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Barth, Andrea

Andrea Barth

Prof. Dr.

Head of Group
Institute of Applied Analysis and Numerical Simulation
Research Group for Computational Methods for Uncertainty Quantification

Contact

+49 711 685 60121
Email

Allmandring 5b
70569 Stuttgart
Germany
Room: 01.034

Publications

2023
1. A. Barth and A. Stein, “A stochastic transport problem with Lévy noise: Fully discrete numerical approximation.,” 2023. [Online]. Available: https://arxiv.org/abs/1910.14657
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  BibTeX
  @preprint{journals/corr/abs-1910-14657, author = {Barth, Andrea and Stein, Andreas}, ee = {http://arxiv.org/abs/1910.14657}, title = {A stochastic transport problem with Lévy noise: Fully discrete numerical approximation.}, url = {https://arxiv.org/abs/1910.14657}, year = 2023 }
  Link
  https://arxiv.org/abs/1910.14657
2. C. A. Beschle and A. Barth, “Quasi continuous level Monte Carlo for random elliptic PDEs,” 2023.
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  @unpublished{beschle2023quasi, archiveprefix = {arXiv}, author = {Beschle, Cedric Aaron and Barth, Andrea}, eprint = {2303.08694}, primaryclass = {math.NA}, title = {Quasi continuous level Monte Carlo for random elliptic PDEs}, year = 2023 }
3. R. Merkle and A. Barth, “On Properties and Applications of Gaussian Subordinated Lévy Fields,” Methodology and computing in applied probability, vol. 25, pp. 1–33, 2023, doi: 10.1007/s11009-023-10033-2.
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  @article{merkle2023properties, author = {Merkle, Robin and Barth, Andrea}, doi = {10.1007/s11009-023-10033-2}, issn = {1573-7713}, journal = {Methodology and computing in applied probability}, language = {eng}, pages = {1-33}, publisher = {Springer}, title = {On Properties and Applications of Gaussian Subordinated Lévy Fields}, volume = 25, year = 2023 }
2022
1. C. Beschle and A. Barth, “Uncertainty visualization: Fundamentals and recent developments, code to produce data and visuals used in Section 5.” 2022. doi: 10.18419/darus-3154.
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  @misc{beschle2022uncertainty, abstract = {Python Code to generate the meshes and FEM solutions to Section 5 of the paper Uncertainty visualization: Fundamentals and recent developments.Commentaries are in the code to explain it.Paraview is used for the visualization. }, affiliation = {Beschle, Cedric/University of Stuttgart}, author = {Beschle, Cedric and Barth, Andrea}, doi = {10.18419/darus-3154}, howpublished = {Software}, note = {Related to: Hägele, David, Schulz, Christoph, Beschle, Cedric, Booth, Hannah, Butt, Miriam, Barth, Andrea, Deussen, Oliver, & Weiskopf, Daniel (2022). Uncertainty visualization: Fundamentals and recent developments. it - Information Technology 64(4-5), 121-132. doi: 10.1515/itit-2022-0033}, orcid-numbers = {Beschle, Cedric/0000-0002-3884-9128}, title = {Uncertainty visualization: Fundamentals and recent developments, code to produce data and visuals used in Section 5}, year = 2022 }
2. D. Hägele et al., “Uncertainty visualization : Fundamentals and recent developments,” Information technology, vol. 64, no. 4–5, Art. no. 4–5, 2022, doi: 10.1515/itit-2022-0033.
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  @article{hagele2022uncertainty, affiliation = {Hagele, D (Corresponding Author), Univ Stuttgart, Visualizat Res Ctr, D-70569 Stuttgart, Germany. Haegele, David; Schulz, Christoph; Weiskopf, Daniel, Univ Stuttgart, Visualizat Res Ctr, D-70569 Stuttgart, Germany. Beschle, Cedric; Barth, Andrea, Univ Stuttgart, Inst Appl Anal & Numer Simulat, D-70569 Stuttgart, Germany. Booth, Hannah, Univ Ghent, Dept Linguist, B-9000 Ghent, Belgium. Butt, Miriam, Univ Konstanz, Dept Linguist, D-78457 Constance, Germany. Deussen, Oliver, Univ Konstanz, Dept Comp & Informat Sci, D-78457 Constance, Germany.}, author = {Hägele, David and Schulz, Christoph and Beschle, Cedric and Booth, Hannah and Butt, Miriam and Barth, Andrea and Deussen, Oliver and Weiskopf, Daniel}, doi = {10.1515/itit-2022-0033}, issn = {{1611-2776} and {2196-7032}}, journal = {Information technology}, language = {eng}, number = {4-5}, pages = {121-132}, publisher = {De Gruyter}, research-areas = {Computer Science}, title = {Uncertainty visualization : Fundamentals and recent developments}, unique-id = {WOS:000847536200001}, volume = 64, year = 2022 }
3. L. Mehl, C. Beschle, A. Barth, and A. Bruhn, “Replication Data for: An Anisotropic Selection Scheme for Variational Optical Flow Methods with Order-Adaptive Regularisation.” 2022. doi: 10.18419/darus-2890.
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  @misc{mehl2022replication, abstract = {Results of our proposed optical flow method on the Sintel and KITTI datasets. We provide the benchmark results before and after applying our refinement approach.Additionally, we provide a supplementary material to our paper with more details on the minimisation, the numerical solution and additional results.The data is structured as follows:The file supplement.pdf contains the supplementary material of the paper.Additionally, there are 10 data folders according to the test results in Table 3 of our paper. They are named using the scheme {input/output}_{datasetName}_{methodName}:input/output: whether the files are the input for our method or the output of our methoddatasetName: one of kitti, sintelClean or sintelFinal relating to either the KITTI dataset [Menze, CVPR 2015] or the Sintel dataset [Butler, ECCV 2012]methodName: one of raft or raftWarm [Teed, ECCV 2020] or the refined variants from our method.The data can be used to build on the output of our method or to compare a novel approach against our method by using the same input data.The dataformat is pdf for the supplementary material and png and flo for the optical flow files as used in the respective benchmarks. }, affiliation = {Mehl, Lukas/Institute for Visualization and Interactive Systems, University of Stuttgart, Beschle, Cedric/Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, Barth, Andrea/Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, Bruhn, Andrés/Institute for Visualization and Interactive Systems, University of Stuttgart}, author = {Mehl, Lukas and Beschle, Cedric and Barth, Andrea and Bruhn, Andrés}, doi = {10.18419/darus-2890}, howpublished = {Dataset}, note = {Related to: L. Mehl, C. Beschle, A. Barth, A. Bruhn: An Anisotropic Selection Scheme for Variational Optical Flow Methods with Order-Adaptive Regularisation. Proc. International Conference on Scale Space and Variational Methods in Computer Vision (SSVM). Lecture Notes in Computer Science, Vol. 10302, 140-152, Springer, 2021. doi: 10.1007/978-3-030-75549-2_12}, orcid-numbers = {Barth, Andrea/0000-0003-1642-3625, Bruhn, Andrés/0000-0003-0423-7411}, title = {Replication Data for: An Anisotropic Selection Scheme for Variational Optical Flow Methods with Order-Adaptive Regularisation}, year = 2022 }
4. R. Merkle and A. Barth, “On Some Distributional Properties of Subordinated Gaussian Random Fields,” Methodology and computing in applied probability, 2022, doi: 10.1007/s11009-022-09958-x.
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  @article{merkle2022distributional, author = {Merkle, Robin and Barth, Andrea}, doi = {10.1007/s11009-022-09958-x}, isbn = {{1387-5841} and {1573-7713}}, journal = {Methodology and computing in applied probability}, language = {eng}, publisher = {Springer}, pubstate = {prepublished}, title = {On Some Distributional Properties of Subordinated Gaussian Random Fields}, year = 2022 }
5. R. Merkle and A. Barth, “Subordinated Gaussian random fields in elliptic partial differential equations,” Stochastics and partial differential equations, 2022, doi: 10.1007/s40072-022-00246-w.
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  @article{merkle2022subordinated, affiliation = {Merkle, R (Corresponding Author), Univ Stuttgart, IANS SimTech, Stuttgart, Germany. Merkle, Robin; Barth, Andrea, Univ Stuttgart, IANS SimTech, Stuttgart, Germany.}, author = {Merkle, Robin and Barth, Andrea}, doi = {10.1007/s40072-022-00246-w}, issn = {{2194-0401} and {2194-041X}}, journal = {Stochastics and partial differential equations}, language = {eng}, publisher = {Springer}, pubstate = {prepublished}, research-areas = {Mathematics}, title = {Subordinated Gaussian random fields in elliptic partial differential equations}, unique-id = {WOS:000770498600001}, year = 2022 }
6. R. Merkle and A. Barth, “Multilevel Monte Carlo estimators for elliptic PDEs with Lévy-type diffusion coefficient,” BIT - numerical mathematics, 2022, doi: 10.1007/s10543-022-00912-4.
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  @article{merkle2022multilevel, affiliation = {Merkle, R (Corresponding Author), Univ Stuttgart, IANS SimTech, Stuttgart, Germany. Merkle, Robin; Barth, Andrea, Univ Stuttgart, IANS SimTech, Stuttgart, Germany.}, author = {Merkle, Robin and Barth, Andrea}, doi = {10.1007/s10543-022-00912-4}, issn = {{0006-3835} and {1572-9125}}, journal = {BIT - numerical mathematics}, language = {eng}, publisher = {Springer}, pubstate = {prepublished}, research-areas = {Computer Science; Mathematics}, title = {Multilevel Monte Carlo estimators for elliptic PDEs with Lévy-type diffusion coefficient}, unique-id = {WOS:000762880200002}, year = 2022 }
2021
1. L. Mehl, C. Beschle, A. Barth, and A. Bruhn, “An Anisotropic Selection Scheme for Variational Optical Flow Methods with Order-Adaptive Regularisation,” Proceedings of the International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), pp. 140--152, 2021, doi: 10.1007/978-3-030-75549-2_12.
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  @article{10.1007/978-3-030-75549-2_12, abstract = {Approaches based on order-adaptive regularisation belong to the most accurate variational methods for computing the optical flow. By locally deciding between first- and second-order regularisation, they are applicable to scenes with both fronto-parallel and ego-motion. So far, however, existing order-adaptive methods have a decisive drawback. While the involved first- and second-order smoothness terms already make use of anisotropic concepts, the underlying selection process itself is still isotropic in that sense that it locally chooses the same regularisation order for all directions. In our paper, we address this shortcoming. We propose a generalised order-adaptive approach that allows to select the local regularisation order for each direction individually. To this end, we split the order-adaptive regularisation across and along the locally dominant direction and perform an energy competition for each direction separately. This in turn offers another advantage. Since the parameters can be chosen differently for both directions, the approach allows for a better adaption to the underlying scene. Experiments for MPI Sintel and KITTI 2015 demonstrate the usefulness of our approach. They not only show improvements compared to an isotropic selection scheme. They also make explicit that our approach is able to improve the results from state-of-the-art learning-based approaches, if applied as a final refinement step – thereby achieving top results in both benchmarks.}, author = {Mehl, Lukas and Beschle, Cedric and Barth, Andrea and Bruhn, Andrés}, booktitle = {Proceedings of the International Conference on Scale Space and Variational Methods in Computer Vision (SSVM)}, doi = {10.1007/978-3-030-75549-2_12}, pages = {140--152}, publisher = {Springer}, title = {An Anisotropic Selection Scheme for Variational Optical Flow Methods with Order-Adaptive Regularisation}, url = {https://link.springer.com/chapter/10.1007%2F978-3-030-75549-2_12}, year = 2021 }
  Link
  https://link.springer.com/chapter/10.1007%2F978-3-030-75549-2_12
2020
1. L. Brencher and A. Barth, “Hyperbolic Conservation Laws with Stochastic Discontinuous Flux Functions,” in Finite Volumes for Complex Applications IX : Methods, Theoretical Aspects, Examples, R. Klöfkorn, E. Keilegavlen, F. A. Radu, and J. Fuhrmann, Eds., in Finite Volumes for Complex Applications IX : Methods, Theoretical Aspects, Examples. Springer, 2020, pp. 265–273. doi: 10.1007/978-3-030-43651-3_23.
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  @inproceedings{brencher2020hyperbolic, abstract = {Hyperbolic conservation laws are utilized to describe a variety of real-world applications, which require the consideration of the influence of uncertain parameters on the solution to the problem. To extend these models, one is often interested in including discontinuities in the state space to the flux function of the conservation law. This paper studies the solution of a stochastic nonlinear hyperbolic partial differential equation (PDE), whose flux function contains random spatial discontinuities. The first part of the paper defines the corresponding stochastic adapted entropy solution and required properties for existence and uniqueness are addressed. The second part contains the numerical simulation of the nonlinear hyperbolic problem as well as the estimation of the expectation of the problem via the multilevel Monte Carlo method.}, address = {Cham}, author = {Brencher, Lukas and Barth, Andrea}, booktitle = {Finite Volumes for Complex Applications IX : Methods, Theoretical Aspects, Examples}, doi = {10.1007/978-3-030-43651-3_23}, editor = {Klöfkorn, Robert and Keilegavlen, Eirik and Radu, Florin A. and Fuhrmann, Jürgen}, eventdate = {2020-06-15/2020-06-19}, eventtitle = {9th International Symposium on Finite Volumes for Complex Applications}, isbn = {{978-3-030-43650-6} and {978-3-030-43651-3}}, language = {eng}, number = 323, pages = {265-273}, publisher = {Springer}, series = {Springer Proceedings in Mathematics & Statistics}, title = {Hyperbolic Conservation Laws with Stochastic Discontinuous Flux Functions}, url = {https://doi.org/10.1007/978-3-030-43651-3_23}, venue = {Online}, year = 2020 }
  Link
  https://doi.org/10.1007/978-3-030-43651-3_23
2019
1. M. Köppel et al., “Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage.” 2019. [Online]. Available: https://zenodo.org/records/933827
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  @misc{UQ_comparison_dataset, abstract = {A variety of methods is available to quantify uncertainties arising within the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of parameters in constitutive relations, and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitrary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation, and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally, we offer suggestions about the methods’ advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond.}, author = {K{\"o}ppel, Markus and Franzelin, Fabian and Kr{\"o}ker, Ilja and Oladyshkin, Sergey and Wittwar, Dominik and Santin, Gabriele and Barth, Andrea and Haasdonk, Bernard and Nowak, Wolfang and Pfl{\"u}ger, Dirk and Rohde, Christian}, howpublished = {Dataset}, owner = {santinge}, title = {{Datasets and executables of data-driven uncertainty quantification benchmark in carbon dioxide storage}}, url = {https://zenodo.org/records/933827}, year = 2019 }
  Link
  https://zenodo.org/records/933827
2018
1. A. Barth and I. Kröker, “Finite Volume Methods for Hyperbolic Partial Differential Equations with Spatial Noise,” in Theory, Numerics and Applications of Hyperbolic Problems I, C. Klingenberg and M. Westdickenberg, Eds., in Theory, Numerics and Applications of Hyperbolic Problems I. Cham: Springer International Publishing, 2018, pp. 125--135.
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  @inproceedings{hyp16-bk, abstract = {Various real-world applications require the consideration of the influence of uncertain parameters on the solution to some nonlinear hyperbolic problem. The topic of this paper is to study the solution to a nonlinear hyperbolic PDE perturbed by a spatial noise term. In the first part of this paper, a definition of the corresponding stochastic entropy solution is defined and the required properties for the existence and uniqueness of the defined solution are discussed. The second part is devoted to numerical simulation. An approximation of the spatial noise is introduced. Further, the influence of the noise on the solution to the nonlinear hyperbolic problems is investigated. Several nonlinear numerical examples illustrate the discussion.}, address = {Cham}, author = {Barth, Andrea and Kr{\"o}ker, Ilja}, booktitle = {Theory, Numerics and Applications of Hyperbolic Problems I}, editor = {Klingenberg, Christian and Westdickenberg, Michael}, isbn = {978-3-319-91545-6}, pages = {125--135}, publisher = {Springer International Publishing}, title = {Finite Volume Methods for Hyperbolic Partial Differential Equations with Spatial Noise}, year = 2018 }
2. A. Barth and A. Stein, “Approximation and simulation of infinite-dimensional Lévy processes,” Stochastics and Partial Differential Equations: Analysis and Computations, vol. 6, pp. 286–334, 2018, doi: 10.1007/s40072-017-0109-2.
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  @article{barth2016approximation, abstract = {In this paper approximation methods for infinite-dimensional Lévy processes, also called (time-dependent) Lévy fields, are introduced. For square integrable fields beyond the Gaussian case, it is no longer given that the one-dimensional distributions in the spectral representation with respect to the covariance operator are independent. When simulated via a Karhunen–Loève expansion a set of dependent but uncorrelated one-dimensional Lévy processes has to be generated. The dependence structure among the one-dimensional processes ensures that the resulting field exhibits the correct point-wise marginal distributions. To approximate the respective (one-dimensional) Lévy-measures, a numerical method, called discrete Fourier inversion, is developed. For this method, $$L^p$$-convergence rates can be obtained and, under certain regularity assumptions, mean square and $$L^p$$-convergence of the approximated field is proved. Further, a class of (time-dependent) Lévy fields is introduced, where the point-wise marginal distributions are dependent but uncorrelated subordinated Wiener processes. For this specific class one may derive point-wise marginal distributions in closed form. Numerical examples, which include hyperbolic and normal-inverse Gaussian fields, demonstrate the efficiency of the approach.}, author = {Barth, Andrea and Stein, Andreas}, doi = {10.1007/s40072-017-0109-2}, journal = {Stochastics and Partial Differential Equations: Analysis and Computations }, language = {eng}, pages = {286-334}, title = {Approximation and simulation of infinite-dimensional Lévy processes}, url = {https://doi.org/10.1007/s40072-017-0109-2}, volume = 6, year = 2018 }
  Link
  https://doi.org/10.1007/s40072-017-0109-2
3. A. Barth and T. Stüwe, “Weak convergence of Galerkin approximations of stochastic partial differential equations driven by additive Lévy noise,” Mathematics and Computers in Simulation, vol. 143, pp. 215--225, 2018, doi: 10.1016/j.matcom.2017.03.007.
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  @article{barth2018convergence, abstract = {This work considers weak approximations of stochastic partial differential equations (SPDEs) driven by Lévy noise. The SPDEs at hand are parabolic with additive noise processes. A weak-convergence rate for the corresponding Galerkin Finite Element approximation is derived. The convergence result is derived by use of the Malliavin derivative rather than the common approach via the Kolmogorov backward equation.}, author = {Barth, Andrea and St\"uwe, Tobias}, doi = {10.1016/j.matcom.2017.03.007}, fjournal = {Mathematics and Computers in Simulation}, issn = {0378-4754}, journal = {Mathematics and Computers in Simulation}, mrclass = {65N75 (35R60 60H15)}, mrnumber = {3698230}, owner = {seusdd}, pages = {215--225}, title = {Weak convergence of {G}alerkin approximations of stochastic partial differential equations driven by additive {L}\'evy noise}, url = {https://doi.org/10.1016/j.matcom.2017.03.007}, volume = 143, year = 2018 }
  Link
  https://doi.org/10.1016/j.matcom.2017.03.007
2017
1. A. Barth and F. G. Fuchs, “Uncertainty quantification for linear hyperbolic equations with stochastic process or random field coefficients,” Applied numerical mathematics, vol. 121, pp. 38–51, Nov. 2017, doi: 10.1016/j.apnum.2017.06.009.
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  @article{barth2017uncertainty, abstract = {In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein–Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings.}, affiliation = {Barth, A (Reprint Author), Univ Stuttgart, SimTech, Pfaffenwaldring 5a, D-70569 Stuttgart, Germany. Barth, Andrea, Univ Stuttgart, SimTech, Pfaffenwaldring 5a, D-70569 Stuttgart, Germany. Fuchs, Franz G., Sintef ICT, Forskningsveien 1, N-0314 Oslo, Norway.}, author = {Barth, Andrea and Fuchs, Franz G.}, doi = {10.1016/j.apnum.2017.06.009}, issn = {{1873-5460} and {0168-9274}}, journal = {Applied numerical mathematics}, language = {eng}, month = {11}, pages = {38-51}, publisher = {Elsevier}, research-areas = {Mathematics}, title = {Uncertainty quantification for linear hyperbolic equations with stochastic process or random field coefficients}, unique-id = {ISI:000410013800003}, url = {https://doi.org/10.1016/j.apnum.2017.06.009}, volume = 121, year = 2017 }
  Link
  https://doi.org/10.1016/j.apnum.2017.06.009
2. A. Barth, B. Harrach, N. Hyvönen, and L. Mustonen, “Detecting stochastic inclusions in electrical impedance tomography,” Inverse problems, vol. 33, no. 11, Art. no. 11, 2017, doi: 10.1088/1361-6420/aa8f5c.
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  @article{barth2017detecting, abstract = {This work considers the inclusion detection problem of electrical impedance tomography with stochastic conductivities. It is shown that a conductivity anomaly with a random conductivity can be identified by applying the factorization method or the monotonicity method to the mean value of the corresponding Neumann-to-Dirichlet map provided that the anomaly has high enough contrast in the sense of expectation. The theoretical results are complemented by numerical examples in two spatial dimensions.}, affiliation = {Hyvonen, N (Reprint Author), Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland. Barth, Andrea, Univ Stuttgart, Dept Math, Stuttgart, Germany. Harrach, Bastian, Goethe Univ Frankfurt, Inst Math, Frankfurt, Germany. Hyvoenen, Nuutti; Mustonen, Lauri, Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland.}, author = {Barth, Andrea and Harrach, Bastian and Hyv\"onen, Nuutti and Mustonen, Lauri}, doi = {10.1088/1361-6420/aa8f5c}, issn = {{1361-6420} and {0266-5611}}, journal = {Inverse problems}, language = {eng}, number = 11, orcid-numbers = {Hyvonen, Nuutti/0000-0001-6715-8337}, pages = 115012, publisher = {IOP Publishing}, research-areas = {Mathematics; Physics}, researcherid-numbers = {Hyvonen, Nuutti/G-2253-2013}, title = {Detecting stochastic inclusions in electrical impedance tomography}, unique-id = {ISI:000414077900001}, url = {https://dx.doi.org/10.1088/1361-6420/aa8f5c}, volume = 33, year = 2017 }
  Link
  https://dx.doi.org/10.1088/1361-6420/aa8f5c
2016
1. A. Barth, R. Burger, I. Kröker, and C. Rohde, “Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic Galerkin approach,” COMPUTERS & CHEMICAL ENGINEERING, vol. 89, pp. 11–26, Jun. 2016, doi: 10.1016/j.compchemeng.2016.02.016.
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  @article{barth2016computational, abstract = {Continuous sedimentation processes in a clarifier-thickener unit can be described by a scalar nonlinear conservation law whose flux density function is discontinuous with respect to the spatial position. In the applications of this model, which include mineral processing and wastewater treatment, the rate and composition of the feed flow cannot be given deterministically. Efficient numerical simulation is required to quantify the effect of uncertainty in these control parameters in terms of the response of the clarifier-thickener system. Thus, the problem at hand is one of uncertainty quantification for nonlinear hyperbolic problems with several random perturbations. The presented hybrid stochastic Galerkin method is devised so as to extend the polynomial chaos approximation by multiresolution discretization in the stochastic space. This approach leads to a deterministic hyperbolic system, which is partially decoupled and therefore suitable for efficient parallelisation. Stochastic adaptivity reduces the computational effort. Several numerical experiments are presented.}, affiliation = {Kroker, I (Reprint Author), Univ Stuttgart, IANS, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Burger, Raimund, Univ Concepcion, CI2MA, Casilla 160-C, Concepcion, Chile. Burger, Raimund, Univ Concepcion, Dipartimento Ingn Matemat, Casilla 160-C, Concepcion, Chile. Barth, Andrea; Kroeker, Ilja; Rohde, Christian, Univ Stuttgart, IANS, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.}, author = {Barth, Andrea and Burger, Raimund and Kr\"oker, Ilja and Rohde, Christian}, doi = {10.1016/j.compchemeng.2016.02.016}, eissn = {1873-4375}, issn = {0098-1354}, journal = {COMPUTERS \& CHEMICAL ENGINEERING}, language = {English}, month = {06}, pages = {11-26}, publisher = {Elsevier}, research-areas = {Computer Science; Engineering}, title = {Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic Galerkin approach}, type = {Article}, unique-id = {ISI:000376202800002}, url = {https://doi.org/10.1016/j.compchemeng.2016.02.016}, volume = 89, year = 2016 }
  Link
  https://doi.org/10.1016/j.compchemeng.2016.02.016
2. A. Barth, C. Schwab, and J. Sukys, “Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier--Stokes Equations,” in Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014, R. Cools and D. Nuyens, Eds., in Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014. Cham: Springer International Publishing, 2016, pp. 209--227. doi: 10.1007/978-3-319-33507-0_8.
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  @inproceedings{Barth2016, address = {Cham}, author = {Barth, Andrea and Schwab, Christoph and Sukys, Jonas}, booktitle = {Monte Carlo and Quasi-Monte Carlo Methods: MCQMC, Leuven, Belgium, April 2014}, doi = {10.1007/978-3-319-33507-0_8}, editor = {Cools, Ronald and Nuyens, Dirk}, isbn = {978-3-319-33507-0}, pages = {209--227}, publisher = {Springer International Publishing}, title = {Multilevel Monte Carlo Simulation of Statistical Solutions to the Navier--Stokes Equations}, url = {https://doi.org/10.1007/978-3-319-33507-0_8}, year = 2016 }
  Link
  https://doi.org/10.1007/978-3-319-33507-0_8
2014
1. A. Barth and S. Moreno-Bromberg, “Optimal risk and liquidity management with costly refinancing opportunities,” Insurance Math. Econom., vol. 57, pp. 31–45, 2014, doi: 10.1016/j.insmatheco.2014.05.001.
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  @article{barth2014optimal, abstract = {In this paper we study risk and liquidity management decisions within an insurance firm. Risk management corresponds to decisions regarding proportional reinsurance, whereas liquidity management has two components: distribution of dividends and costly equity issuance. Contingent on whether proportional or fixed costs of reinvestment are considered, singular stochastic control or stochastic impulse control techniques are used to seek strategies that maximize the firm value. We find that, in a proportional-costs setting, the optimal strategies are always mixed in terms of risk management and refinancing. In contrast, when fixed issuance costs are too high relative to the firm’s profitability, optimal management does not involve refinancing. We provide analytical specifications of the optimal strategies, as well as a qualitative analysis of the interaction between refinancing and risk management.}, author = {Barth, Andrea and Moreno-Bromberg, Santiago}, doi = {10.1016/j.insmatheco.2014.05.001}, issn = {0167-6687}, journal = {Insurance Math. Econom.}, language = {eng}, pages = {31-45}, publisher = {Elsevier}, title = {Optimal risk and liquidity management with costly refinancing opportunities}, url = {https://doi.org/10.1016/j.insmatheco.2014.05.001}, volume = 57, year = 2014 }
  Link
  https://doi.org/10.1016/j.insmatheco.2014.05.001
2013
1. A. Abdulle, A. Barth, and C. Schwab, “Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs,” Multiscale modeling & simulation, vol. 11, no. 4, Art. no. 4, 2013, doi: 10.1137/120894725.
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  BibTeX
  @article{abdulle2013multilevel, abstract = {In this paper Monte Carlo finite element approximations for elliptic homogenization problems with random coefficients, which oscillate on n a priori known, separated microscopic length scales, are considered. The convergence of multilevel Monte Carlo finite element discretizations is analyzed. In particular, it is considered that the multilevel finite element discretization resolves the finest physical length scale, but the coarsest finite element mesh does not, so that the so-called resonance case occurs at intermediate multilevel Monte Carlo sampling levels. It is shown that for first order finite elements in two space dimensions, the multilevel Monte Carlo finite element method converges at the same rate as the corresponding single-level Monte Carlo finite element method, despite the majority of samples being underresolved in the multilevel Monte Carlo finite element estimator. It is proved that switching to a hierarchic multiscale finite element method such as the finite element heterogeneous multiscale method to compute the multilevel Monte Carlo finite element estimator, when only meshes are used which underresolve all physical length scales, implies optimal convergence. Specifically, both methods proposed here allow one to obtain estimates of the expectation of the random solution, with accuracy versus work that is identical to the solution of a single deterministic problem. In the case of the finite element heterogeneous multiscale method the estimate is, moreover, robust with respect to the physical length scales. Numerical experiments corroborate our analytical findings.}, author = {Abdulle, Assyr and Barth, Andrea and Schwab, Christoph}, doi = {10.1137/120894725}, issn = {{1540-3467} and {1540-3459}}, journal = {Multiscale modeling & simulation}, language = {eng}, number = 4, pages = {1033-1070}, publisher = {SIAM}, title = {Multilevel Monte Carlo methods for stochastic elliptic multiscale PDEs}, volume = 11, year = 2013 }
2. A. Barth, A. Lang, and C. Schwab, “Multilevel Monte Carlo method for parabolic stochastic partial differential equations,” BIT : numerical mathematics, vol. 53, no. 1, Art. no. 1, 2013, doi: 10.1007/s10543-012-0401-5.
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  @article{barth2013multilevel, abstract = {We analyze the convergence and complexity of multilevel Monte Carlo discretizations of a class of abstract stochastic, parabolic equations driven by square integrable martingales. We show under low regularity assumptions on the solution that the judicious combination of low order Galerkin discretizations in space and an Euler–Maruyama discretization in time yields mean square convergence of order one in space and of order 1/2 in time to the expected value of the mild solution. The complexity of the multilevel estimator is shown to scale log-linearly with respect to the corresponding work to generate a single path of the solution on the finest mesh, resp. of the corresponding deterministic parabolic problem on the finest mesh.}, author = {Barth, Andrea and Lang, Annika and Schwab, Christoph}, doi = {10.1007/s10543-012-0401-5}, issn = {{1572-9125} and {0006-3835}}, journal = {BIT : numerical mathematics}, language = {eng}, number = 1, pages = {3-27}, publisher = {Springer}, title = {Multilevel Monte Carlo method for parabolic stochastic partial differential equations}, url = {https://doi.org/10.1007/s10543-012-0401-5}, volume = 53, year = 2013 }
  Link
  https://doi.org/10.1007/s10543-012-0401-5
2012
1. A. Barth and A. Lang, “Multilevel Monte Carlo method with applications to stochastic partial differential equations,” International journal of computer mathematics, vol. 89, no. 18, Art. no. 18, 2012, doi: 10.1080/00207160.2012.701735.
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  @article{barth2012multilevel, abstract = {In this work, the approximation of Hilbert-space-valued random variables is combined with the approximation of the expectation by a multilevel Monte Carlo (MLMC) method. The number of samples on the different levels of the multilevel approximation are chosen such that the errors are balanced. The overall work then decreases in the optimal case to O(h^{−2}) if h is the error of the approximation. The MLMC method is applied to functions of solutions of parabolic and hyperbolic stochastic partial differential equations as needed, for example, for option pricing. Simulations complete the paper.}, author = {Barth, Andrea and Lang, Annika}, doi = {10.1080/00207160.2012.701735}, issn = {0020-7160}, journal = {International journal of computer mathematics}, language = {eng}, number = 18, pages = {2479-2498}, publisher = {Taylor & Francis}, title = {Multilevel Monte Carlo method with applications to stochastic partial differential equations}, url = {https://doi.org/10.1080/00207160.2012.701735}, volume = 89, year = 2012 }
  Link
  https://doi.org/10.1080/00207160.2012.701735
2011
1. A. Barth, F. E. Benth, and J. Potthoff, “Hedging of spatial temperature risk with market-traded futures,” Appl. Math. Finance, vol. 18, no. 2, Art. no. 2, 2011, doi: 10.1080/13504861003722385.
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  BibTeX
  @article{barth2011hedging, abstract = {The main objective of this work is to construct optimal temperature futures from available market-traded contracts to hedge spatial risk. Temperature dynamics are modelled by a stochastic differential equation with spatial dependence. Optimal positions in market-traded futures minimizing the variance are calculated. Examples with numerical simulations based on a fast algorithm for the generation of random fields are presented.}, author = {Barth, Andrea and Benth, Fred Espen and Potthoff, Jürgen}, doi = {10.1080/13504861003722385}, fjournal = {Applied Mathematical Finance}, issn = {1350-486X}, journal = {Appl. Math. Finance}, mrclass = {91G80}, mrnumber = {2786978 (2012c:91255)}, number = 2, owner = {barthaa}, pages = {93--117}, title = {Hedging of spatial temperature risk with market-traded futures}, url = {http://dx.doi.org/10.1080/13504861003722385}, volume = 18, year = 2011 }
  Link
  http://dx.doi.org/10.1080/13504861003722385
2. A. Barth, C. Schwab, and N. Zollinger, “Multi-level Monte Carlo Finite Element Method for Elliptic PDEs with Stochastic Coefficients.,” Numerische Mathematik, vol. 119, pp. 123–161, 2011, doi: 10.1007/s00211-011-0377-0.
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  @article{barth2011multilevel, abstract = {In Monte Carlo methods quadrupling the sample size halves the error. In simulations of stochastic partial differential equations (SPDEs), the total work is the sample size times the solution cost of an instance of the partial differential equation. A Multi-level Monte Carlo method is introduced which allows, in certain cases, to reduce the overall work to that of the discretization of one instance of the deterministic PDE. The model problem is an elliptic equation with stochastic coefficients. Multi-level Monte Carlo errors and work estimates are given both for the mean of the solutions and for higher moments. The overall complexity of computing mean fields as well as k-point correlations of the random solution is proved to be of log-linear complexity in the number of unknowns of a single Multi-level solve of the deterministic elliptic problem. Numerical examples complete the theoretical analysis.}, author = {Barth, Andrea and Schwab, Christoph and Zollinger, Nathaniel}, coden = {NUMMA7}, doi = {10.1007/s00211-011-0377-0}, fjournal = {Numerische Mathematik}, journal = {Numerische Mathematik}, mrclass = {65N30 (35J25 35R60 60H15 65C05)}, mrnumber = {2824857 (2012i:65252)}, mrreviewer = {Erich Novak}, owner = {barthaa}, pages = {123-161}, title = {Multi-level Monte Carlo Finite Element Method for Elliptic PDEs with Stochastic Coefficients.}, url = {http://dx.doi.org/10.1007/s00211-011-0377-0}, volume = 119, year = 2011 }
  Link
  http://dx.doi.org/10.1007/s00211-011-0377-0
2010
1. A. Barth, “A finite element method for martingale-driven stochastic partial differential equations,” Communications on Stochastic Analysis, vol. 4, no. 3, Art. no. 3, 2010, doi: 10.31390/cosa.4.3.04.
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  BibTeX
  @article{barth2010finite, abstract = {The main objective of this work is to describe a Galerkin approximation for stochastic partial differential equations driven by square–integrable martingales. Error estimates in the semidiscrete case, where discretization is only done in space, and in the fully discrete case are derived. Parabolic as well as transport equations are studied.}, author = {Barth, Andrea}, doi = {10.31390/cosa.4.3.04}, issn = {0973-9599}, journal = {Communications on Stochastic Analysis}, language = {eng}, number = 3, pages = {355-375}, title = {A finite element method for martingale-driven stochastic partial differential equations}, url = {https://repository.lsu.edu/cosa/vol4/iss3/4}, volume = 4, year = 2010 }
  Link
  https://repository.lsu.edu/cosa/vol4/iss3/4
2009
1. A. Barth, “Stochastic Partial Differential Equations: Approximations and Applications,” Dissertation, University of Oslo, 2009. [Online]. Available: http://urn.nb.no/URN:NBN:no-24072
  - BibTeX
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  @phdthesis{barth2009stochastic, author = {Barth, Andrea}, language = {eng}, school = {University of Oslo}, title = {Stochastic Partial Differential Equations: Approximations and Applications}, type = {Dissertation}, url = {http://urn.nb.no/URN:NBN:no-24072}, year = 2009 }
  Link
  http://urn.nb.no/URN:NBN:no-24072

Teaching

Current and previous lectures can be found here.

Supervision of highly qualified personnel

PhD theses:

O. König: Uncertainty Quantification for data-limited Bayesian Inverse Problems, since 2022
F. Musco: Deep Learning for Random Partial Differential Equations, since 2021
C. Beschle: Continuous Level Monte Carlo Methods, since 2020
R. Merkle: Analysis and Simulation of Lévy Random Fields, 2019 - 2022
L. Brencher: Analysis of Stochastic Partial Differential Equations and their efficient Simulation, 2018 - 2022
A. Stein: Approximations of Stochastic Partial Differential Equations with Lévy-Noise, 2016 - 2020

Possible topics for Bachelor's and Master's theses can be chosen from the following topics:

Stochastic (partial) differential equations
Random partial differential equations
Monte Carlo methods
Random fields
Bayesian inverse problems
Uncertainty Quantification for complex systems

Excerpt of completed theses:

Bachelor's:

Numerical Simulations on Momentum Coupling and Orbit Modification in Laser-Debris Removal
Central Limit Theorems with finite and infinite Variance
About Bayesian Inversion Theory for Parabolic Partial Differential Equations
Exit Time Problems and Multilevel Monte-Carlo Methods
The Dividend Problem: An Overview

Master's:

Simulation of infinite dimensional Lévy fields
Multilevel Monte Carlo Methods for Wong-Zakai Approximations
Optimal dividend distribution under stochastic refinancing costs
Application of the Functional Ito Calculus on Weak Convergence Problems for SDEs
Supervised deep learning for stochastic lid-driven cavity flow
Using Deep Neural Networks to price Basket and Rainbow Options
Weak convergence of Galerkin Finite Element approximations of Lévy SPDEs
Probability density approximation by the Monte Carlo Maximum Entropy method

More information can be found here.

Vita

since 08/2017	W3-Professor for Computational Methods for Uncertainty Quantification at the Excellence Cluster for Simulation Technology, IANS, University of Stuttgart, Germany
12/2013 -08/2017	Juniorprofessor at the Excellence Cluster for Simulation Technology, University of Stuttgart, Germany
01/2010 - 11/2013	Lecturer and postdoctoral researcher at the Seminar for Applied Mathematics, ETH Zürich, Switzerland
09/2006 -12/2009	Ph.D. student in Mathematics at the Center of Mathematics for Applications, University of Oslo, Norway Thesis: Stochastic Partial Differential Equations: Approximations and Applications Supervisors: Prof. Dr. Fred Espen Benth, Center of Mathematics for Applications, University of Oslo, Norway Prof. Dr. Jürgen Potthoff, University of Mannheim, Germany

Third party funding

2019 - 2025	Principal Investigator: ExC 2075 "Data-Integrated Simulation Science"
2019 - 2023	Principal Investigator: SFB/TRR 161 "Quantitative Methods for Visual Computing"
2018 - 2021	Doctorate Project from the SC SimTech (ExC 310 / ExC 2075), funded by the DFG: Simulation of Lévy-type stochastic partial differential equations
2018 - 2019	Post-doctoral Project from RISC, funded by the MWK: Polynomial Chaos for Lévy fields
2016 - 2017	Doctorate Project from the SRC SimTech, funded by the DFG: Elliptic Equations with Lévy field coefficients
2014 - 2017	Doctorate Project from the Juniorprofessorship-Program Baden-Württemberg: New Methods for Weak Approximations of Stochastic Partial Differential Equations with Lévy-Noise
2014 - 2017	Doctorate Project from the SRC SimTech, funded by the DFG: Random field solutions of hyperbolic partial differential equations

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