Neuroscience inspired scientific machine learning (Part-2): Variable
  spiking wavelet neural operator
Shailesh Garg Souvik Chakraborty
We propose, in this paper, a Variable Spiking Wavelet Neural Operator
(VS-WNO), which aims to bridge the gap between theoretical and practical
implementation of Artificial Intelligence (AI) algorithms for mechanics
applications. With recent developments like the introduction of neural
operators, AI's potential for being used in mechanics applications has
increased significantly. However, AI's immense energy and resource requirements
are a hurdle in its practical field use case. The proposed VS-WNO is based on
the principles of spiking neural networks, which have shown promise in reducing
the energy requirements of the neural networks. This makes possible the use of
such algorithms in edge computing. The proposed VS-WNO utilizes variable
spiking neurons, which promote sparse communication, thus conserving energy,
and its use is further supported by its ability to tackle regression tasks,
often faced in the field of mechanics. Various examples dealing with partial
differential equations, like Burger's equation, Allen Cahn's equation, and
Darcy's equation, have been shown. Comparisons have been shown against wavelet
neural operator utilizing leaky integrate and fire neurons (direct and encoded
inputs) and vanilla wavelet neural operator utilizing artificial neurons. The
results produced illustrate the ability of the proposed VS-WNO to converge to
ground truth while promoting sparse communication.