Philipp Krah

About Me

I am a computational physicist located in Marseille, interested in various fields of mathematical physics and numerical analysis. I like to dive with one breath and make music with my friends.

Characteristics:

Physics-love, Algorithms-fun, Rhythm-freedom, Water-needed.

Research Interests

• Numerical Methods for PDEs: adaptive multiresolution, wavelets, volume penalization, conservation laws, high performance computing
• Model Order Reduction: shifted proper orthogonal decomposition, front transport reduction, hyper-reduction, transport-dominated systems, low-rank approxiamtion
• Machine Learning and Optimization: physics guided learning, alternating direction methods, matrix product states
• Physics: quantum link models, quantum field theory, fluid flows, plasma flows

News

• [Sept. 2025] What is the intrinsic dimension of your data? Find it out: [Article]
• [July 2025] This is a big one: My ANR-Project “CROKE” got funded! Webpage and open positions coming soon!
• [Jun. 2025] I will be giving a talk at the [CIRM Masterclass ANADEAL]
• [Mar. 2025] I am proud of my first article in SIAM [Article][Video]
• [Feb. 2025] Our shifted POD deep learning paper was published in ACOM [Article]
• [Jan. 2025] I officially joint the theory and numerical simulation group of CEA-IRFM in Cadarache france
• [Nov. 2024] New preprint is out: Ideal MHD with Characteristic Mapping [Article]
• [Nov. 2024] Giving a talk at the APS conference in Salt Lake City [Abstract]
• [Nov. 2024] I will be first speaker at NumKin2024 [Program]
• [Oct. 2024] Two new master thesis available for computational physicists or applied mathematicians [Proposal-1 ,Proposal-2]

Publications

• Intrinsic Dimension Estimating Autoencoder (IDEA) Using CancelOut Layer and a Projected Loss
  Antoine Orioua, Philipp Krah, Julian Koellermeier
  Preprint arXiv:2509.10011
  [Article][Code - comming soon]

• Gyselalib++: A Portable C++ Library for Semi-Lagrangian Kinetic and Gyrokinetic Simulations
  Emily Bourne, Virginie Grandgirard, Yuuichi Asahi, Julien Bigot, Peter Donnel, Alexander Hoffmann, Abdelhadi Kara, Philipp Krah, Baptiste Legouix, Etienne Malaboeuf, Yann Munschy, Kevin Obrejan, Thomas Padioleau, Matthieu Protais, Pauline Vidal
  Journal of Open Source Software, 10(113), 8582 (2025)
  [Article][Code]

• A robust shifted proper orthogonal decomposition: Proximal methods for decomposing flows with multiple transports
  Philipp Krah, Arthur Marmin, Beata Zorawski, Julius Reiss, Kai Schneider
  SIAM J. Sci. Comput. 47 (2025) A633–A656
  [Article][PDF][Code][Video]

• Parametric model order reduction for a wildland fire model via the shifted POD based deep learning method
  Shubhaditya Burela, Philipp Krah, Julius Reiss
  Adv Comput Math 51, 9 (2025)
  [Article][PDF][Code]

• A Characteristic Mapping Method with Source Terms: Applications to Ideal Magnetohydrodynamics
  X.-Y. Yin, P. Krah, J.-C. Nave, K. Schneider
  Preprent arXiv:2411.13772 (2024)
  [PDF]

• Automated transport separation using the neural shifted proper orthogonal decomposition
  Beata Zorawski, Shubhaditya Burela, Philipp Krah, Arthur Marmin, Kai Schneider
  ECCOMAS 2024
  [Article][Code]

• Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: A study using POD-Galerkin and dynamical low rank approximation
  Julian Koellermeier, Philipp Krah, Jonas Kusch
  Adv Comput Math 50, 76 (2024)
  [Article][PDF][Code]

• Synthesizing impurity clustering in the edge plasma of tokamaks using neural networks
  Zetao Lin, Thibault Maurel-Oujia, Benjamin Kadoch, Philipp Krah, Nathaniel Saura, Sadruddin Benkadda, Kai Schneider
  Phys. Plasmas 31, 032505 (2024)
  [Article]

• A Characteristic Mapping Method for Vlasov-Poisson with Extreme Resolution Properties
  Philipp Krah, Xi-Yuan Yin, Julius Bergmann, Jean-Christophe Nave, Kai Schneider
  Commun. Comput. Phys., 35, pp. 905-937 (2024)
  [Article][PDF][Code][Video]

• Model Order Reduction for the 1D Boltzmann-BGK Equation: Identifying Intrinsic Variables Using Neural Networks
  Julian Koellermeier, Philipp Krah, Julius Reiss, Zachary Schellin
  Microfluid Nanofluid 28, 16 (2024)
  [PDF][Arxiv]

• Crystalline Phases at Finite Winding Densities in a Quantum Link Ladder
  Paolo Stornati, Debasish Banerjee, Karl Jansen, Philipp Krah
  Phys. Rev. D 107, L031504 (2023)
  [PDF][Code]

• Front Transport Reduction for Complex Moving Fronts
  Philipp Krah, Steffen Büchholz, Matthias Häringer, Julius Reiss
  Sci Comput 96, 28 (2023)
  [PDF][Code]

• Wavelet Adaptive Proper Orthogonal Decomposition for Large Scale Flow Data
  Philipp Krah, Thomas Engels, Kai Schneider, Julius Reiss
  Adv Comput Math 48, 10 (2022).
  [PDF][Code]

• Supervised Learning for Multi Zone Sound Field Reproduction under Harsh Environmental Conditions
  Henry Sallandt, Philipp Krah, Mathias Lemke
  Preprint arXiv:2112.07349, under review
  [PDF][Code]

• Phases at finite winding number of an Abelian lattice gauge theory
  Paolo Stornati, Debasish Banerjee, Karl Jansen, Philipp Krah
  Lattice Conference 2021
  [PDF][Code]

• Model Order Reduction of Combustion Processes with Complex Front Dynamics
  Philipp Krah, Mario Sroka, Julius Reiss
  Numerical Mathematics and Advanced Applications ENUMATH 2019
  [PDF][Code]

• SU(3) Yang Mills theory at small distances and fine lattices
  Nikolai Husung Mateusz Koren, Philipp Krah and Rainer Sommer
  EPJ Web of Conferences 175, 14024 (2018)
  [PDF]