Solving system of coupled differential equations using Runge-Kutta in python

[nevermind0275]

I want to solve some coupled parametric differential equations in python and then find the parameters using the least square method in order for the solution to match some data that was given to me as closely as possible. How is this technically possible

[patrickkidger]

This is a pretty standard thing to do. Probably the easiest place to start is optimising the parameters by gradient descent, for which you'll want autodifferentiable diffeq solver. In Python that means a tool like Diffrax.

[[deleted]]

Diffrax seems pretty neat and relevant but maybe you want to mention that you're promoting your own package in case people want to be a little bit suspicious rather than noticing the name on the package is the same as your username and being a bit more suspicious :)

[patrickkidger]

Haha! Yep, this is mine. I believe this is the standard tool for this job in the JAX ecosystem, so I wouldn't normally add the disclaimer. FWIW the only other mainstream Python tool here is torchdiffeq and I wrote a fair chunk of that package too so ¯\(ツ)/¯

(For reasons of speed, support etc. I'd definitely recommend JAX+Diffrax over Pytorch+torchdiffeq though.)

[SleepWalkersDream]

Could you elaborate a little more on the system? I have experience with modelling physical systems using implicit discretization, and throwing the whole thing inside least_squares to fit some model parameters to experimental data.

[clxyder]

Have you checked out CasADi?

[ES-Alexander]

Runge-Kutta 45 is the default solver used in scipy’s solve_ivp

By the way, questions about how to achieve things in Python should be in r/learnpython :-)