We introduce a method to convert Physics-Informed Neural Networks (PINNs), commonly used in scientific machine learning, to Spiking Neural Networks (SNNs), which are expected to have higher energy efficiency compared to traditional Artificial Neural Networks (ANNs). We first extend the calibration technique of SNNs to arbitrary activation functions beyond ReLU, making it more versatile, and we prove a theorem that ensures the effectiveness of the calibration. We successfully convert PINNs to SNNs, enabling computational efficiency for diverse regression tasks in solving multiple differential equations, including the unsteady Navier-Stokes equations. We demonstrate great gains in terms of overall efficiency, including Separable PINNs (SPINNs), which accelerate the training process. Overall, this is the first work of this kind and the proposed method achieves relatively good accuracy with low spike rates.

翻译：我们提出了一种将物理信息神经网络（PINNs，常用于科学机器学习）转换为脉冲神经网络（SNNs）的方法，相比传统人工神经网络（ANNs），SNNs预期具有更高的能效。首先，我们将SNN的校准技术从ReLU扩展到任意激活函数，使其更具通用性，并证明了一个确保校准有效性的定理。我们成功地将PINNs转换为SNNs，从而在多种微分方程（包括非稳态Navier-Stokes方程）的求解过程中，为不同回归任务实现了计算效率的提升。我们展示了在整体效率方面的显著优势，包括可分离PINNs（SPINNs），该方法可加速训练过程。总体而言，这是该领域的首项工作，所提出的方法在低脉冲发射率下达到了相对良好的精度。