Exploration of methods for computing sensitivities in ODE models at dynamic and steady states
arxiv(2024)
Abstract
Estimating parameters of dynamic models from experimental data is a
challenging, and often computationally-demanding task. It requires a large
number of model simulations and objective function gradient computations, if
gradient-based optimization is used. The gradient depends on derivatives of the
state variables with respect to parameters, also called state sensitivities,
which are expensive to compute. In many cases, steady-state computation is a
part of model simulation, either due to steady-state data or an assumption that
the system is at steady state at the initial time point. Various methods are
available for steady-state and gradient computation. Yet, the most efficient
pair of methods (one for steady states, one for gradients) for a particular
model is often not clear. Moreover, depending on the model and the available
data, some methods may not be applicable or sufficiently robust. In order to
facilitate the selection of methods, we explore six method pairs for computing
the steady state and sensitivities at steady state using six real-world
problems. The method pairs involve numerical integration or Newton's method to
compute the steady-state, and – for both forward and adjoint sensitivity
analysis – numerical integration or a tailored method to compute the
sensitivities at steady-state. Our evaluation shows that the two method pairs
that combine numerical integration for the steady-state with a tailored method
for the sensitivities at steady-state were the most robust, and amongst the
most computationally-efficient. We also observed that while Newton's method for
steady-state computation yields a substantial speedup compared to numerical
integration, it may lead to a large number of simulation failures. Overall, our
study provides a concise overview across current methods for computing
sensitivities at steady state, guiding modelers to choose the right methods.
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