Information Field Theory Torsten Enßlin MPI for Astrophysics Ludwig Maximilian University Munich
Information Field Theory signal field: degrees of freedom data set: finite additional information needed information: physical laws, symmetries, continuity, statistical homogeneity/isotropy,... most important: space, time, & fields are continuous combining concrete (data) & abstract (knowledge) information information theory for fields
Information Hamiltonian Theory inference problem as information statistical field theory
IFT Dictionary Translation: field inference problem Dictionary: log joint PDF evidence Wiener variance noise weighted data inference algorithms maximum a Posteriori uncertainty corrections Shannon information = = = = = = statistical field theory negative Hamiltonian partition function Z information propagator information source Feynman diagrams classical solution loop corrections negative entropy
An information field theory is defined over continuous space, But calculations can be performed in sufficiently fine discretized spaces.
Free Theory Gaussian signal & noise, linear response
Free Theory Gaussian signal & noise, linear response
Free filter Theory Wiener theory Gaussian signal noise, linear response known&for 60 years
Reconstruction of Primordial gravitational Potential 3D reconstruction expensive reconstruct slice by slice Signal: potential on sphere of chosen radius Noise: anything else influencing the data Wiener filter: [Yadav & Wandelt 2005, Dorn, Greiner, Enßlin 2015]
Reconstruction of Primordial gravitational Potential
Free Theory Gaussian signal & noise, linear response Interacting Theory non-gaussian signal, noise, or non-linear response use field theory toobox: Feynman diagrams, renormalization, resummation, effective action (=MaxEnt), mean field theory (variational Bayes),...
Interacting Theory non-gaussian signal, noise, or non-linear response
Wiener filter information propagator information source (data) non-linear filtering by combining Wiener filter uncertainty loop correction
Primordial non-gaussianity measurement
signal field: electron density mock signal from known power spectrum
data = integrated signal
information source
reconstruction
Greiner, Schnitzler, Enßlin (2016)
NIFTY - Numerical Information Field Theory Selig et al. (arxiv:1301.4499) Code & Docu @ http://www.mpa-garching.mpg.de/ift/nifty/ pip pip install install ift_nifty ift_nifty
Faraday Sky Faraday depth:
Faraday Sky Taylor et al. (2009) Faraday depth:
Faraday Sky Oppermann et al. (2012) Faraday depth:
Faraday Sky Oppermann et al. (2012) Faraday depth:
Faraday Sky Oppermann et al. (2012) Faraday depth:
LOFAR Extended VLA Extended VLA SKA ALMA APERTIF Meerkat ASKAP
Radio Interferometry Visibilities Correlated voltages of two Antennas Visibilities Interferometer baseline coordinates Fourier domain of the sky Sky Brightness Flat sky coordinates
Data model known unknown covariances: unknown known response known
Data model known unknown covariances: unknown known response known
Radio Interferometry Junklewitz et al. (arxiv:1311.5282) low noise, 40% uv-coverage
Radio Interferometry Junklewitz et al. (arxiv:1311.5282) low noise, 40% uv-coverage
Radio Interferometry Junklewitz et al. (arxiv:1311.5282) simulated signal
Radio Interferometry Junklewitz et al. (arxiv:1311.5282) low noise, 40% uv-coverage
Radio Interferometry Junklewitz et al. (arxiv:1311.5282) high noise, 40% uv-coverage
Radio Interferometry Junklewitz et al. (in prep.) low noise, 10% uv-coverage
Abell 2219 @ 8415 MHz data by Valentina Vacca
Abell 2219 @ 8415 MHz CLEAN map by Valentina Vacca
Abell 2219 @ 8415 MHz fast-resolve map by Maksim Greiner
Abell 2219 @ 8415 MHz fast-resolve uncertainty map by Maksim Greiner
Denoising, Deconvolving, and Decomposing Photon Observations Selig et al. (2014) www.mpa-garching.mpg.de/ift/d3po / \ (oo ) \=/ / \ // /o\ \\ // \ / \ / (' \ / ') [] [] /_] [_\
3 D PO challenges & assumptions Selig & Enßlin (2014) arxiv: 1311.1888 signal fields diffuse point-like superposition photon flux instrument response functions photon counts Poissonian shot noise data
3 D PO challenges & assumptions log-normal Selig & Enßlin (2014) arxiv: 1311.1888 power spectrum diffuse point-like photon flux photon counts data likelihood
3 D PO challenges & assumptions Selig & Enßlin (2014) arxiv: 1311.1888 1+2+2 model parameters smoothness prior log-normal independent inverse-gamma power spectrum diffuse point-like photon flux photon counts data likelihood
3 D PO challenges & assumptions Selig & Enßlin (2014) arxiv: 1311.1888 1+2+2 model parameters smoothness prior log-normal independent inverse-gamma power spectrum diffuse point-like photon flux photon counts data likelihood
3 D PO challenges & assumptions Selig & Enßlin (2014) arxiv: 1311.1888
3 D PO 1D scenario
D3PO a guided demo The Response operator
D3PO a guided demo raw input data D1PO denoised observations
D3PO a guided demo demasked flux D2PO denoised observations
D3PO a guided demo demasked flux D2PO deconvolved flux
D3PO a guided demo reconvolved point sources D2PO deconvolved flux
D3PO a guided demo reconvolved point sources D3PO diffuse flux
γ-ray sky
photon data relative residuals diffuse flux relative difference point-liketoflux Fermi map
γ-ray sky
energy
log-data denoised deconvolved decomposed
log-data denoised deconvolved decomposed
log-data denoised deconvolved decomposed
log-data denoised deconvolved decomposed
log-data denoised deconvolved decomposed
Selig, Vacca, Oppermann, Enßlin (2015) log-data denoised deconvolved decomposed
First D³PO Fermi Point Source Candidates Catalog (1DF) catalog with 3106 candidates, 1897 of them known in 3FGL
Diffuse gamma-ray sky
Diffuse gamma-ray sky bulge -like bubble -like cloud -like
Spectra of diffuse components mix of hadronic + leptonic? hadronic? π0 decay Inverse Compton leptonic? Inverse Compton
diffuse flux superposition cloud -like bubble -like
cloud -like
Planck dust map
cloud -like = cold/dense ISM
bubble-like Photon spectral index: 2.4 Inverse Compton?
Panck-haze @ 30GHz (Planck 2013) Photon spectral index: 2.56 Synchrotron?
bubble-like
Planck 2013 low frequency component Free-free and synchrotron emission tracing hot ISM
buble -like = hot/dilute ISM
Conclusions Information field theory is information theory for fields Methods from QFT/SFT can be used Nummerical IFT in coordinate free way via NIFTy Applications so far: radio interferometry, galactic tomography, Faraday studies, CMB studies, cosmography, gamma ray imaging, gravitational wave signal classification, simulation scheme construction,... Gamma ray sky: morphological & spectral decomposition most diffuse galactic emission from hot & cold ISM phases
Online resources Online material (info/codes/docu/data/maps): IFT: www.mpa-garching.mpg.de/ift NIFTy: www.mpa-garching.mpg.de/ift/nifty D³PO: www.mpa-garching.mpg.de/ift/d3po Data: www.mpa-garching.mpg.de/ift/fermi
Thank you! www.mpa-garching.mpg.de/ift