Dr. Claudine von Hallern

@article{08085ea3a52c433db6ead498660ba4e2,

title = "An exponential stochastic Runge-Kutta type method of order up to 1.5 for SPDEs of Nemytskii-type",

keywords = "Exponential integrator, Higher order method, Stochastic evolution equation, Stochastic partial differential equation, Stochastic runge-kutta type method",

author = "{von Hallern}, Claudine and Ricarda Missfeldt and Andreas Roessler",

year = "2024",

month = oct,

day = "16",

doi = "10.1093/imanum/drae064",

language = "English",

journal = "IMA Journal of Numerical Analysis",

issn = "0272-4979",

publisher = "Oxford University Press",

@article{2e21e38b4abc495687eb360d09cc662c,

title = "A CMA‐ES Algorithm Allowing for Random Parameters in Model Calibration",

abstract = "In geoscience and other fields, researchers use models as a simplified representation of reality. The models include processes that often rely on uncertain parameters that reduce model performance in reflecting real‐world processes. The problem is commonly addressed by adapting parameter values to reach a good match between model simulations and corresponding observations. Different optimization tools have been successfully applied to address this task of model calibration. However, seeking one best value for every single model parameter might not always be optimal. For example, if model equations integrate over multiple real‐world processes which cannot be fully resolved, it might be preferable to consider associated model parameters as random parameters. In this paper, a random parameter is drawn from a wide probability distribution for every singe model simulation. We developed an optimization approach that allows us to declare certain parameters random while optimizing those that are assumed to take fixed values. We designed a corresponding variant of the well known Covariance Matrix Adaption Evolution Strategy (CMA‐ES). The new algorithm was applied to a global biogeochemical circulation model to quantify the impact of zooplankton mortality on the underlying biogeochemistry. Compared to the deterministic CMA‐ES, our new method converges to a solution that better suits the credible range of the corresponding random parameter with less computational effort.",

keywords = "misfit expectation, model calibration, parametric uncertainty",

author = "Volkmar Sauerland and {von Hallern}, Claudine and Iris Kriest and Julia Getzlaff",

year = "2023",

month = aug,

day = "1",

doi = "10.1029/2022ms003390",

language = "English",

volume = "15",

journal = "Journal of Advances in Modeling Earth Systems (JAMES)",

issn = "1942-2466",

publisher = "American Geophysical Union",

number = "8",

@article{aa7f8b0d2906415ebc75dcbcef26ee41,

title = "A derivative-free Milstein type approximation method for SPDEs covering the non-commutative noise case",

abstract = "We propose a derivative-free Milstein type scheme to approximate the mild solution of stochastic partial differential equations (SPDEs) that do not need to fulfill a commutativity condition for the noise term. The newly developed derivative-free Milstein type scheme differs significantly from schemes that are appropriate for the case of commutative noise. As a key result, the new derivative-free Milstein type scheme needs only two stages that are specifically tailored based on a technique that, compared to the original Milstein scheme, allows for a reduction of the computational complexity by one order of magnitude. Moreover, the proposed derivative-free Milstein scheme can flexibly be combined with some approximation method for the involved iterated stochastic integrals. As the main result, we prove the strong L^2-convergence of the introduced derivative-free Milstein type scheme, especially if it is combined with any suitable approximation algorithm for the necessary iterated stochastic integrals. We carry out a rigorous analysis of the error versus computational cost and derive the effective order of convergence for the derivative-free Milstein type scheme in the case that the truncated Fourier series algorithm for the approximation of the iterated stochastic integrals is applied. As a further novelty, we show that the use of approximations of iterated stochastic integrals based on truncated Fourier series together with the proposed derivative-free Milstein type scheme improves the effective order of convergence compared to that of the Euler scheme and the original Milstein scheme. This result is contrary to well known results in the finite dimensional SDE case where the use of merely truncated Fourier series does not improve the effective order of convergence in the L^2-sense compared to that of the Euler scheme. ",

keywords = "Iterated stochastic integral, Milstein scheme, Non-commutative noise, Numerical analysis, Stochastic evolution equation, Stochastic partial differential equation",

author = "{von Hallern}, Claudine and Andreas R{\"o}{\ss}ler",

year = "2022",

month = oct,

day = "4",

doi = "10.1007/s40072-022-00274-6",

language = "English",

volume = "11",

pages = "1672–1731",

journal = "Stochastics and Partial Differential Equations: Analysis and Computations",

issn = "2194-0401",

publisher = "Springer New York",

@article{2252df09ac1042eb9e0555b224ab036d,

title = "Iterated stochastic integrals in infinite dimensions: approximation and error estimates",

abstract = "Higher order numerical schemes for stochastic partial differential equations that do not possess commutative noise require the simulation of iterated stochastic integrals. In this work, we extend the algorithms derived by Kloeden et al. (Stoch Anal Appl 10(4):431–441, 1992. https://doi.org/10.1080/07362999208809281) and by Wiktorsson (Ann Appl Probab 11(2):470–487, 2001. https://doi.org/10.1214/aoap/1015345301) for the approximation of two-times iterated stochastic integrals involved in numerical schemes for finite dimensional stochastic ordinary differential equations to an infinite dimensional setting. These methods clear the way for new types of approximation schemes for SPDEs without commutative noise. Precisely, we analyze two algorithms to approximate two-times iterated integrals with respect to an infinite dimensional Q-Wiener process in case of a trace class operator Q given the increments of the Q-Wiener process. Error estimates in the mean-square sense are derived and discussed for both methods. In contrast to the finite dimensional setting, which is contained as a special case, the optimal approximation algorithm cannot be uniquely determined but is dependent on the covariance operator Q. This difference arises as the stochastic process is of infinite dimension.",

author = "Claudine Leonhard and Andreas R{\"o}{\ss}ler",

year = "2019",

doi = "10.1007/s40072-018-0126-9",

language = "English",

volume = "7",

pages = "209--239",

journal = "Stochastics and Partial Differential Equations: Analysis and Computations",

issn = "2194-0401",

publisher = "Springer New York",

@article{cee51911e81c4f0ab6f0a27518dd24af,

title = "Enhancing the Order of the Milstein Scheme for Stochastic Partial Differential Equations with Commutative Noise",

abstract = "We consider a higher-order Milstein scheme for stochastic partial differential equations (SPDEs) with trace class noise which fulfill a certain commutativity condition. A novel technique to generally improve the order of convergence of Taylor schemes for SPDEs is introduced. The key tool is an efficient approximation of the Milstein term by particularly tailored nested derivative-free terms. For the resulting derivative-free Milstein scheme the computational cost is, in general, considerably reduced by some power. Further, a rigorous computational cost model is considered, and the so-called effective order of convergence is introduced, which allows direct comparison of various numerical schemes in terms of their efficiency. As the main result, we prove for a broad class of SPDEs, including equations with operators that do not need to be pointwise multiplicative, that the effective order of convergence of the proposed derivative-free Milstein scheme is significantly higher than for the original Milstein scheme. In this case, the derivative-free Milstein scheme outperforms the Euler scheme as well as the original Milstein scheme due to the reduction of the computational cost. Finally, we present some numerical examples that confirm the theoretical results.",

author = "Claudine Leonhard and Andreas R{\"o}{\ss}ler",

year = "2018",

doi = "10.1137/16m1094087",

language = "English",

journal = "SIAM Journal on Numerical Analysis",

issn = "0036-1429",

publisher = "Society for Industrial and Applied Mathematics Publications",

@article{d366315d9b0a4c0a8891d54a740c4542,

title = "Error assessment of biogeochemical models by lower bound methods (NOMMA-1.0)",

abstract = "Biogeochemical models, capturing the major feedbacks of the pelagic ecosystem of the world ocean, are today often embedded into Earth system models which are increasingly used for decision making regarding climate policies. These models contain poorly constrained parameters (e.g., maximum phytoplankton growth rate), which are typically adjusted until the model shows reasonable behavior. Systematic approaches determine these parameters by minimizing the misfit between the model and observational data. In most common model approaches, however, the underlying functions mimicking the biogeochemical processes are nonlinear and non-convex. Thus, systematic optimization algorithms are likely to get trapped in local minima and might lead to non-optimal results. To judge the quality of an obtained parameter estimate, we propose determining a preferably large lower bound for the global optimum that is relatively easy to obtain and that will help to assess the quality of an optimum, generated by an optimization algorithm. Due to the unavoidable noise component in all observations, such a lower bound is typically larger than zero. We suggest deriving such lower bounds based on typical properties of biogeochemical models (e.g., a limited number of extremes and a bounded time derivative). We illustrate the applicability of the method with two real-world examples. The first example uses real-world observations of the Baltic Sea in a box model setup. The second example considers a three-dimensional coupled ocean circulation model in combination with satellite chlorophyll a.",

author = "Volkmar Sauerland and Ulrike L{\"o}ptien and Claudine Leonhard and Andreas Oschlies and Anand Srivastav",

year = "2018",

doi = "10.5194/gmd-11-1181-2018",

language = "English",

volume = "11",

journal = "Geoscientific Model Development",

issn = "1991-959X",

publisher = "Copernicus Publications",

number = "3",

@article{9cbe0f69daa44d5296a15c8c5de20680,

title = "Stress-Related Changes in Body Form: Results from the Whitehall II Study",

abstract = "Objective: Stress is associated with body mass gain in some people but with body mass loss in others. When the stressor persists, some people adapt with their stress responses, whereas others do not. Heart rate variability (HRV) reflects autonomic variability and is related to stress responses to psychosocial challenges. It was hypothesized that the combined effects of stress exposure and autonomic variability predict long-term changes in body form. Methods: Data of 1,369 men and 612 women from the Whitehall II cohort were analyzed. BMI, hip-to-height ratio, and waist-to-height ratio were measured at three time points over a 10-year period. HRV and psychological distress (General Health Questionnaire) were assessed. Results: Men with high psychological distress were at risk of developing an increased waist-to-height ratio (F = 3.4, P = 0.038). Men with high psychological distress and low HRV were prone to develop an increased body mass and hip-to-height ratio (psychological distress: F = 4.3, P = 0.016; HRV: F = 5.0, P = 0.008). Statistical trends showed that women displayed similar patterns of stress-related changes in body form (P = 0.061; P = 0.063). Conclusions: Assessing psychological distress and autonomic variability predicts changes in body form. Psychological distress was found to be associated with an increased risk of developing the wide-waisted phenotype, while psychological distress combined with low autonomic variability was associated with an increased risk of developing the corpulent phenotype.",

keywords = "Aged, Cohort Studies, Female, Heart Rate/physiology, Humans, Male, Middle Aged, Stress, Psychological/physiopathology",

author = "Britta Kubera and Claudine Leonhard and Andreas R{\"o}{\ss}ler and Achim Peters",

year = "2017",

month = sep,

doi = "10.1002/oby.21928",

language = "English",

volume = "25",

pages = "1625--1632",

journal = "Obesity",

issn = "1930-7381",

publisher = "John Wiley and Sons Inc.",

number = "9",