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

2019 ◽  
Author(s):  
Eva-Maria Kapfer ◽  
Paul Stapor ◽  
Jan Hasenauer

AbstractMathematical models based on ordinary differential equations have been employed with great success to study complex biological systems. With soaring data availability, more and more models of increasing size are being developed. When working with these large-scale models, several challenges arise, such as high computation times or poor identifiability of model parameters. In this work, we review and illustrate the most common challenges using a published model of cellular metabolism. We summarize currently available methods to deal with some of these challenges while focusing on reproducibility and reusability of models, efficient and robust model simulation and parameter estimation.

2021 ◽  
Author(s):  
Kor de Jong ◽  
Marc van Kreveld ◽  
Debabrata Panja ◽  
Oliver Schmitz ◽  
Derek Karssenberg

<p>Data availability at global scale is increasing exponentially. Although considerable challenges remain regarding the identification of model structure and parameters of continental scale hydrological models, we will soon reach the situation that global scale models could be defined at very high resolutions close to 100 m or less. One of the key challenges is how to make simulations of these ultra-high resolution models tractable ([1]).</p><p>Our research contributes by the development of a model building framework that is specifically designed to distribute calculations over multiple cluster nodes. This framework enables domain experts like hydrologists to develop their own large scale models, using a scripting language like Python, without the need to acquire the skills to develop low-level computer code for parallel and distributed computing.</p><p>We present the design and implementation of this software framework and illustrate its use with a prototype 100 m, 1 h continental scale hydrological model. Our modelling framework ensures that any model built with it is parallelized. This is made possible by providing the model builder with a set of building blocks of models, which are coded in such a manner that parallelization of calculations occurs within and across these building blocks, for any combination of building blocks. There is thus full flexibility on the side of the modeller, without losing performance.</p><p>This breakthrough is made possible by applying a novel approach to the implementation of the model building framework, called asynchronous many-tasks, provided by the HPX C++ software library ([3]). The code in the model building framework expresses spatial operations as large collections of interdependent tasks that can be executed efficiently on individual laptops as well as computer clusters ([2]). Our framework currently includes the most essential operations for building large scale hydrological models, including those for simulating transport of material through a flow direction network. By combining these operations, we rebuilt an existing 100 m, 1 h resolution model, thus far used for simulations of small catchments, requiring limited coding as we only had to replace the computational back end of the existing model. Runs at continental scale on a computer cluster show acceptable strong and weak scaling providing a strong indication that global simulations at this resolution will soon be possible, technically speaking.</p><p>Future work will focus on extending the set of modelling operations and adding scalable I/O, after which existing models that are currently limited in their ability to use the computational resources available to them can be ported to this new environment.</p><p>More information about our modelling framework is at https://lue.computationalgeography.org.</p><p><strong>References</strong></p><p>[1] M. Bierkens. Global hydrology 2015: State, trends, and directions. Water Resources Research, 51(7):4923–4947, 2015.<br>[2] K. de Jong, et al. An environmental modelling framework based on asynchronous many-tasks: scalability and usability. Submitted.<br>[3] H. Kaiser, et al. HPX - The C++ standard library for parallelism and concurrency. Journal of Open Source Software, 5(53):2352, 2020.</p>


1962 ◽  
Vol 84 (1) ◽  
pp. 13-20 ◽  
Author(s):  
L. Markus ◽  
E. B. Lee

The problem of existence of various types of optimum controls for controlling processes which are described by ordinary differential equation models is considered. The results presented enable one to test if there does exist an optimum control in the class of controls under consideration before proceeding to the construction of an optimal control.


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