On the topic of simulations, I've been learning about Modelica, which is a engineering simulator. Basically, many real world devices can be described using system dynamics and their behaviour codified as differential equations. Modelica allows us to build such models, including mixed-domain models (electrical, mechanics, thermal, chemical, etc.), then the Modelica compiler produces highly optimized C++ code you can run to perform the simulation. It's heavily used in the car industry in Europe, but not widely known in academia.

Here are some talks about Modelica: https://www.youtube.com/watch?v=-mvEUuc-sWE&t=153 and https://www.youtube.com/watch?v=39F___xyI0k

Here is a complete course if you want to dig in: https://spoken-tutorial.org/tutorial-search/?search_foss=Ope...

And if you're wondering "Will it emscripten and run in the browser?", the answer is yes, of course: http://tshort.github.io/mdpad/mdpad.html?Modelica.Electrical...

Context: I'm researching a new book on ordinary differential equations through various real-world simulations, so like an ODEs theory book, but actually applying the concepts to real world systems. Get in touch by email if you're interested in seeing advanced preview of some of the projects that will be developed this summer. Contact info in profile.