The main computational task of Scientific Machine Learning (SciML) is function regression. Physics-informed Neural Networks (PINNs) and neural operators (e.g. Deep Operator Network, DeepONet) are very effective in solving Partial Differential Equations (PDEs), but they tax computational resources heavily and cannot be readily adopted for edge computing. We address this issue by considering Spiking Neural Networks (SNNs), which have shown promise in significantly reducing energy consumption. SNNs are widely explored for classification, but not for regression due to the inherent difficulty in representing a continuous function input and output values as spikes. We first propose a new method for encoding continuous values into spikes based on a triangular matrix. Next, we demonstrate that using a naive SNN architecture we can achieve relatively accurate function regression results. We explore each component of the SNN and propose methods to make them more efficient. Then, we introduce the Spiking DeepONet, where we either replace the branch or the trunk by an SNN. We demonstrate this new approach for classification using the SNN in the branch, achieving results comparable to the literature. Finally, we demonstrate regression capabilities using a DeepONet with a SNN trunk, and achieve good accuracy for solutions of PDEs.