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.


Black hole as video: M87* in time, space and frequency

In April 2017 the Event Horizon Telescope (EHT) observed the super-massive black hole M87* and provided a first image of its shadow that went around the world. Researchers at the Max Planck Institute for Astrophysics have now reconstructed a video of the immediate surroundings of a black hole from the same underlying data. This not only confirms previous findings, video of the immediate surroundings of a black hole from the same underlying data. This not only confirms previous findings, it also hints at new structures and dynamics in the gas disk around the black hole.

Watch stars move around the Milky Way’s supermassive black hole in deepest images yet

The European Southern Observatory’s Very Large Telescope Interferometer (ESO’s VLTI) has obtained the deepest and sharpest images to date of the region around the supermassive black hole at the centre of our galaxy. The new images zoom in 20 times more than what was possible before the VLTI and have helped astronomers find a never-before-seen star close to the black hole. By tracking the orbits of stars at the centre of our Milky Way, the team has made the most precise measurement yet of the black hole’s mass.

Algorithmic improvements for radio interferometry

Radio telescopes observe the sky in a very indirect fashion. Sky images in the radio frequency range therefore have to be computed using sophisticated algorithms. Scientists at the MPI for Astrophysics have developed a series of improvements for these algorithms, which help to improve the telescopes' resolution considerably.

Artificial intelligence combined

Artificial intelligence expands into all areas of the daily life, including research. Neural networks learn to solve complex tasks by training them on the basis of enormous amounts of examples. Researchers at the Max Planck Institute for Astrophysics in Garching have now succeeded in combining several networks, each one specializing in a different task, to jointly solve tasks using Bayesian logic in areas none was originally trained on. This enables the recycling of expensively trained networks and is an important step towards universally deductive artificial intelligence.

Next generation imaging

The Information Field Theory Group at the Max Planck Institute for Astrophysics has released a new version of the NIFTy software for scientific imaging. NIFTy5 generates an optimal imaging algorithm from the complex probability model of a measured signal. Such algorithms have already proven themselves in a number of astronomical applications and can now be used in other areas as well.

The embarrassment of false predictions -
How to best communicate probabilities?

Complex predictions such as election forecasts or the weather reports often have to be simplified before communication. But how should one best simplify these predictions without facing embarrassment? In astronomical data analysis, researchers are also confronted with the problem of simplifying probabilities. Two researchers at the Max Planck Institute for Astrophysics now show that there is only one mathematically correct way to measure how embarrassing a simplified prediction can be. According to this, the recipient of a prediction should be deprived of the smallest possible amount of information.

Galactic anatomy with gamma rays

The anatomy of the Milky Way as seen in gamma light is full of mysteries. For example, there are gigantic bubbles of unknown origin above and below the center of the Milky Way that emit a lot of this high-energy radiation. A new method for imaging, developed at the Max Planck Institute for Astrophysics, now divided the Galactic gamma-radiation into three fundamental components: radiation from point sources, radiation from reactions of energetic protons with dense cold gas clouds, and radiation from electrons scattering light in the thin, hot, Galactic gas. The anatomic insights gained unravel some Galactic mysteries. Thus, it appears that the gamma-ray bubbles are simply outflows of ordinary, hot gas from the central region of the Milky Way.

New all-sky map shows the magnetic fields of the Milky Way with the highest precision

With a unique new all-sky map, scientists at MPA have made significant progress toward measuring the magnetic field structure of the Milky Way in unprecedented detail. Specifically, the map is of a quantity known as Faraday depth, which among other things, depends strongly on the magnetic fields along a particular line of sight. To produce the map, data were combined from more than 41,000 individual measurements using a novel image reconstruction technique. The work was a collaboration between scientists at the Max Planck Institute for Astrophysics (MPA), who are specialists in the new discipline of information field theory, and a large international team of radio astronomers. The new map not only reveals the structure of the galactic magnetic field on large scales, but also small-scale features that provide information about urbulence in the galactic gas.

D3PO: Denoising, Deconvolving, and Decomposing Photon Observations

A common problem for scientists analysing astronomical images is the separation of diffuse and point-like components. This analysis has now become easier: scientists at the Max Planck Institute for Astrophysics have recently published the D3PO algorithm, which removes noise effects and instrumental artefacts from the observed images, while simultaneously separating diffuse and point-like contributions.

Resolving the radio sky

Radio astronomers obtain extremely high resolution sky images by using interferometers, instruments where several single radio telescopes are linked together. However, optimal data analysis procedures for such an instrument are significantly more involved than for a single telescope. Scientists from the Max Planck Institute for Astrophysics have now developed the algorithm RESOLVE which solves a number of outstanding problems in radio imaging.

Data analysis and steam engines

As astronomical telescopes become more and more sensitive, the analysis techniques become ever more sophisticated. But do we need a new theoretical approach for a modern image reconstruction method? Not necessarily, a well-known theory, originally developed for a better understanding of steam engines, does the trick: thermodynamics. Two researchers at the Max Planck Institute for Astrophysics have now shown that the so called Gibbs energy in thermodynamics, known for more than a century, can be applied to the development of new, optimal imaging techniques.

Mathematics of digital senses: Information Field Theory for signal recognition

The correct interpretation of signals through our senses is not only an essential problem of living creatures, but also of fundamental scientific relevance. Scientists at the Max-Planck-Institute for Astrophysics have shown that mathematical methods from particle physics can be used for developing image reconstruction techniques. These yield optimal results even for incomplete, defective, and distorted data. Information Field Theory, which is used to develop such image reconstruction techniques, provides us with algorithms, i.e. mathematical instructions, for computing complicated perception processes in engineering and science, such as in cosmology.

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