An Efficient Flash-Based Computing-in-Memory (CIM) Demonstration of High-Precision (32-bit) Nonlinear Partial Differential Equation (PDE) Solver With Ultra-High Endurance and Reliability

Solving partial differential equations (PDEs) requires precise numerical iterations that impose significant demands on computational resources and memory capacities, which can be addressed by adopting computing-in-memory (CIM) architecture to reduce the latency and power consumption during data transmission. Among PDEs, nonlinear PDEs present heightened complexities in both analytical investigations and numerical simulations as the presence of nonlinear terms introduces intricate dynamics and mathematical intricacies. The high-precision requirements of PDE solvers, particularly for nonlinear PDE solvers, pose challenges in constructing CIM PDE solvers. In this work, a flash-based high-precision PDE solver has been demonstrated to solve the intractable nonlinear partial differential equation. It’s based on 55nm NOR flash technology with well-optimized Program/Erase (PE) schemes. Utilizing the proposed optimization scheme, the PE endurance can be largely enhanced up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{10}$ </tex-math></inline-formula> cycles, which is a record high with suppressed cell degradation and robust reliabilities. Then, applying the Fourier neural operator (FNO) to the optimized flash-based high-precision CIM (32-bit) in the hardware system, a series of nonlinear PDEs can be solved with ~2TOPS/W high energy efficiency, which is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 110\times $ </tex-math></inline-formula> higher than CPU. Our optimization strategies make it feasible to use flash-based CIM for high-precision computing with frequent weight updating and the demonstrated PDE solver provides an energy-saving solution to implement general-purpose computation tasks.