diffrax is absolutely magical. I had to integrate a lot of ODEs during my PhD, so I spent quite some time choosing and tuning the scipy solvers for my problems, and I thought that I came close to the fastest I could do in Python. Recently, out of curiosity I rewrote a stiff system that I was studying to solve it with diffrax, and was astonished when I saw it being solved 150x faster.
And if you're doing implicit methods, then you may be interested to hear that today's release of Diffrax now includes IMEX solvers! Sil3, KenCarp3, KenCarp4, KenCarp5.
I did see that on my GitHub feed this morning, it was the good news of the day :)
Thank you for creating and maintaining this library! I also really enjoyed your blogpost "How to succeed in a machine learning PhD" which is a trove of interesting things to learn.
It is a system of four coupled ODEs from biology. I was using LSODA with relatively tight rtol and atol. Now in diffrax I use Tsit5, with adaptive step size control.
Something really annoying about this system is that for a non-negligible portion of the parameter space, an adaptive step solver would fail and give up at some point during the integration because the step size converges to zero. This was preventing me from doing large parameter searches. Now, because diffrax makes it easy to specify the step size controller, I first try to solve the system with a PID step size control, and if this fails, I rerun it with small fixed steps, which is slower but always goes through the end. This guarantees that I will always get a complete solution, and that it will still be fast in 95% of cases, which is really a huge improvement.
