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Beschle, Cedric

Cedric Beschle

M.Sc.

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

Contact

+49 711 685 61717
+4971168552022
Email

Allmandring 5b
70569 Stuttgart
Deutschland
Room: 0.35

Subject

Multilevel Monte Carlo Methods
Uncertainty Quantification
Randomized Partial Differential Equations
Adaptive algorithms

Publications

2022
1. 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.
  - BibTeX
  BibTeX
  @article{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 }
2. C. Beschle, “Uncertainty visualization: Fundamentals and recent developments, code to produce data and visuals used in Section 5,” 2022, doi: 10.18419/darus-3154.
  - BibTeX
  BibTeX
  @article{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}, 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 }
3. C. Beschle and B. Kovács, “Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces,” Numerische Mathematik, pp. 1--48, 2022, doi: 10.1007/s00211-022-01280-5.
  - BibTeX
  BibTeX
  @article{10.1007/s00211-022-01280-5, abstract = {{In this paper, we consider a non-linear fourth-order evolution equation of Cahn–Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix–vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments.}}, author = {Beschle, Cedric and Kovács, Balázs}, doi = {10.1007/s00211-022-01280-5}, issn = {0029-599X}, journal = {Numerische Mathematik}, note = {\url{https://rdcu.be/cKKTQ}}, pages = {1--48}, title = {{Stability and error estimates for non-linear Cahn–Hilliard-type equations on evolving surfaces}}, year = 2022 }
4. D. Hägele et al., “Uncertainty Visualization: Fundamentals and Recent Developments,” it - Information Technology, vol. 64, no. 4–5, Art. no. 4–5, 2022, doi: 10.1515/itit-2022-0033.
  - BibTeX
  - Link
  BibTeX
  @article{haegeleIt2022, abstract = {This paper provides a brief overview of uncertainty visualization along with some fundamental considerations on uncertainty propagation and modeling. Starting from the visualization pipeline, we discuss how the different stages along this pipeline can be affected by uncertainty and how they can deal with this and propagate uncertainty information to subsequent processing steps. We illustrate recent advances in the field with a number of examples from a wide range of applications: uncertainty visualization of hierarchical data, multivariate time series, stochastic partial differential equations, and data from linguistic annotation.}, author = {H\"agele, 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}, journal = {it - Information Technology}, number = {4–5}, pages = {121–132}, title = {Uncertainty Visualization: Fundamentals and Recent Developments}, url = {https://doi.org/10.1515/itit-2022-0033}, volume = 64, year = 2022 }
  Link
  https://doi.org/10.1515/itit-2022-0033
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.
  - BibTeX
  - Link
  BibTeX
  @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

Teaching

Summer term 2023	Teaching Assistant, University of Stuttgart	Numerical Mathematics 2
Summer term 2022	Teaching Assistant, University of Stuttgart	Numerische Grundlagen
Winter term 2021/2022	Teaching Assistant, University of Stuttgart	Special Aspects of Numerical Mathematics
Summer term 2021	Teaching Assistant, University of Stuttgart	Advanced Numerics of Partial Differential Equations
Winter term 2020/2021	Teaching Assistant, University of Stuttgart	Stochastik und Angewandte Mathematik für das Lehramt
Summer term 2019	Undergraduate Assistant, University of Tübingen	Numerics of Stationary Differential Equations
Summer term 2018	Undergraduate Assistant, University of Tübingen	Nonlinear Optimization

Vita

Since 2020	PhD-Student at the Institute of Applied Analysis and Numerical Simulation, University of Stuttgart Advisor: Prof. Dr. Andrea Barth
2017 – 2019	Master of Science in Mathematics, University of Tübingen, Germany Thesis: “Error estimates for the Cahn – Hilliard equation on evolving surfaces” Supervisor: Prof. Dr. Christian Lubich, Dr. Balázs Kovács
2019	Working student at EY - Financial Services Advisory, Risk Management, Stuttgart Internship at MAHLE Behr GmbH & Co. KG – Method development: 3D simulations, Stuttgart
2018	Internship at EY - Financial Services Advisory, Risk Management, Stuttgart
2013 – 2018	Working student at Automotive Lighting GmbH – Development, Testing, Experiment, Reutlingen
2017	Semester abroad at the University of Rome
2015	Semester abroad at the University of Oslo
2013 – 2017	Bachelor of Science in Mathematics, University of Tübingen, Germany Thesis: “A time efficient numerical method for the Schrödinger equation” Supervisor: Prof. Dr. Christian Lubich

Third party funding

Since 2020	Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project-ID 251654672—TRR 161
2018 – 2019	Deutschlandstipendium from the University of Tübingen

Cedric Beschle

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2022

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Cedric Beschle

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2022

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2021

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