Challenges in the calibration of large-scale ordinary differential equation models

Kapfer, Eva-Maria; Stapor, Paul; Hasenauer, Jan

doi:10.1101/690222

Cited by 2 publications

(1 citation statement)

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“…Unfortunately, for this task only "rule-of-thumb" methods exist and it is up to the user how to properly choose these configuration parameters for a beneficial outcome in applications. Because of the strong dependence of the proper choices of the algorithms and configurations on the model size and quality of data, optimization is still considered as a major bottleneck in the field of mathematical models for life sciences [10,14,17,18].…”

Section: Introductionmentioning

confidence: 99%

Optimal Paths Between Parameter Estimates in Non-linear ODE Systems Using the Nudged Elastic Band Method

2019

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Ordinary differential equation (ODE) models are frequently used to mathematically represent the dynamic behavior of cellular components, e.g., for describing biochemical reaction networks. Solutions of these ODE models depend non-linearly on parameters, which can be estimated using experimental data by minimizing the discrepancy between data and the model trajectories. In realistic applications, only relative, sparse, and noisy data is available which makes model fitting a challenging optimization problem. In order to take account for the non-convexity of the objective function and to reveal the existence of local optima within the parameter search space, optimization is performed with multiple initial guesses. For statistically valid conclusions it is of general interest, whether distinct optimization outcomes are correctly identified as local optima originating from the non-convexity of the objective function as typically presumed, or if they are only a result of incompletely converged optimization runs and could be merged by a connecting path to a single optimum by e.g., fine-tuning of the numeric algorithms. To clarify this question in application settings, we present an approach for finding optimal paths between parameter estimates in complex objective function landscapes. By analyzing the profiles of these paths, conclusions about non-trivial connections of parameter estimates can be made and by this, it can be reliably determined if two different optimization results belong to the same or to distinct local optima. For optimal path finding, we adapt the nudged elastic band (NEB) method and apply our approach to a benchmark model with a suboptimal optimization result, which yields a preferable grouping of fits afterwards.

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Section: Introductionmentioning

confidence: 99%

Optimal Paths Between Parameter Estimates in Non-linear ODE Systems Using the Nudged Elastic Band Method

2019

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Mini-batch optimization enables training of ODE models on large-scale datasets

Stapor

Schmiester

Wierling

et al. 2019

Preprint

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Quantitative dynamical models are widely used to study cellular signal processing. A critical step in modeling is the estimation of unknown model parameters from experimental data. As model sizes and datasets are steadily growing, established parameter optimization approaches for mechanistic models become computationally extremely challenging. However, mini-batch optimization methods, as employed in deep learning, have better scaling properties. In this work, we adapt, apply, and benchmark minibatch optimization for ordinary differential equation (ODE) models thereby establishing a direct link between dynamic modeling and machine learning. On our main application example, a large-scale model of cancer signaling, we benchmark mini-batch optimization against established methods, achieving better optimization results and reducing computation by more than an order of magnitude. We expect that our work will serve as a first step towards mini-batch optimization tailored to ODE models and enable modeling of even larger and more complex systems than what is currently possible.

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Challenges in the calibration of large-scale ordinary differential equation models

Cited by 2 publications

References 50 publications

Optimal Paths Between Parameter Estimates in Non-linear ODE Systems Using the Nudged Elastic Band Method

Optimal Paths Between Parameter Estimates in Non-linear ODE Systems Using the Nudged Elastic Band Method

Mini-batch optimization enables training of ODE models on large-scale datasets

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