Algorithmic Differentiation in Python with Application Examples

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PART II: Advanced Applications Examples Sebastian F. Walter, Humboldt-Universität zu Berlin Algorithmic () Differentiation in Python with Application Examples Wednesday, 10.07.2010 24 / 27
Optimum Experimental Design in Chemical Engineering Tetramethyl Cyclohexadien + k2 + Cat Pi−Complex + Cat λ Maleinacid Anhydrid Maleinacid Anhydrid Deactiv. Cat k1 k3 Diels−Alder Product − Cat non-catalyzed and catalyzed reaction path deactivation of the catalyst batch process measurements: product mass concentration control of educt molar numbers, catalyst concentration, temperature profile five unknown model parameters ṅ 1 = −k · n1 · n 2 m tot , n 1 (0) = n a1 ṅ 2 = −k · n1 · n 2 m tot , n 2 (0) = n a2 ṅ 3 = k · n1 · n 2 m tot , n 3 (0) = 0 k = k 1 · exp − E 1 R · 1 T − 1 !! T ref + k kat · c kat · exp (−λ · t) · exp − E kat R · n 4 = n a4 T = ϑ + 273 m tot = n 1 · M 1 + n 2 · M 2 + n 3 · M 3 + n 4 · M 4 1 T − 1 !! T ref Sebastian F. Walter, Humboldt-Universität zu Berlin Algorithmic () Differentiation in Python with Application Examples Wednesday, 10.07.2010 25 / 27
Page 1 and 2: Algorithmic Differentiation in Pyth
Page 3 and 4: What is Algorithmic Differentiation
Page 5 and 6: Why not Symbolic Differentiation A
Page 7 and 8: Why not Finite Differences Problem:
Page 9 and 10: Part I: Intro Algorithmic Different
Page 11 and 12: Code Tracing with PYADOLC and ALGOP
Page 13 and 14: Univariate Taylor Polynomial Arithm
Page 15 and 16: Univariate Taylor Polynomial Arithm
Page 17 and 18: Live Example: Directional Derivativ
Page 19 and 20: The Reverse Mode by Hand: Recall: y
Page 21 and 22: Forward Mode vs Reverse Mode Task:
Page 23: A Minimal Surface Problem part of u
Page 27 and 28: Algorithm: Forward UTPM of the Rect
Page 29 and 30: Sebastian F. Walter, Humboldt-Unive

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