Lecture 6 Part 1 Adjoint Differentiation of ODE Solutions
[SQUEAKING] [RUSTLING] [CLICKING] FRANK SCHAFER: Yeah, so, yeah, I plan to split it in two parts, so the first part is about ordinary differential equations, so just a quick recap what an ordinary differential equation actually is, and then we'll go into this kind of sensitivity analysis, so how to compute derivatives of solutions of ordinary differential equations. And specifically, we will pick out one very important of these methods. So, yeah, an ordinary differential equation is basically described by this kind of initial value problem, where we have the state at a given initial time t0 is equal to u0, and then the dynamics of this state is described by this kind of time evolution. So we have that the derivative of u is-- the time derivative of u is equal to this function f that can depend on time, on the state itself, and on some parameters p. And the first natural question to ask is, basically, how do we solve such an ODE? And let's say the probably simplest...