Lecture 6 Part 1: Adjoint Differentiation of ODE Solutions

MIT 18.S096 Matrix Calculus For Machine Learning And Beyond, IAP 2023
Instructors: Alan Edelman, Steven G. Johnson

Description: Many systems are modeled by ordinary differential equations (ODEs), and often you want the derivative of the ODE solution with respect to parameters of the equations. An efficient way to do this is often to solve a second “adjoint” ODE.

License: Creative Commons BY-NC-SA

[hannahnelson]

22:10 THANK YOU SO MUCH FOR THE CLARIFICATION! I honestly had no idea what he was aiming for before Doctor Johnson clarified it. I was very confused.

[yangpiao]

For those who find it difficult to follow, the accompanying note provides a clearer illustration. I suggest referring to the note for a better understanding of what's happening here.

[vijitdey]

So, Eq((3) misses parenthesis on the integrand of the first term, so does eq(6)-eq(7) and eq(10)- the equations refer to the main pdf .

[bipinprasad]

This is hard to follow because the writing is so small and illegible.

[hannahnelson]

31:39 Why do we need to solve for u in order to solve for lambda? I can see that lambda's ODE relies on partial f / partial u and partial g / partial u. But I wouldn't normally consider either of these requiring knowing u to compute?

Could someone explain this part? I don't think I understand what we are going for there.

[titicaca-fxcs]

It is so hard to see what he wrote on the blackboard.