adjoint - 6.581J / 20.482J Foundations of Algorithms and...

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6.581J / 20.482J Foundations of Algorithms and Computational Techniques in Systems Biology Professor Bruce Tidor Professor Jacob K. White 6.581 / 20 .482 J Foundations of Algorithms and Computational Techniques in Systems Biology Adjoint Sensitivity Analysis for Optimization From: Cao Y, Li ST, Petzold L, Serban R, Adjoint sensitivity analysis or differential-algebraic equations: The adjoint DAE system and its numerical solution, SIAM Journal on Scientific Computing 24 : 1076–1089 (2003). Courtesy of: Joshua F. Apgar, Jared E. Toettcher, Jacob K. White, and Bruce Tidor. Sensitivity Problem For Dynamic Systems ( & , , ( , ), Dynamic System: Fxxutp p ) = 0 ( Initial Condition: x (0) = x p ) 0 T ( ( ( ), ) Derived Function: Gp ) = gxt pd t 0 dG = ?? dp 1
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6.581J / 20.482J Foundations of Algorithms and Computational Techniques in Systems Biology Professor Bruce Tidor Professor Jacob K. White Forward Method ( & , , ( , ), Dynamic System: Fxxutp p ) = 0 ( Initial Condition: x (0) = x p ) 0 T ( ( ( ), ) Derived Function: Gp ) = gxt pd t 0 dG T g dx g dt = + dp 0 x dp p Trick 1: Augment The Problem T Gp ( ( ), T ( & ,, , ) () = gxt p ) + λ Fxxtpd t
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adjoint - 6.581J / 20.482J Foundations of Algorithms and...

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