I am a professor at Otto-von-Guericke Universität Magdeburg where I am affiliated with the Institute for Simulation and Graphics. My research centers around the development of effective simulation techniques for computer graphics, in particular for light and fluids. This work often takes me to questions in applied mathematics and mathematical physics that I also pursue.

- May 2023: Slides from my talk on GAMM 2023 on neural networks and partial differential equations.
- May 2023: Slides from my talk on AtmoRep presented at ECMWF.
- April 2023: I presented AtmoRep at EGU 2023. Slides.
- April 2023: Martin Schultz, Matthew Chantry and myself are organizing a workshop on Large-scale deep learning for the Earth System. Registration and abstract submission will open on 4th May.
- April 2023: In the spring term 2023, I will be teaching GPU Programming.
- March 2023: I will be presenting an invited lecture at GAMM 2023 in the scientific computing session.
- March 2023: atmorep.org is now online.
- March 2023: I presented Representation Learning for Science at the AI in Imaging Club at the University of Kiel.
- March 2023: I presented AtmoRep at the IntelliAQ workshop in Cologne. Slides are available here.
- The preprint of our work on the neXtSIM-DG dynamical core, developed as part of the SASIP project, is now available on EGUSphere.
- February 2023: I am now an associate editor for Artificial Intelligence for the Earth Systems, a journal of the American Meteorological Society.
- February 2023: Our AtmoDist work on self-supervised representation learning for atmospheric data has been accepted to Environemental Data Science. The final paper can be found on the publisher website and the code on github.
- February 2023: I presented the AtmoRep project at the NSF AI Institute for Research on Trustworthy AI in Weather, Climate, and Coastal Oceanography. Slides and a recording are online.
- December 2022: AtmoRep will present an online poster at AGU on Tuesday, Dec. 13th..
- December 2022:
Our work on weather extremes using machine learning was awarded
**Best Paper: ML Innovation**at the NEURIPS workshop on climate change. - December 2022: Our work on predicting the statistics of extreme weather events was selected as a spotlight talk for the NEURIPS workshop on climate change.
- September 2022: I am now the deparmental vice-chair for student affairs in the Department for Computer Science.
- September 2022: Slides from my talk on AtmoRep at the transformer workshop.
- September 2022: Slides from my talk at the RAISE Center of Excellence on transformer models for science and engineering.
- September 2022: Our workshop on Transformers in Environmental Science had over 40 in-person participants in Magdeburg and many more online. Thanks to all participants for joining and making the workshop a success! Many talks and posters can still be found on the workshop website.
- In the fall/winter term I will be teaching the following courses: Please do not hesitate to contact me if you have any questions on
- July 2022: Our article on variational isospectral symplectic Runge-Kutta methods has been published in BIT Numerical Mathematics. Reference implementations are available on the project page.
- June 2022: Together with Martin Schultz's group from JSC Juelich we are organizing a workshop on Transformer neural networks in the Earth sciences on 22/23 September 2022 in Magdeburg. The registration is now open and
- Slides as well as the video from my talk at th Juelich Supercomputing Center on representation learning for the Earth Sciences.
- At the BULK Reaction 2022 workshop we presented our work on particle image velocimetry of fluids with ray tracing based correction. Talk slides and poster.
- Slides from the introduction to the Masters in Visual Computing as part of the Mastertage 2022 at Otto-von-Guericke-Universitaet Magdeburg.
- May 2022: My group will be presenting two projects at EGU 2022 in Vienna: an extension of AtmoDist as a data-driven model for atmospheric predictability (Tuesday, 24 May 2022, 10:26 CEST, room N1, slides) and work on the derivation and extension of the matrix model for the barotropic vorticity equation (Wednesday, 25 May 2022, 14:14 CEST, room 1.34, slides).
- May 2022: Talks from my webinar at OceaniX can be found here.
- March 2022: Two abstracts, one on representation learning and predictibility of atmospheric dynamics and one on structure preserving integrators for the atmosphere, have been accepted to the EGU General Assembly in Vienna in May.
- January 2022: The final version of our DNN-MG hybrid method that combines a classical multigrid solver for the Navier-Stokes equations with a neural network is now online.
- December 2021: Clauson and myself just uploaded our new manuscript on Variational Symplectic Diagonally Implicit Runge-Kutta Methods for Isospectral Systems to the ArXiv.
- November 2021: Slides from my talk at the Kavli Institute for Theoretical Physics on Representation Learning and Custom Loss Functions for Atmospheric Data. I will also be part of the program on Machine Learning and the Physics of Climate there.
- October 2021: Our short paper on AtmoDist has been accepted to the Neurips Workshop on Climate Change as a poster. Congratulations to Sebastian for his first paper!
- September 2021: We will have a Welcome Meeting for our Master in Visual Computing program on 7 October 2021 at 13:00. It will be hybrid with an in person meeting in G29-335 and online participation via BigBlueButton (633837).
- September 2021: Thomas Richter and myself gave a talk at the IMPRS summer school 2021. Slides and code are available here.
- September 2021: Sebastian Hoffmann and myself just uploaded our manuscript about representation learning and data-driven metrics for atmospheric dynamics.
- September 2021: In the fall term 2021 I am teaching the following classes:
- Scientific Computing II (ODEs and PDES)
- Scientific Computing V (Geometric mechanics and structure Preserving Discretizations)
- Mathematics and Numerics of Deep Neural Networks for Physical Simulations (Seminar, M.Sc., with Thomas Richter)

- July 2021: Slides from my talk at Ecole Polytechnique.
- June 2021: On 30. June, 14:30, I will be giving an introduction to our new Master in Visual Computing as part of the Masters Days at Otto-von-Guericke-Universitat Magdeburg. Please see the official page for more information and how to sign up. Slides are available here.
- May 2021: As part of the "Lange Nacht der Wissenschaften" I was part of a panel discussion on the societal relevance of computer science. A live stream is available here.
- May 2021: Our paper "A data-driven framework for the stochastic reconstruction of small-scale features in climate data sets" has been accepted to Journal of Computational Physics. More details following soon.
- April 2021: We are looking for a student assistant (preferrably at the M.Sc. level) for the GPU parallelization of a Lattice-Boltzmann code for fluid simulation. This can also be pursued as a M.Sc. thesis or started as a Hiwi and completed as a thesis. If you might be interested then do not hesitate to get in touch with me.
- April 2021: We are starting a new Master program in Visual Computing in fall. If you are currently finishing your Bachelor degree and want to pursue a career in visual computing (in particular visualization, computer vision, computer graphics) then please consider applying. More information can be found on the following page.
- April 2021: We are looking for a student assistant interested in ray tracing. The research project is concerned with heat propagation but we will largely use the same tools as for photorealistic image synthesis. More details can be found here.
- In the spring / summer term 2021 I will be teaching the following courses (please see the LSF links and Moodle pages for the courses for details):
- December 2020: Nils Margenberg, Thomas Richter and myself just uploaded our preprint on Structure Preservation for the Deep Neural Network Multigrid Solver to ArXiv.
- In the fall / winter 2020/21 term I will be teaching the following courses (please see the LSF links for details; all information subject to change until 16/10/2020!):
- GPU Programmierung (Lecture, B.Sc.)
- Scientific Computing II: Introduction to Dynamical Systems (Lecture, B.Sc. / M.Sc.)
- Scientific Computing V: Structure Preserving Simulations and Geometric Mechanics (Lecture, M.Sc.)
- Mathematics and Numerics of Deep Neural Networks for Physical Simulations (Seminar, M.Sc., with Thomas Richter)

- October 2020: My work on Psiec, a local spectral exterior calculus, has been accepted to Applied and Computational Harmonic Analysis. A reference implementation is available on the project page.
- Nils Margenberg, Dirk Hartmann, Thomas Richter and myself just uploaded our manuscript A neural network multigrid solver for the Navier-Stokes equations to the ArXiv. In the work we show how a multigrid solver and neural networks can be combined to improve the overall efficiency of simulations of the Navier-Stokes equations.
- Thomas Richter (from the Dept. of Mathematics) and myself will be offering a seminar on the use of neural networks and deep learning for physical simulations in the fall / winter term 2020/21.
- The Question and Answer session for my paper Local Fourier Slice Photography at Siggraph 2020 will be 24. August 2020 from 2:00 - 2:30 PST.
- I wrote a small note for my tensor analysis class that details why the anti-symmetry of differential forms is required for the covariance of the exterior derivative. Perhaps other people find this useful as well.
- June 2020: A trailer for my Siggraph presentation in July is now available.
- May 2020: I am part of the new Sonderforschungsbereich "BULK REACTION" funded by the DFG. The official press release can be found here.

C. C. da Silva and C. Lessig, Variational Symplectic Diagonally Implicit Runge-Kutta Methods for Isospectral Systems, Submitted to BIT Numerical Mathematics, 2021.

C. C. da Silva, B. Dodov, H. Dijkstra, T. Sapsis, and C. Lessig, A Local Spectral Exterior Calculus for the Sphere and Application to the Shallow Water Equations, Submitted to Journal of Computational Physics, 2020.

N. Margenberg, D. Hartmann, C. Lessig, and T. Richter, A Neural Network Multigrid Solver for the Navier-Stokes Equations, Journal of Computational Physics, 2020.

Z. Y. Wan, B. Dodov, C. Lessig, H. Dijkstra, and T. P. Sapsis, A Data-Driven Framework for the Stochastic Reconstruction of Small-Scale Features in Climate Data Sets, 442, p. 110484, Journal of Computational Physics, 2021.

N. Margenberg, C. Lessig, and T. Richter, Structure Preservation for the Deep Neural Network Multigrid Solver, Accepted to Electronic Transactions of Numerical Analysis, 2021.

C. Lessig, PsiEC: A Local Spherical Exterior Calculus, Applied and Computational Harmonic Analysis, 51:56–103, March 2021.

C. Lessig, Local Fourier Slice Photography, ACM Transactions on Graphics, 39(3), Apr. 2020.

C. Lessig, Divergence Free Polar Wavelets for the Analysis and Representation of Fluid Flows, Journal of Mathematical Fluid Dynamics, vol. 21, no. 18, 2019.

C. Lessig, P. Petersen, and M. Schäfer, Bendlets: A second-order shearlet transform with bent elements, Appl. Comput. Harmon. Anal., vol. 46, no. 2, p. 384--399, 2019.

C. Lessig, A local Fourier slice equation, Optics Express, vol. 26, no. 23, p. 29769, Nov. 2018.

F. J. W. A. Martins, C. C. da Silva, C. Lessig, and K. Zähringer, Ray-Tracing Based Image Correction of Optical Distortion for PIV Measurements in Packed Beds, JAOP Journal of Advanced Optics and Photonics, vol. 1, no. 2, pp. 71–94, 2018.

X. Wang, D. Lindlbauer, C. Lessig, M. Maertens, and M. Alexa, Measuring the Visual Salience of 3D Printed Objects, IEEE Computer Graphics and Applications, vol. 36, no. 4, 2016

C. Lessig, M. Desbrun, and E. Fiume, A Constructive Theory of Sampling for Image Synthesis Using Reproducing Kernel Bases, ACM Trans. Graph. (Proceedings SIGGRAPH 2014), 33(4), 1–14, 2014.

T. de Witt, C. Lessig, and E. Fiume, Fluid Simulation Using Laplacian Eigenfunctions, ACM Trans. Graph., 31(1), 1–11, 2012.

C. Lessig, T. de Witt, and E. Fiume, Efficient and Accurate Rotation of Finite Spherical Harmonics Expansions, J. Comp. Phys., 231(2), 243–250, 2012.

C. Lessig and E. Fiume, On the Effective Dimension of Light Transport, Comput. Graph. Forum (Proceedings of EGSR 2010), 29(4), 1399–1403, 2010.

C. Lessig and E. Fiume, SOHO: Orthogonal and Symmetric Haar Wavelets on the Sphere, ACM Trans. Graph., 27(1) 2008.

X. Wang, D. Lindlbauer, C. Lessig, and M. Alexa, Accuracy of Monocular Gaze Tracking on 3D Geometry, Eye Tracking and Visualization, 2017.

C. Lessig and A. L. Castro, The Geometry of Phase Space Lifts: From Maxwell's Equations to Radiative Transfer Theory, in Geometry, Mechanics and Dynamics: the Legacy of Jerry Marsden, Springer, 2014; also presented at the SIAM Annual conference 2013.

S. Hoffmann and C. Lessig. Towards representation learning for atmospheric data. In NEURIPS 2021 Workshop on Climate Change (poster), 2021

N. Margenberg, R. Jendersie, T. Richter, C. Lessig, Deep neural networks for geometric multigrid methods, ECCOMAS 2021, 2021.

N. Margenberg, T. Richter, C. Lessig, D. Hartmann, A deep learning based multigrid multiscale method for solving the Navier-Stokes-equations, International Workshop on Scientific Machine Learning, University of Cologne, 2020.

T. Sapsis, Z. Y. Wan, B. Dodov, H. A. Dijkstra, and C. Lessig, Data-assisted reduced-order modeling of climate dynamics, in EGU 2019 orals, 2019.

B. Dodov, C. Lessig, T. Sapsis, and H. Dijkstra, Multiresolution Formulation of a Global Circulation Model Specifically Designed for Data-Driven Machine Learning Assistance, in EGU 2019 orals, 2019.

C. C. da Silva, C. Lessig, B. Dodov, H. A. Dijkstra, and T. Sapsis, A Local Spectral Exterior Calculus for the Primitive Equations, in EGU 2019 orals, 2019.

F. J. W. A. Martins, A. C. da Silva, C. Lessig, and K. Zähringer, Ray-Tracing Based Image Correc- tion of Optical Distortions Caused by Transparent Spheres for Application in PIV, 19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics, 2018.

C. Lessig, Controlling and Sampling Visibility Information on the Image Plane, Eurographics Symposium on Rendering 2017, 2017.

X. Wang, D. Lindlbauer, C. Lessig, and M. Alexa, Accuracy of Monocular Gaze Tracking on 3D Geometry, ETVIS 2015: Workshop on Eye Tracking and Visualization, 2015.

G. Mason, C. Lessig, and M. Desbrun, Discretization of Hamiltonian Incompressible Fluids, in 17th US National Conference of Theoretical and Applied Mathematics, 2014.

C. Lessig and P. Bientinesi, On Parallelizing the MRRR Algorithm for Data-Parallel Coprocessors, in Proceedings of PPAM 2010: Part I, 396–402, 2010.

C. Lessig, D. Nowrouzezahrai, and K. Singh, GPU-Accelerated Ray Casting of Node-Based Implicit Surfaces, in Siggraph 2006 Posters, 2006.

H.-F. Pabst, J. P. Springer, A. Schollmeyer, R. Lenhardt, C. Lessig, and B. Fröhlich, Ray Casting of Trimmed NURBS Surfaces on the GPU, in The 2006 IEEE Symposium on Interactive Ray Tracing, 2006.

M. Moehring, C. Lessig, and O. Bimber, Video See-Through and Optical Tracking with Consumer Cell Phones, in Siggraph 2004 Sketches and Applications, 2004.

M. Moehring, C. Lessig, and O. Bimber, Video See-Through AR on Consumer Cell-Phones, in Third IEEE and ACM International Symposium on Mixed and Augmented Reality, 2004, pp. 252–253.

- Implementation of fluid simulator based on ((V. Y. Zeitlin. Algebraization of 2-D Ideal Fluid Hydrodynamical Systems and Their Finite-Mode Approx- imations. In Advances in Turbulence 3, pages 257–260. Springer Berlin Heidelberg, Berlin, Heidelberg, 1991) and (K. Modin and M. Viviani. A casimir preserving scheme for long-time simulation of spherical ideal hydrodynamics. Journal of Fluid Mechanics, 884:A22, 2020.))
- Deep learning-based sub-grid scale models for (geophysical and computer graphics) fluid dynamics: The thesis explores the use of recurrent neural networks as subgrid scale models for (geophysical) fluid dynamics.
- Local all-focus light field reconstruction: The thesis develops an extension of local Fourier slice photography that allows for all-focus light field reconstruction.
- Efficient implementation of fast marching for triangle meshes.

Scientific Computing I, OVGU Magdeburg.

GPU Programming, OVGU Magdeburg.

Scientific Computing II, OVGU Magdeburg.

GPU Programming, OVGU Magdeburg.

Scientific Computing I, OVGU Magdeburg.

GPU Programming, OVGU Magdeburg.

Scientific Computing II, OVGU Magdeburg.

Scientific Computing I, OVGU Magdeburg.

GPU Programming, OVGU Magdeburg.

Scientific Computing II, OVGU Magdeburg.

Scientific Computing I, OVGU Magdeburg.

Fall 2017

GPU Programming, OVGU Magdeburg.

Fall 2017

Advanced Image Synthesis, OVGU Magdeburg.

Spring 2017

Team Project: Post-Processing for Rendering, OVGU Magdeburg.

Spring 2017

Mathematical Methods for Computer Graphics, OVGU Magdeburg.

Fall 2016

GPU Programming, , OVGU Magdeburg

October 2015

Mathematical Methods for Computer Graphics, University of Toronto.

Fall/Winter 2015

Introduction to Scientific Computing, TU Berlin.

Fall/Winter 2014

Introduction to Scientific Computing, TU Berlin.

Spring/Summer 2014

Computer Graphics 2 (Geometric Representations), TU Berlin.

February 2014

Mathematical Methods for Computer Graphics, University of Toronto.

Fall/Winter 2013

Introduction to Scientific Computing, TU Berlin.

Spring/Summer 2013

Algorithms and Data Structures, TU Berlin.

Fall/Winter 2011

Computer Graphics 1, TU Berlin.

Spring/Summer 2011

Advanced Image Synthesis, TU Berlin.

2016 - present

Juniorprofessor (assistant professor) at Otto-von-Guericke Universität Magdeburg

2013 - 2016

Post-doc with Marc Alexa in the computer graphics group at TU Berlin

2012 - 2013

Post-doc with Mathieu Desbrun in the Department of Computing+Mathematical Sciences at the California Institute of Technology

2007 - 2012

Ph.D. student with Eugene Fiume at the University of Toronto (Thesis: Modern Foundations of Light Transport Simulation)

2005 - 2007

M.Sc. student with Eugene Fiume at the University of Toronto (Thesis: Symmetric and Orthogonal Wavelets on the Sphere)

2005 - 2007

Summer intern in the developer technology group at NVIDIA working with Mark Harris

2001 - 2005