Information Field Theory

Information field theory (IFT) is information theory, logic under uncertainty, applied to fields. A field can be any quantity defined over some space, such as the air temperature over Europe, the magnetic field strength in the Milky Way, or the matter density in the Universe. IFT describes how data and knowledge can be used to infer field properties. Mathematically it is a statistical field theory and exploits many of the tools developed for such. Practically, it is a framework for signal processing and image reconstruction. IFT is fully Bayesian. How else can infinitely many field degrees of freedom be constrained by finite data? It can be used without the knowledge of Feynman diagrams. There is a full toolbox of methods. It reproduces many known well working algorithms. This should be reassuring. And, there were certainly previous works in a similar spirit, like Bayesian Field Theory (BFT). See below for IFT & BFT publications and previous works. Anyhow, in many cases IFT provides novel rigorous ways to extract information from data.


Radiation biology, radio astronomy and cosmic rays using information field theory

What do radiation biology, radio astronomy and cosmic ray measurements have in common? For one thing, radiation occurs in all of them. For another, all of these fields are explored using large-scale research facilities and require intelligent algorithms to visualize the quantities that occur in the process. In order to advance this imaging in an interdisciplinary way, the Federal Ministry of Education and Research (BMBF) is now funding the project "Information Field Theory for Experiments at Large-scale Research Facilities". Seven German universities, the Max Planck Institute for Astrophysics (MPA) and Erium GmbH, founded by former MPA students, are involved.

IFT Introduction


IFT Applications


  • Analysis of Dynamical Field Inference in a Supersymmetric Theory
    Margret Westerkamp, Igor Ovchinnikov, Philipp Frank, Torsten A. Enßlin, Phys. Sci. Forum 2022, 5(1), 27;
  • Dynamical field inference and supersymmetry
    Margret Westerkamp, Igor Ovchinnikov, Torsten A. Enßlin, Entropy 2021, 23(12), 1652; arXiv:2010.15414
  • Probabilistic simulation of partial differential equations
    Philipp Frank, Torsten A. Enßlin, 2020, submitted, arXiv:2010.06583
  • Field dynamics inference for local and causal interactions
    Philipp Frank, Reimar Leike, Torsten A. Enßlin, 2021, Annalen der Physik, 2000486, arXiv:1902.02624
  • Towards information-optimal simulation of partial differential equations
    Reimar Leike, Torsten A. Enßlin, 2018, Physical Review E, 97, 033314; journal article, arXiv:1709.02859
  • Consistency and convergence of simulation schemes in Information field dynamics
    Martin Dupont, Torsten A. Enßlin, 2018, Physical Review E, Vol. 98, No. 4, DOI: 10.1103/PhysRevE.98.043307, arXiv:1802.00971
  • Field dynamics inference via spectral density estimation
    Philipp Frank, Theo Steininger, Torsten A. Enßlin, Phys. Rev. E 96, 052104 (2017) arXiv:1708.05250
  • Supersymmetric theory of stochastic ABC model
    Igor Ovchinikov, Yuquan Sun, Torsten A. Enßlin and Kang L. Wang, J. Phys. Commun. (2018)
  • Dynamic system classifier
    Daniel Pumpe, Maksim Greiner, Ewald Mueller, Torsten A. Enßlin, Physical Review E (Vol.94, No.1) DOI: 10.1103/PhysRevE.94.012132 arXiv:1601.07901
  • Kinematic dynamo, supersymmetry breaking, and chaos
    Igor Ovchinikov, Torsten A. Enßlin, Physical Review D, Volume 93, Issue 8, id.085023 (2016) arXiv:1512.01651
  • Mathematical foundation of Information Field Dynamics
    Christian Muench, master thesis, Technical University Munich arXiv:1412.1226
  • Simulation of stochastic network dynamics via entropic matching
    Tiago Ramalho, Marco Selig, Ulrich Gerland, Torsten A. Enßlin, Phys. Rev. E 87, 022719 (2013) arXiv:1209.3700
  • Information field dynamics for simulation scheme construction
    Torsten A. Enßlin, 2013, Phys. Rev. E 87, 013308 arXiv:1206.4229

IFT Tools

Further literature

  • DIP -- Diagnostics for Insufficiencies of Posterior calculations in Bayesian signal inference
    Sebastian Dorn, Niels Oppermann, Torsten A. Enßlin, Phy. Rev. E 88 arXiv:1307.3889
  • Lectures on Probability, Entropy, and Statistical Physics
    A. Caticha arXiv:0808.0012
  • MAGIC: Exact Bayesian Covariance Estimation and Signal Reconstruction for Gaussian Random Fields
    B. Wandelt arXiv:ph/0401623