NODEFit.jl

Fit time-series data with a Neural Differential Equation in Julia!

This repository contains time-series data fit capabilities using both Neural Ordinary Differential Equations and Neural Stochastic Differential Equations

Also checkout its Python version

How to install and execute?

Just instantiate the package and you can run the examples

julia fit_nsde.jl

The following program illustrates a basic example

using NODEFit
using Lux: Chain, Dense

#######
# Define the networks
#######
# Network dimensions
ndim, nhid = 2, 4
drift_net = Chain(x -> x .^ 3, Dense(ndim, nhid, tanh), Dense(nhid, ndim))
diff_net = Dense(ndim, ndim)

#######
# Define the data
#######
tsteps = collect(Float32, range(0.0f0, 1.0f0; length=30))
sde_data, sde_data_vars = # Matrices of time-series data and variances

#######
# Fit the data
#######
result_nsde = NODEFit.fit_nsde(drift_net, diff_net, tsteps, sde_data, sde_data_vars)

Full examples are provided in the examples folder

Sample Output

Why use Julia?

Once compiled, Julia is much faster than Python and the following article provides comparison for the underlying routines

Neural SDE fits for 500 iterations were performed on Early 2015 MacBook Pro in real-time (as seen in output) compared to ~10 seconds per iteration in NODEFit

Whom to contact?

Please direct your queries to gpavanb1 for any questions.

Acknowledgements

This package would not be possible without the supporting packages. The assistance provided in Julia Slack groups is also gratefully acknowledged. Documentation of DiffEqFlux.jl served as guidance for some of the routines.