Partial Evaluation of Automatic Differentiation for Differential-Algebraic Equati...
summary
Partial evaluation of forward-mode AD reduces runtime overhead for DAE index reduction and Jacobian generation by producing a low-index residual and a sparse Jacobian callback that mixes symbolic and AD code. Implementation in the Miking framework (OCaml target, Sundials backend) uses an online partial evaluator paval and a parameterized Forward mode PAD that bounds specialization by v; on a 143-equation nonlinear model (55 equations differentiated) it outperforms pure AD, while a 48-equation linear circuit (2 differentiated) shows no gain. Artifacts available.
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chapters (20)
- 0:00Introduction
- 0:21Motivation
- 1:22Differential-algebraic equations
- 3:31Symbolic vs automatic differentiation
- 4:33Partial evaluation approach
- 5:36Proposed transformation
- 6:42High vs low index DAEs
- 8:27Input program analysis
- 9:12Abstract syntax
- 10:13Forward mode AD
- 11:16Index reduction with AD
- 11:57Pendulum example
- 13:00Code improvement
- 14:01Jacobian callback
- 15:30Sparse Jacobian
- 16:55Experimental results
- 19:02Execution time analysis
- 20:29Summary
- 21:13Future work
- 21:34Q&A
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