AD Tutorial at the TU Berlin
AD Tutorial at the TU Berlin
AD Tutorial at the TU Berlin
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Optimum Experimental Design in Chemical Engineering (Cont.)<br />
Dynamics: Defined by ODE<br />
Goal: Estim<strong>at</strong>e parameters p = (k 1 , k k<strong>at</strong> , E k<strong>at</strong> )<br />
Problem: Errors in <strong>the</strong> measurements η result in errors in parameters p.<br />
nonlinear regression with additive iid normal errors<br />
η m = h m(t m, x(t m), p, q) + ε m ,<br />
ε m ∼ N (0, σ 2 m )<br />
m = 1, . . . , N M<br />
η m are measurements, h measurement model function (connects model to <strong>the</strong> real world)<br />
Controls q = (n a1 , n a2 , n a4 , c k<strong>at</strong> , θ) influence <strong>the</strong> error propag<strong>at</strong>ion.<br />
Therefore: Find controls q such th<strong>at</strong> <strong>the</strong> “uncertainty” in p is as “small” as possible.<br />
η 2<br />
ˆη(q 1 )<br />
ˆη(q 2 )<br />
J † (q)<br />
p 2<br />
ˆp(q 1 )<br />
ˆp(q 2 )<br />
Sebastian F. Walter, HU <strong>Berlin</strong> () Not So Short <strong>Tutorial</strong> OnAlgorithmic Differenti<strong>at</strong>ion Wednesday, 04.06.2010 19 / 39<br />
η 1<br />
p 1
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