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It's often the case that describing how a complex system changes with its input variables is much easier than writing the function from the variable to the stat
by seanhunter 9mo ago
It's often the case that describing how a complex system changes with its input variables is much easier than writing the function from the variable to the state.
A PDE is a precise description of some unknown function in terms of how it changes, so it's really the ideal framework for doing the kind of simulation you're talking about.
- seanhunter 9mo agoI should have added this in my original note, but as a programmer, if you’re interested in learning about this I highly recommend Steve Brunton’s course in differential equations and dynamical systems on you tube https://youtu.be/9fQkLQZe3u8?si=Cu7F5QQyljjiG4K8 https://youtu.be/9fQkLQZe3u8?si=Cu7F5QQyljjiG4K8 He’s a really amazing teacher and he goes through all the maths on a lightboard and then writes simulations of all the systems he talks about in python and matlab. All the course materials are available free online. It’s quite extraordinary.