Add model fitting functionality to BrainPy

[chaoming0625]

Please:

• Check for duplicate requests.
• Describe your goal, and if possible provide a code snippet with a motivating example.

BrainPy is a useful Python library for analyzing and modeling neuroscience data. However, it currently lacks functionality for fitting models to data. I propose adding a model fitting module to BrainPy that would allow users to easily fit predefined models to their data.

Proposed Implementation:

• Create a new module in BrainPy called brainpy.fitting

• Support general classes for common neuron and population models used in neuroscience, such as:

  • Leaky integrate-and-fire models
  • Hodgkin-Huxley models
  • Wilson-Cowan models
  • Neural mass models

• Support common fitting algorithms like gradient descent, Nelder-Mead, etc.

• The module could also include convenience functions for things like:

  • Automatically estimating good initial parameters
  • Performing cross-validation
  • Statistical model comparison

• Model classes should track goodness of fit metrics like R^2, MSE, etc.

• Plotting methods to visualize fits against data

• Support fitting models to diverse data types: spike trains, LFP, EEG, fMRI, etc.

• Include options to parallelize fitting across multiple CPUs or GPUs.