Support approximations

[maedoc]

Approximations allow us to include model components that don't have autodiff-friendly implementations.

• A first test case will be approximating the local coupling term in a neural field model
• A second case will be the transitions from xt to x{t+1}

Several other use cases have been discussed in the team, such as incorporating spiking simulation dynamics.

@dhrunia

[dhrunia]

Looks like there is a lot of recent literature/interest in solving PDEs using deep neural networks: Here are a few papers that might be useful in developing our approximations.

• Physics informed neural networks (PINNs)
• Deep Operator Networks (DeepONets)
• Fourier Neural Operator (FNO)
• Physicis Informed Neural operator (PINO)