arXiv subjects

Thomas Slawig

Publications and source records attributed to Thomas Slawig.

14 recordsLinked to original sources

arXiv2025

Prediction of steady states in a marine ecosystem model by a machine learning technique

We used precomputed steady states obtained by a spin-up for a global marine ecosystem model as training data to build a mapping from the small number of biogeochemical model parameters onto the three-dimensional converged steady annual cycle. The mapping was performed by a conditional variational autoencoder (CVAE) with mass correction. Applied for test data, we show that the prediction obtained by the CVAE already gives a reasonable good approximation of the steady states obtained by a regular spin-up. However, the predictions do not reach the same level of annual periodicity as those obtained in the original spin-up data. Thus, we took the predictions as initial values for a spin-up. We could show that the number of necessary iterations, corresponding to model years, to reach a prescribed stopping criterion in the spin-up could be significantly reduced compared to the use of the originally uniform, constant initial value. The amount of reduction depends on the applied stopping criterion, measuring the periodicity of the solution. The savings in needed iterations and, thus, computing time for the spin-up ranges from 50 to 95\%, depending on the stopping criterion for the spin-up. We compared these results with the use of the mean of the training data as an initial value. We found that this also accelerates the spin-up, but only by a much lower factor.

physics.ao-ph↗

arXiv2023

A Micro-Macro parallel-in-time Implementation for the 2D Navier-Stokes Equations

In this paper the Micro-Macro Parareal algorithm was adapted to PDEs. The parallel-in-time approach requires two meshes of different spatial resolution in order to compute approximations in an iterative way to a predefined reference solution. When fast convergence in few iterations can be accomplished the algorithm is able to generate wall-time reduction in comparison to the serial computation. We chose the laminar flow around a cylinder benchmark on 2-dimensional domain which was simulated with the open-source software OpenFoam. The numerical experiments presented in this work aim to approximate states local in time and space and the diagnostic lift coefficient. The Reynolds number is gradually increased from 100 to 1,000, before the transition to turbulent flows sets in. After the results are presented the convergence behavior is discussed with respect to the Reynolds number and the applied interpolation schemes.

math.NA↗

arXiv2023

A micro/macro parallel-in-time (parareal) algorithm applied to a climate model with discontinuous non-monotone coefficients and oscillatory forcing

We present the application of a micro/macro parareal algorithm for a 1-D energy balance climate model with discontinuous and non-monotone coefficients and forcing terms. The micro/macro parareal method uses a coarse propagator, based on a (macroscopic) 0-D approximation of the underlying (microscopic) 1-D model. We compare the performance of the method using different versions of the macro model, as well as different numerical schemes for the micro propagator, namely an explicit Euler method with constant stepsize and an adaptive library routine. We study convergence of the method and the theoretical gain in computational time in a realization on parallel processors. We show that, in this example and for all settings, the micro/macro parareal method converges in fewer iterations than the number of used parareal subintervals, and that a theoretical gain in performance of up to 10 is possible.

math.NA↗

arXiv2022

The Parareal Algorithm Applied to the FESOM 2 Ocean Circulation Model

In this work the parallel-in-time algorithm Parareal was applied to the ocean-circulation and sea-ice model FESOM2 developed by the Alfred-Wegener Institut (AWI). The climate model provides one time integration method and hence, the coarse and fine propagators were defined by time step width. The coarse method was executed at the CFL condition limit, while fine step-sizes where gradually refined. As a first assessment of the performance of Parareal a low-resolution test mesh was used with default settings provided by the AWI. An introduction to FESOM2 and the straightforward implementation of Parareal on the DKRZ cluster is given. The evaluation of numerical results for different simulation intervals and fine propagator configurations shows strong dependence on the simulation time and time step-size of the fine propagator. Increasing the latter leads to stagnation and eventually divergence of the Parareal algorithm.

math.NA↗

arXiv2022

Adaptive Time Step Algorithms for the Simulation of marine Ecosystem Models using the Transport Matrix Method Implementation Metos3D

The reduction of the computational effort is desirable for the simulation of marine ecosystem models. Using a marine ecosystem model, the assessment and the validation of annual periodic solutions (i.e., steady annual cycles) against observational data are crucial to identify biogeochemical processes, which, for example, influence the global carbon cycle. For marine ecosystem models, the transport matrix method (TMM) already lowers the runtime of the simulation significantly and enables the application of larger time steps straightforwardly. However, the selection of an appropriate time step is a challenging compromise between accuracy and shortening the runtime. Using an automatic time step adjustment during the computation of a steady annual cycle with the TMM, we present in this paper different algorithms applying either an adaptive step size control or decreasing time steps in order to use the time step always as large as possible without any manual selection. For these methods and a variety of marine ecosystem models of different complexity, the accuracy of the computed steady annual cycle achieved the same accuracy as solutions obtained with a fixed time step. Depending on the complexity of the marine ecosystem model, the application of the methods shortened the runtime significantly. Due to the certain overhead of the adaptive method, the computational effort may be higher in special cases using the adaptive step size control. The presented methods represent computational efficient methods for the simulation of marine ecosystem models using the TMM but without any manual selection of the time step.

q-bio.PE↗

arXiv2021

Unique steady annual cycle in marine ecosystem model simulations

Marine ecosystem models are an important tool to assess the role of the ocean biota in climate change and to identify relevant biogeochemical processes by validating the model outputs against observational data. For the assessment of the marine ecosystem models, the existence and uniqueness of an annual periodic solution (i.e., a steady annual cycle) is desirable. To analyze the uniqueness of a steady annual cycle, we performed a larger number of simulations starting from different initial concentrations for a hierarchy of biogeochemical models with an increasing complexity. The numerical results suggested that the simulations finished always with the same steady annual cycle regardless of the initial concentration. Due to numerical instabilities, some inadmissible approximations of the steady annual cycle, however, occurred in some cases for the three most complex biogeochemical models. Our numerical results indicate a unique steady annual cycle for practical applications.

q-bio.PE↗

arXiv2021

Surrogate-based optimization using an artificial neural network for a parameter identification in a 3D marine ecosystem model

Parameter identification for marine ecosystem models is important for the assessment and validation of marine ecosystem models against observational data. The surrogate-based optimization (SBO) is a computationally efficient method to optimize complex models. SBO replaces the computationally expensive (high-fidelity) model by a surrogate constructed from a less accurate but computationally cheaper (low-fidelity) model in combination with an appropriate correction approach, which improves the accuracy of the low-fidelity model. To construct a computationally cheap low-fidelity model, we tested three different approaches to compute an approximation of the annual periodic solution (i.e., a steady annual cycle) of a marine ecosystem model: firstly, a reduced number of spin-up iterations (several decades instead of millennia), secondly, an artificial neural network (ANN) approximating the steady annual cycle and, finally, a combination of both approaches. Except for the low-fidelity model using only the ANN, the SBO yielded a solution close to the target and reduced the computational effort significantly. If an ANN approximating appropriately a marine ecosystem model is available, the SBO using this ANN as low-fidelity model presents a promising and computational efficient method for the validation.

physics.ao-ph↗

arXiv2021

Shortening the runtime using larger time steps for the simulation of marine ecosystem models

The reduction of computational costs for marine ecosystem models is important for the investigation and detection of the relevant biogeochemical processes because such models are computationally expensive. In order to lower these computational costs by means of larger time steps we investigated the accuracy of steady annual cycles (i.e., an annual periodic solution) calculated with different time steps. We compared the accuracy for a hierarchy of biogeochemical models showing an increasing complexity and computed the steady annual cycles with offline simulations that are based on the transport matrix approach. For each of these biogeochemical models, we obtained practically the same solution even though larger time steps. This indicates that larger time steps shortened the runtime with an acceptable loss of accuracy.

q-bio.PE↗

arXiv2021

Simulation of scour around arbitrary offshore foundations based on the Volume-of-Fluid method combined with a Bingham model

This paper presents a method for the simulation of scour around arbitrary offshore structures. It is based on the solution of the Reynolds-Averaged-Navier-Stokes equations implemented in the OpenFOAM framework. The sediment is simulated with the help of a Bingham model, which basically models a solid sediment behavior by introducing a very high viscosity. The relative pressure used by the Bingham model is estimated with a new approach based on the solution of a Poisson equation. The position of the sediment surface is calculated with the Volume-of-Fluid approach using a high-resolution scheme. To keep the typical wall characteristics without demanding a fine grid, the common wall functions are transferred to the domain internal sediment walls. Furthermore, additional modifications are applied to model a solid sediment wall inside the solution domain. The new internal wall function implementation is validated with a 2D test case. The results show a very good agreement to common wall functions and a significant improvement compared to its negligence. Furthermore the solver is used to simulate the scour downstream of an apron and the scour around a vertical cylinder in current. The results are compared to experiments presented in the literature and show good agreement. The applicability onto arbitrary structures is demonstrated by applying the solver onto a vertical cylinder with a mudplate. The current development state is able to resolve all important physical flow and scour phenomena. The results also unveil that modeling of the suspension and the treatment of the internal wall need additional attention.

physics.flu-dyn↗

arXiv2020

Single precision arithmetic in ECHAM radiation reduces runtime and energy consumption

We converted the radiation part of the atmospheric model ECHAM to single precision arithmetic. We analyzed different conversion strategies and finally used a step by step change of all modules, subroutines and functions. We found out that a small code portion still requires higher precision arithmetic. We generated code that can be easily changed from double to single precision and vice versa, basically using a simple switch in one module. We compared the output of the single precision version in the coarse resolution with observational data and with the original double precision code. The results of both versions are comparable. We extensively tested different parallelization options with respect to the possible performance gain, in both coarse and low resolution. The single precision radiation itself was accelerated by about 40%, whereas the speed-up for the whole ECHAM model using the converted radiation achieved 18% in the best configuration. We further measured the energy consumption, which could also be reduced.

physics.ao-ph↗

arXiv2015

Mathematical analysis of a marine ecosystem model with nonlinear coupling terms and non-local boundary conditions

We investigate the weak solvability of initial boundary value problems associated with an ecosystem model of the marine phosphorus cycle. The analysis covers the model equations themselves as well as their linearization which is important in the model calibration via parameter identification. We treat both cases simultaneously by investigating a system of advection-diffusion-reaction equations coupled by general reaction terms and boundary conditions. We derive a weak formulation of the generalized equations and prove two theorems about its unique solvability provided that the reaction terms consist of Lipschitz continuous and monotone operators. In the proofs, we adapt different techniques (Galerkin approximation, Banach's Fixed Point Theorem) to the multi-dimensional model equation. By applying the general theorems to the problems associated with the phosphorus model we obtain results about existence and uniqueness of their solutions. Actually, by assuming a generalized setting the theorems establish the basis for the mathematical analysis of the whole model class to which the investigated phosphorus model belongs.

math.AP↗

arXiv2015

Mathematical analysis of the $PO_4$-$DOP$-$Fe$ marine ecosystem model driven by 3-D ocean transport

Marine ecosystem models are developed to understand and simulate the biogeochemical processes involved in marine ecosystems. Parekh, Follows and Boyle introduced the $PO_4$-$DOP$-$Fe$ model of the coupled phosphorus and iron cycles in 2005. Especially the part describing the phosphorus cycle ($PO_4$-$DOP$ model) is often applied in the context of parameter identification. The mathematical analysis presented in this study is concerned with the existence of solutions and the reconstruction of parameters from given data. Both are important questions in the numerical model's assessment and validation not answered so far. In this study, we obtain transient, stationary and periodic solutions (steady annual cycles) of the $PO_4$-$DOP$-$Fe$ model equations after a slight change in the equation modeling iron. This result confirms the validity of the solutions computed numerically. Furthermore, we present a calculation showing that four of the $PO_4$-$DOP$ model's parameters are possibly dependent, i.e. different parameter values might be associated with the same model output. Thereby, we identify a relevant source of uncertainty in parameter identification. On the basis of the results, possible ways to overcome this deficit can be proposed. In addition, the stated mathematical conditions for solvability are universal and thus applicable to the analysis of other ecosystem models as well.

math.AP↗

arXiv2014

The Idea and Concept of Metos3D: A Marine Ecosystem Toolkit for Optimization and Simulation in 3D

The simulation and parameter optimization of coupled ocean circulation and ecosystem models in three space dimensions is one of the most challenging tasks in numerical climate research. Here we present a scientific toolkit that aims at supporting researchers by defining clear coupling interfaces, providing state-of-the-art numerical methods for simulation, parallelization and optimization while using only freely available and (to a great extend) platform-independent software. Besides defining a user-friendly coupling interface (API) for marine ecosystem or biogeochemical models, we heavily rely on the Portable, Extensible Toolkit for Scientific computation (PETSc) developed at Argonne Nat. Lab. for a wide variety of parallel linear and non-linear solvers and optimizers. We specifically focus on the usage of matrix-free Newton-Krylov methods for the fast computation of steady periodic solutions, and make use of the Transport Matrix Method (TMM) introduced by Khatiwala et al.

physics.ao-ph↗

arXiv2014

Nontrivial Periodic Solutions of Marine Ecosystem Models of N-DOP type

We investigate marine ecosystem models of N-DOP type with regard to nontrivial periodic solutions. The elements of this important, widely-used model class typically consist of two coupled advection-diffusion-reaction equations. The corresponding reaction terms are divided into a linear part, describing the transformation of one model variable into the other, and a bounded nonlinear part. Additionally, the model equations conserve the mass contained in the system, i.e. the masses of both variables add up to a constant total mass. In particular, the trivial function is a periodic solution. In this paper, we prove that there is at least one periodic solution for every prescribed total mass. The proof makes use of the typical properties of N-DOP type models by combining results from monotone operator theory and a fixed point argument. In the end, we apply the theorem to the PO4-DOP model, an N-DOP type model which is well-known and often used.

math.AP↗