Surrogate-Based Optimization for Marine Ecosystem Models

Marine ecosystem models are of great importance for understanding the oceanic uptake of carbon dioxide and for projections of the marine ecosystem’s responses to climate change. The applicability of a marine ecosystem model for prognostic simulations crucially depends on its ability to resemble the actually observed physical and biogeochemical processes. An assessment of the quality of a given model is typically based on its calibration against observed quantities. This calibration or optimization process is intrinsically linked to an adjustment of typically poorly known model parameters. Straightforward calibration attempts by direct adjustment of the model parameters using conventional optimization algorithms are often tedious or even beyond the capabilities of modern computer power as they normally require a large number of simulations. This typically results in prohibitively high computational cost, particularly if already a single model evaluation involves time-consuming computer simulations. The optimization of coupled hydrodynamical marine ecosystem models simulating biogeochemical processes in the ocean is here a representative example. Computing times of hours up to several days already for a single model evaluation are not uncommon. A computationally efficient optimization of expensive simulation models can be realized using for example surrogate-based optimization. Therein, the optimization of the expensive, so-called high-fidelity (or fine) model is carried out by means of a surrogate – a fine model’s fast but yet reasonably accurate representation. This work comprises an investigation and application of surrogate-based optimization methodologies employing physics-based low-fidelity (or coarse) models. Seeking a computationally efficient calibration of marine ecosystem models serves as the fundamental aim. As a case study, two illustrative marine ecosystem models are considered. Here, coarse models obtained by a coarser temporal resolution and by a truncated model spin-up are investigated. The accuracy of these computationally cheaper coarse models is typically not sufficient to directly exploit them in the optimization loop in lieu of the fine model. I investigate suitable correction techniques to ensure that the corrected coarse model (the surrogate) provides a reliable prediction of the fine model optimum. Firstly, I focus on Aggressive Space Mapping as one of the original Space Mapping approaches. It will be shown that this optimization method allows to achieve a reasonable reduction in the optimization costs, provided that the considered coarse and fine model are sufficiently “similar”. A multiplicative response correction approach, subsequently investigated, turned out to be very suitable for the considered marine ecosystem models. A reliable surrogate can be obtained. Exploiting the latter in a surrogate-based optimization algorithm, a computationally cheap but yet accurate solution is achieved. The optimization costs can be significantly reduced compared to what is achieved by the Aggressive Space Mapping algorithm. The proposed methodologies, particularly the multiplicative response correction approach, serve as initial parts of a set of tools for a computationally efficient calibration of marine ecosystem models. The investigation of further enhancements of the presented algorithms as well as other promising approaches in the framework of surrogate-based optimization will be highly valuable

Aggressive Space Mapping for the Optimization of a Marine Ecosystem Model

In this paper we apply the Aggressive Space Mapping (ASM) algorithm by Bandler et. al. to the parameter optimization of a one-dimensional marine ecosystem model of NPZD type. We show that this approach leads to a very satisfactory solution while yielding a significant reduction in the total optimization cost. The ecosystem model, developed by Oschlies and Garcon, simulates the distribution of nitrogen, phytoplankton, zooplankton and detritus in a water column and is driven by ocean circulation data. A key issue is to optimize model parameters in order to minimize the misfit between the model output and given observational data. In the ASM approach, reducing the overall optimization cost by avoiding expensive function and derivative evaluations is achieved by using a surrogate model that replaces the original one. Furthermore the ASM algorithm solves a nonlinear system of equations which is conditionally equivalent to use this surrogate in the optimization run. We use a coarser time discretization for obtaining a suitable low-fidelity model. This is then corrected to create a physically-based surrogate, where the correction is obtained through a parameter mapping which provides the minimizer of the distance between the fine and the coarse model output. We show that this surrogate provides a good approximation of the fine model. The applicability of the ASM technique to the problem at hand is verified by using synthetic target data. Results are compared to those of the direct fine model optimization. We show that a very reasonable fit of the target data can be obtained with an average reduction in the computational cost of about 65 %

Surrogat-Basierte Optimierung für Marine Ökosystem-Modelle

Marine ecosystem models are of great importance for understanding the oceanic uptake of carbon dioxide and for projections of the marine ecosystem’s responses to climate change. The applicability of a marine ecosystem model for prognostic simulations crucially depends on its ability to resemble the actually observed physical and biogeochemical processes. An assessment of the quality of a given model is typically based on its calibration against observed quantities. This calibration or optimization process is intrinsically linked to an adjustment of typically poorly known model parameters. Straightforward calibration attempts by direct adjustment of the model parameters using conventional optimization algorithms are often tedious or even beyond the capabilities of modern computer power as they normally require a large number of simulations. This typically results in prohibitively high computational cost, particularly if already a single model evaluation involves time-consuming computer simulations. The optimization of coupled hydrodynamical marine ecosystem models simulating biogeochemical processes in the ocean is here a representative example. Computing times of hours up to several days already for a single model evaluation are not uncommon. A computationally efficient optimization of expensive simulation models can be realized using for example surrogate-based optimization. Therein, the optimization of the expensive, so-called high-fidelity (or fine) model is carried out by means of a surrogate – a fine model’s fast but yet reasonably accurate representation. This work comprises an investigation and application of surrogate-based optimization methodologies employing physics-based low-fidelity (or coarse) models. Seeking a computationally efficient calibration of marine ecosystem models serves as the fundamental aim. As a case study, two illustrative marine ecosystem models are considered. Here, coarse models obtained by a coarser temporal resolution and by a truncated model spin-up are investigated. The accuracy of these computationally cheaper coarse models is typically not sufficient to directly exploit them in the optimization loop in lieu of the fine model. I investigate suitable correction techniques to ensure that the corrected coarse model (the surrogate) provides a reliable prediction of the fine model optimum. Firstly, I focus on Aggressive Space Mapping as one of the original Space Mapping approaches. It will be shown that this optimization method allows to achieve a reasonable reduction in the optimization costs, provided that the considered coarse and fine model are sufficiently “similar”. A multiplicative response correction approach, subsequently investigated, turned out to be very suitable for the considered marine ecosystem models. A reliable surrogate can be obtained. Exploiting the latter in a surrogate-based optimization algorithm, a computationally cheap but yet accurate solution is achieved. The optimization costs can be significantly reduced compared to what is achieved by the Aggressive Space Mapping algorithm. The proposed methodologies, particularly the multiplicative response correction approach, serve as initial parts of a set of tools for a computationally efficient calibration of marine ecosystem models. The investigation of further enhancements of the presented algorithms as well as other promising approaches in the framework of surrogate-based optimization will be highly valuable.Marine Ökosystem-Modelle sind von großer Bedeutung, um die ozeanische Aufnahme von Kohlendioxid zu verstehen sowie Vorhersagen über die Reaktionen des marinen Ökosystems auf den Klimawandel treffen zu können. Die Anwendbarkeit eines marinen Ökosystem-Modells für prognostische Simulationen hängt entscheidend von seiner Fähigkeit ab, die tatsächlich beobachteten physikalischen und biogeochemischen Prozesse wiederzugeben. Um die Qualität von verschiedenen Modellen zu validieren, werden diese typischerweise an vorhandene Beobachtungsdaten angeglichen. Diese Validierung (oder Parameter- Identifikation) erfordert die Anpassungen von in der Regel wenig bekannten Modellparametern. Die direkte Kalibrierung des Modells mit Hilfe konventioneller Optimierungsalgorithmen ist üblicherweise ein langwieriger Prozess, der gegebenenfalls sogar jenseits verfügbarer Rechenressourcen liegt. Ein Grund dafür ist die meist große Zahl erforderlicher Modellsimulationen. Dies führt insbesondere dann zu einem erheblichen Rechenaufwand, wenn bereits eine einzelne Modellauswertung teure Computersimulationen notwendig macht. Ein Beispiel hierfür ist die Kalibrierung gekoppelter mariner Ökosystem-Modelle. Rechenzeiten von Stunden bis hin zu mehreren Tagen für eine einzelne Modellauswertung sind nicht unüblich. Eine effiziente Optimierung von teuren Computermodellen lässt sich beispielsweise mit Hilfe von surrogat-basierten Optimierungsverfahren realisieren. Ein Surrogat – eine schnelle aber dennoch ausreichend genaue Approximation des sogenannten feinen Modells – ermöglicht hierbei dessen Optimierung. Diese Arbeit umfasst die Untersuchung und Anwendung von Verfahren im Rahmen surrogat-basierter Optimierungsalgorithmen, bei denen die Surrogate auf sogenannten physikalischen groben Modellen beruhen. Übergreifendes Ziel ist eine effiziente und schnelle Kalibrierung von marinen Ökosystem-Modellen. Es werden zwei illustrative Modelle betrachtet. Die dazugehörigen groben Modelle werden beispielhaft durch grobe zeitliche Diskretisierung sowie durch einen verkürzten Modell-Spin-Up gewonnen. In der Regel sind solche groben Modelle nicht genau genug, um sie in der Optimierung direkt als Ersatz der feinen Modelle zu verwenden. Mit Hilfe geeigneter Techniken zur Korrektur der groben Modelle konstruiere ich daher ausreichend genaue Surrogate. Zuerst nutze ich hierfür Aggressive Space Mapping, einen der ursprünglichen Space Mapping-Algorithmen. Es wird gezeigt, dass dieses Optimierungsverfahren eine hinreichende Reduktion der Optimierungskosten erzielen kann, vorausgesetzt, das grobe und feine Modell stimmen ausreichend überein. Anschließend betrachte ich eine multiplikative Korrektur. Wie gezeigt wird, ist dieser Ansatz für die betrachteten Modelle gut geeignet. Zusätzlich ist die Optimierung der damit konstruierten Surrogate kostengünstig, erzielt aber dennoch eine ausreichend präzise Lösung. Die Optimierungskosten lassen sich hierbei deutlich gegenüber dem Aggressive Space Mapping-Algorithmus senken. Die vorgestellten Verfahren, insbesondere die multiplikative Korrektur, stellen erste Teile einer Sammlung von Tools für eine effiziente Kalibrierung mariner Ökosystem-Modelle dar. Die Untersuchung weiterer Verbesserungen der betrachteten Methoden sowie anderer möglicher Ansätze im Rahmen surrogat-basierter Optimierung ist vielversprechend

Surrogate-Based Optimization of Climate Model Parameters Using Response Correction

We present a computationally efficient methodology for the optimization of climate model parameters applied to a (one-dimensional) representative of a class of marine ecosystem models. We use a response correction technique to create a surrogate from a temporarily coarser discretized physics-based low-fidelity model. We demonstrate that replacing the direct parameter optimization of the high-fidelity ecosystem model by iteratively updating and re-optimizing the surrogate leads to a very satisfactory solution while yielding significant cost saving - about 84\% when compared to the direct high-fidelity model optimization

A Fast and Robust Optimization Methodology for a Marine Ecosystem Model Using Surrogates

Model calibration in climate science plays a key role for simulations and predictions of the earth's climate system. Straightforward attempts by employing the high-fidelity (or fine) model under consideration directly in an optimization loop using conventional optimization algorithms are often tedious or even infeasible, since typically a large number of computationally expensive fine model evaluations are required. The development of faster methods becomes critical, where the optimization of coupled marine ecosystem models, which simulate biogeochemical processes in the ocean, are a representative example. In this paper, we introduce a surrogate-based optimization (SBO) methodology where the expensive fine model is replaced by its fast and yet reasonably accurate surrogate. As a case study, we consider a representative of the class of one-dimensional marine ecosystem models. The surrogate is obtained from a temporarily coarser discretized physics-based low-fidelity (or coarse) model. and a multiplicative response correction technique. In our previous work, a basic formulation of this surrogate was sufficient to create a reliable approximation, yielding a remarkably accurate solution at low computational costs. This was verified by model generated, attainable data. The application on real data is covered in this paper. Enhancements of the basic formulation by utilizing additionally fine and coarse model sensitivity information as well as trust-region convergence safeguards allow us to further improve the robustness of the algorithm and the accuracy of the solution. The trade-offs between the solution accuracy and the extra computational overhead related to sensitivity calculation will be addressed. We demonstrate that SBO is able to yield a very accurate solution at still low computational costs. The optimization process - when compared to the direct fine model optimization - is significantly speed up to about 85 \%