High-concurrency tri-mode memristor-based ordinary differential equation solver

Area of Science:

• Computational Science and Engineering
• Materials Science and Engineering
• Computer Architecture

Background:

• Numerical solutions of ordinary differential equations (ODEs) are computationally intensive on traditional hardware.
• High-order ODEs and complex systems demand significant time and energy resources.
• Existing Von Neumann architectures present bottlenecks for efficient ODE solving.

Purpose of the Study:

• To develop a high-concurrency, memristor-based ODE solver.
• To support arbitrary order ODEs with configurable accuracy modes (coarse, fine, coarse-to-fine).
• To enhance computational efficiency and reduce energy consumption for ODE numerical integration.

Main Methods:

• Implementation of a reconfigurable hardware architecture utilizing memristors.
• Employment of analog and digital compute-in-memory for coarse and fine solvers, respectively.
• Integration of Parareal methods for a coarse-to-fine look-ahead solver.
• Utilization of History-based Memristor Programming (HMP) for accelerated device programming.

Main Results:

• Achieved significant speedups (601× to 6.92×10³×) compared to CPU/GPU.
• Demonstrated substantial energy improvements (1.71×10³× to 3.93×10³×) over CPU/GPU.
• Validated performance on diverse problems including exponential functions, Lorenz attractors, and three-body problems.
• Showcased high concurrency and arbitrary order support for ODE solving.

Conclusions:

• The memristor-based tri-mode solver represents a new paradigm for ODE hardware acceleration.
• This approach offers orders of magnitude improvements in concurrency and efficiency.
• The developed solver meets diverse accuracy requirements for complex scientific and engineering computations.