs a solution for a QAP using the internal dynamics of the network. In the second system, 300-dimensional analog chaotic neuro-dynamics drive a tabu-search algorithm. We demonstrate experimentally that both systems efficiently solve QAPs through physical chaotic dynamics. We also qualitatively analyze the underlying mechanism of the highly parallel and collective analog computations by observing global and local dynamics. Furthermore, we introduce spatial and temporal mutual information to quantitatively evaluate the system dynamics. The experimental results confirm the validity and efficiency of the proposed computational paradigm with the physical analog chaotic neuro-dynamics.
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