We demonstrate that scalable neuromorphic hardware can implement the finite element method, which is a critical numerical method for engineering and scientific discovery. Our approach maps the sparse interactions between neighboring finite elements to small populations of neurons that dynamically update according to the governing physics of a desired problem description. We show that for the Poisson equation, which describes many physical systems such as gravitational and electrostatic fields, this cortical-inspired neural circuit can achieve comparable levels of numerical accuracy and scaling while enabling the use of inherently parallel and energy-efficient neuromorphic hardware. We demonstrate that this approach can be used on the Intel Loihi 2 platform and illustrate how this approach can be extended to nontrivial mesh geometries and dynamics.

翻译：我们证明了可扩展的神经形态硬件能够实现有限元法，这是工程与科学发现中至关重要的数值方法。我们的方法将相邻有限元之间的稀疏相互作用映射到小型神经元群，这些神经元根据目标问题描述的支配物理规律进行动态更新。我们表明，对于描述引力场和静电场等诸多物理系统的泊松方程，这种受皮层启发的神经电路能够实现可比的数值精度与扩展性，同时充分利用了神经形态硬件固有的并行性与高能效特性。我们在英特尔Loihi 2平台上验证了该方法的可行性，并阐述了如何将其扩展到非平凡网格几何结构与动态系统。