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

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

doi:10.1016/j.ifacol.2019.12.236

Cited by 12 publications

(7 citation statements)

References 31 publications

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“…(2019). This method has been shown to scale roughly linearly with respect to the number of free parameters (Kapfer et al., 2019). The cost also depends on the number of equations.…”

Section: Discussionmentioning

confidence: 99%

PyBioNetFit and the Biological Property Specification Language

et al. 2019

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SummaryIn systems biology modeling, important steps include model parameterization, uncertainty quantification, and evaluation of agreement with experimental observations. To help modelers perform these steps, we developed the software PyBioNetFit, which in addition supports checking models against known system properties and solving design problems. PyBioNetFit introduces Biological Property Specification Language (BPSL) for the formal declaration of system properties. BPSL allows qualitative data to be used alone or in combination with quantitative data. PyBioNetFit performs parameterization with parallelized metaheuristic optimization algorithms that work directly with existing model definition standards: BioNetGen Language (BNGL) and Systems Biology Markup Language (SBML). We demonstrate PyBioNetFit's capabilities by solving various example problems, including the challenging problem of parameterizing a 153-parameter model of cell cycle control in yeast based on both quantitative and qualitative data. We demonstrate the model checking and design applications of PyBioNetFit and BPSL by analyzing a model of targeted drug interventions in autophagy signaling.

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“…(2019). This method has been shown to scale roughly linearly with respect to the number of free parameters (Kapfer et al., 2019). The cost also depends on the number of equations.…”

Section: Discussionmentioning

confidence: 99%

PyBioNetFit and the Biological Property Specification Language

et al. 2019

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“…High performing software packages for ODE integration. It has been shown in several studies that it is critical to use high-performance ODE solver toolboxes written in compiled languages such as C++ or FOR-TRAN, since those have shown to reduce computation time by two to three orders of magnitude 8,30 . For this reason, we focused on the C-based ODE solvers in CVODES, which is part of the SUNDIALS solver package 9 and the LSODA algorithm from the FORTRAN-based ODEPACK suite.…”

Section: Methodsmentioning

confidence: 99%

Benchmarking of numerical integration methods for ODE models of biological systems

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Schälte

Schmiester

et al. 2021

Sci Rep

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Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when unknown parameters need to be inferred. This renders efficient and reliable numerical integration methods essential. However, these methods depend on various hyperparameters, which strongly impact the ODE solution. Despite this, and although hundreds of published ODE models are freely available in public databases, a thorough study that quantifies the impact of hyperparameters on the ODE solver in terms of accuracy and computation time is still missing. In this manuscript, we investigate which choices of algorithms and hyperparameters are generally favorable when dealing with ODE models arising from biological processes. To ensure a representative evaluation, we considered 142 published models. Our study provides evidence that most ODEs in computational biology are stiff, and we give guidelines for the choice of algorithms and hyperparameters. We anticipate that our results will help researchers in systems biology to choose appropriate numerical methods when dealing with ODE models.

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“…Large-scale ODE systems arise in many fields of science and technology, including simulation of orbital dynamics [24]. One of the known computationally expensive tasks in this area is the simulation of N gravitationally connected bodies, especially when N ≥ 3.…”

Section: Three-body Problemmentioning

confidence: 99%

Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

Тутуева

Butusov

2021

Mathematics

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The increasing complexity of advanced devices and systems increases the scale of mathematical models used in computer simulations. Multiparametric analysis and study on long-term time intervals of large-scale systems are computationally expensive. Therefore, efficient numerical methods are required to reduce time costs. Recently, semi-explicit and semi-implicit Adams–Bashforth–Moulton methods have been proposed, showing great computational efficiency in low-dimensional systems simulation. In this study, we examine the numerical stability of these methods by plotting stability regions. We explicitly show that semi-explicit methods possess higher numerical stability than the conventional predictor–corrector algorithms. The second contribution of the reported research is a novel algorithm to generate an optimized finite-difference scheme of semi-explicit and semi-implicit Adams–Bashforth–Moulton methods without redundant computation of predicted values that are not used for correction. The experimental part of the study includes the numerical simulation of the three-body problem and a network of coupled oscillators with a fixed and variable integration step and finely confirms the theoretical findings.

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

Cited by 12 publications

References 31 publications

PyBioNetFit and the Biological Property Specification Language

PyBioNetFit and the Biological Property Specification Language

Benchmarking of numerical integration methods for ODE models of biological systems

Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

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