profile picture   Dr. Sebastian Krämer

Institut für Geometrie und Praktische Mathematik
RWTH Aachen
Templergraben 55
52056 Aachen
Germany

research group(s):
Prof. Markus Bachmayr and Prof. Lars Grasedyck
office:
Hauptgebäude 104.2
phone:
+49 241 80-94875
email:
kraemer@igpm.rwth-aachen.de


In Preparation

[2] Low-Rank Eigenvalue Solvers for Block-Sparse Matrix Product States.
M. Bachmayr, S. Krämer and M. Pfeffer, In Preparation for Submission
[1] Affine Rank Minimization via Asymptotic Log-Det Iteratively Reweighted Least Squares.
S. Krämer, In Revision at JMLR (Journal of Machine Learning Research) (first submitted 2023)

Preprints

[2] Asymptotic log-det sum-of-ranks minimization via tensor (alternating) iteratively reweighted least squares.
S. Krämer, arXiv:2106.15201 (2021)
[arXiv]
[1] Asymptotic log-det rank minimization via (alternating) iteratively reweighted least squares.
S. Krämer, arXiv:2106.14644 (2021)
[arXiv]

Publications

[5] Stable Truncation and Root-Independent Normalization of Tree Tensor Networks.
L. Grasedyck, S. Krämer and D. Moser, Springer Nature: Multiscale, Nonlinear and Adaptive Approximation II, book contribution (2024)
[4] Quasi-orthogonalization for alternating non-negative tensor factorization.
L. Grasedyck, M. Klever and S. Krämer, ETNA Electronic Transactions on Numerical Analysis, 62, pp. 22-57 (2024)
[etna]
[3] A geometric description of feasible singular values in the tensor train format.
S. Krämer, SIAM Journal on Matrix Analysis and Applications, 40, pp. 1153-1178 (2019)
[epubs.siam]
[2] Stable ALS approximation in the TT-format for rank-adaptive tensor completion.
L. Grasedyck and S. Krämer, Numer. Math. 143, 855–904 (2019)
[springer link]
[1] Variants of alternating least squares tensor completion in the tensor train format.
L. Grasedyck, M. Kluge, and S. Krämer, SIAM Journal on Scientific Computing 37, pp. A2424-A2450 (2015)
[epubs.siam]

PhD Thesis

Tree tensor networks, associated singular values and high-dimensional approximation.
S. Krämer, RWTH Aachen University (2020)
[publications.rwth-aachen]

Talks (little excerpt)

[i_5] Iteratively Reweighted Least Squares Recovery on Tensor Tree Networks.
SIAM LA 2024, Paris, France, (2024)
[SIAM LA24]
ICIAM 2023, Tokio, Japan, (2023)
[ICIAM]
GAMM Annual Meeting, Aachen, Germany, (2022)
[Aachen]
[i_4] Guaranteed and fast construction of tensors with prescribed largest multilinear singular values.
Online Minisymposium on Low-rank Geometry and Computation, organized by MPI, Leipzig, Germany (2020)
[online]
[i_3] Approximate interpolation of high dimensional, scattered data in tree tensor formats.
Algorithms and Applications of High Dimensional Approximation, Bath, England (2019)
[Bath]
[i_2] Feasible singular values for hierarchical tensors.
Algebraic Geometry, Approximation, and Optimisation, Creswick, Australia (2018)
[Crezwick]
[i_1] Stable ALS Approximation for Rank-Adaptive Tensor Completion.
GAMM Jahrestagung, Munich, Germany (2018)
[Munich]

Repositories

notebooks HDAD (2022) Course Material: Numerical Tensor Methods
Jupyter notebook exercises (in Julia) for the 2022 research school "High Dimensional Approximation and Deep Learning"
at the Henri Lebesgue Center, Nantes, France, for the course "Approximation with Hierarchical Low Rank Tensors".
[Git Repository]
paths network (A)IRLS Library
Matlab implementations of (alternating) IRLS algorithms for affine vector cardinality, matrix rank and tensor sum-of-rank minimization.
[Git Repository]
button plot Button Plot
Custom plot function that iteratively combines clusters of visually intersecting disks in a scatter plot avoiding quadratic complexity.
[Mathworks File Exchange]
tensor node network Tensor Node Toolbox (beta version)
Toolbox for labeled, automatized tensor network arithmetic.
[Git Repository] [Live Script Walkthrough]
hive TT Feasibility Mini-Toolbox
Mini-toolbox for "A Geometrical Description of Feasible Singular Values in the Tensor Train Format"
[Git Repository] [Live Script Walkthrough]
g2s3 G2S3 (2017) Updated Course Material: Low Rank Tensor Formats
Updated exercises for the 2017 Gen Golub Summer School on Data Sparse Approximations and Algorithms for the course Low Rank Tensor Formats.
[Git Repository]
sing spec SALSA Implementation
Implementation of SALSA for "Stable ALS Approximation in the TT-Format for Rank-Adaptive Tensor Completion"
[Git Repository] [Singular Value Plot]
Code Golf Art: Savanna
Runs in Matlab command window (modified submission to the Matlab Central 20th Anniversary Minihack Contest)

figure;X=-10:.02:10;colormap([pink.*autumn;1,1,.9]);image(782./abs(X+1i*X'-3i));
hold;U=@(p)p+.5i*diff(p)*[4;0;4;4-1i+1i^cos(431*norm(p))^.5];
t=@(S,C)C{(abs(diff(S))<.01)+1}(U(S),C);f=@(P,C)[P(2);t(P(3:4),C);t(P(4:5),C);P(6)];
E=42*f(U(0:1),{f,@(P,C)[]});I=790-E/1i;fill(E+520,I,0);h=scatter(E+520,I,50,-14*abs(E));
alpha(h,.1);camva(3);


Teaching Activities

[WS2223] Mathematik für die Biowissenschaften (for biologists, bio technicians and further), one time substitutional lecturer, assistant
[2022] Research School "High Dimensional Approximation and Deep Learning" (Henri Lebesgue Center, Nantes, France), assistant and creator of course material
[SS21] Numerische Mathematik II (for mathematicians), two times substitutional lecturer, assistant
[WS1920 / WS2021] Numerische Mathematik I (for mathematicians), assistant
[WS1819 / SS19 / SS20 / WS2122] Mathematik I/II (for civil engineers), assistant
[SS18] Begleitpraktikum II (for mathematicians), assistant
[2017] Gene Golub Summer School on Data Sparse Approximations and Algorithms (SIAM), assistant and creator of course material
[WS1617 / WS1718] Numerische Mathematik IV (for mathematicians), assistant
[SS17] Numerische Mathematik (for electrical engineers), assistant
[SS16 / WS2122] Seminar "Aktuelle Themen der Numerik" (for mathematicians) / Numerische Multilineare Algebra (for mathematicians), assistant
[WS1415 / SS15 / WS1516] Numerische Mathematik I-III (for mathematicians), assistant
[Several years during studies] Begleitpraktikum I / II (for mathematicians), student assistant / examiner

Other

[since 2017] GAMM membership and regular participation in yearly conference
[since 2015] Review activity for SIAM