A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions
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The derivatives of differential equation solutions are commonly used as model diagnostics and as part of parameter estimation routines. In this manuscript we investigate an implementation of Discrete local Sensitivity Analysis via Automatic Differentiation (DSAAD). A non-stiff Lotka-Volterra model, a discretization of the two dimensional (N × N) Brusselator stiff reaction-diffusion PDE, a stiff non-linear air pollution and a non-stiff pharmacokinetic/pharmacodynamic (PK/PD) model were used as prototype models for this investigation. Our benchmarks show that on sufficiently small (<100 parameters) stiff and non-stiff systems of ODEs, forward-mode DSAAD is more efficient than both reverse-mode DSAAD and continuous forward/adjoint sensitivity analysis. The scalability of continuous adjoint methods is shown to result in better efficiency for larger ODE systems such as PDE discretizations. In addition to testing efficiency, results on test equations demonstrate the applicability of DSAAD to differential-algebraic equations, delay differential equations, and hybrid differential equation systems where the event timing and effects are dependent on model parameters. Together, these results show that language-level automatic differentiation is an efficient method for calculating local sensitivities of a wide range of differential equation models.
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