DS-TIDE: Harnessing Dynamical Systems for Efficient Time-Independent Differential Equation Solving

Time-Independent Differential Equations (TIDEs) are central to modeling equilibrium behavior across a wide range of scientific and engineering domains.Conventional numerical solvers offer reliable solutions but incur significant computational costs due to fine-grained discretization and iterative procedures.Machine learning-based approaches address this by replacing iterative solving with one-time inference; however, they inevitably sacrifice accuracy and incur even higher costs once the training of sophisticated models is taken into account.Consequently, designing a TIDE solver that achieves high accuracy, broad applicability, and exceptional computational efficiency remains a fundamental challenge.In this paper, we propose DS-TIDE, a novel hardware solver that is inspired by, and subsequently leverages, the intrinsic connection between Dynamical Systems (DS) and Differential Equations (DE) to efficiently and accurately solve TIDEs.DS-TIDE employs a CMOS-compatible DS-based processor, whose physical states evolve under carefully designed DE-driven dynamics and naturally converge to equilibria -the solutions of the target TIDE within ∼ 1𝜇𝑠.To enhance expressivity, DS-TIDE incorporates Heterogeneous Dynamics with Temporal Layering (HDTL), which solves TIDEs through a three-stage DS evolution -conditioning, solving, and decoding -each governed by specialized dynamics.The entire evolution process is analogous to an infinitely deep neural network temporally unrolled, offering the system the capability of representing complex equations.Furthermore, DS-TIDE is equipped