Here I use Julia to fit models specified with (partial) differential equations to noisy data (aka mechanistic-statistical models). The code and outputs can be seen at https://oliviergimenez.github.io/mecastat-in-julia/.
To familiarize myself with Julia, I've watched some of these excellent video tutorials. To run the code from the Notebook fit-diffeq-data.ipynb, I recommend using Visual Studio Code.
A cool book on mechanistic-statistical models is that by Lionel Roques (in French) entitled Modèles de réaction-diffusion pour l'écologie spatiale. I'm a big fan of Chris Rackauckas' work on differential equations, check out his webpage and YouTube channel.