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

• [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]
• [Oct. 2024] Beata, Arthur, Julius, Kai, and I have published our robust shifted POD paper in SIAM SISC!
• [July 2024] Congrats to my master student Beata for her amazing work that led to this nice preprint: [Preprint]
• [July 2024] Micro-macro model order reduction for shallow water flows published in ACOM: [Article]
• [May 2024] Vlasov-Poisson Article published in CiCP [Article]
• [May 2024] I will be speaking about dynamic low rank approximation at the FRUMAM workshop “Low rank optimization”, 31st of May [Link]
• [Mar. 2024] My first cooperation with the signal team of the Institut de Mathématiques de Marseille has led to this nice work [PDF]
• [Mar. 2024] New co-authored article on impurity clustering in plasmas of Tokamaks [Article]
• [Feb. 2024] I will be giving a talk on kinetic plasma simulations, 14.05.2024 at Séminaire Analyse Appliquée

Publications

• 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
  Preprint arXiv:2407.17539 (2024)
  [Arxiv][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]

• A robust shifted proper orthogonal decomposition: Proximal methods for decomposing flows with multiple transports
  Philipp Krah, Arthur Marmin, Beata Zorawski, Julius Reiss, Kai Schneider
  Preprint arXiv:2403.04313, accepted in SIAM SISC 1.October
  [Arxiv][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]

• Parametric model order reduction for a wildland fire model via the shifted POD based deep learning method
  Shubhaditya Burela, Philipp Krah, Julius Reiss
  Preprint arXiv:2304.14872
  [PDF][Code]

• 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]