
 Mathematical Foundations of Deep Learning
 Connections between Partial Differential Equations and Convolutional Neural Networks
Journal Papers

P. Peter, K. Schrader, T. Alt, J. Weickert:
Deep Spatial and Tonal Optimisation for Homogeneous Diffusion Inpainting.
To appear in Pattern Analysis and Applications.
Invited Paper.
Also available as arXiv:2208.14371 [eess.IV], revised September 2022. 
T. Alt, K. Schrader, M. Augustin, P. Peter, J. Weickert:
Connections between Numerical Algorithms for PDEs and Neural Networks.
Journal of Mathematical Imaging and Vision.
Invited Paper.
Also available as arXiv:2107.14742 [math.NA], revised March 2022. 
T. Alt, K. Schrader, J. Weickert, P. Peter, M. Augustin:
Designing Rotationally Invariant Neural Networks from PDEs and Variational Methods.
Research in the Mathematical Sciences.
Also available as arXiv:2108.13993 [cs.LG], revised March 2022. 
K. Schrader, P. Peter, N. Kämper, J. Weickert:
Efficient neural generation of 4K masks for homogeneous diffusion inpainting.
In L. Calatroni, M. Donatelli, S. Morigi, M. Prato, M. Santavesaria (Eds.): Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Springer, Cham, 2023.
Also available as arXiv:2303.10096 [eess.IV], March 2023. 
K. Schrader, T. Alt, J. Weickert, M. Ertel:
CNNbased Euler’s Elastica Inpainting with Deep Energy and Deep Image Prior.
In Proceedings of the 10th European Workshop on Visual Information Processing, Lisbon, 2022.
Also available as arXiv:2207.07921 [cs.CV], July 2022. 
T. Alt, P. Peter, J. Weickert, K. Schrader:
Translating numerical concepts for PDEs into neural architectures.
In A. Elmoataz, J. Fadili, Y. Quéau, J. Rabin, L. Simon (Eds.): Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, Springer, Cham, 2021.
Also available as arXiv:2103.15419 [math.NA], March 2021. 
K. Schrader, J. Weickert, M. Krause:
Anisotropic Diffusion Stencils: From Simple Derivations over Stability Estimates to ResNet Implementations.
arXiv:2309.05575 [math.NA], September 2023. 
K. Schrader:
Translating Anisotropic Diffusion into Residual Networks.
M.Sc. Thesis in Visual Computing,
Saarland University, Saarbrücken, Germany, October 2020.
 Winter term 2020:
Seminar Deep Learning and Optimisation for Visual Computing  Summer term 2021:
Seminar Connections of Deep Learning and PDEs for Visual Computing
Proseminar Naturinspirierte Optimierung  Winter term 2021:
Seminar Milestones and Advances in Image Analysis
Proseminar Simulation der Welt  Summer term 2022:
Lecture Modeldriven Deep Learning Lab for Image Analysis  Winter term 2022:
Teaching Assistant and Tutor for Differential Equations in Image Processing and Computer Vision  Summer term 2023:
Tutor for Image Compression
Seminar Probabilistic Diffusion: Theory and Applications  Winter term 2024:
Teaching Assistant for Mathematics for Computer Scientists I
Conference Papers
Technical Reports
Theses
Courses