Information Field Theory. Torsten Enßlin MPI for Astrophysics Ludwig Maximilian University Munich
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1 Information Field Theory Torsten Enßlin MPI for Astrophysics Ludwig Maximilian University Munich
2
3 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
4 Information Hamiltonian Theory inference problem as information statistical field theory
5 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
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8 An information field theory is defined over continuous space, But calculations can be performed in sufficiently fine discretized spaces.
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11 Free Theory Gaussian signal & noise, linear response
12 Free Theory Gaussian signal & noise, linear response
13 Free filter Theory Wiener theory Gaussian signal noise, linear response known&for 60 years
14 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]
15 Reconstruction of Primordial gravitational Potential
16 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),...
17 Interacting Theory non-gaussian signal, noise, or non-linear response
18 Wiener filter information propagator information source (data) non-linear filtering by combining Wiener filter uncertainty loop correction
19 Primordial non-gaussianity measurement
20 signal field: electron density mock signal from known power spectrum
21 data = integrated signal
22 information source
23 reconstruction
24
25 Greiner, Schnitzler, Enßlin (2016)
26 NIFTY - Numerical Information Field Theory Selig et al. (arxiv: ) Code & pip pip install install ift_nifty ift_nifty
27 Faraday Sky Faraday depth:
28 Faraday Sky Taylor et al. (2009) Faraday depth:
29 Faraday Sky Oppermann et al. (2012) Faraday depth:
30 Faraday Sky Oppermann et al. (2012) Faraday depth:
31 Faraday Sky Oppermann et al. (2012) Faraday depth:
32 LOFAR Extended VLA Extended VLA SKA ALMA APERTIF Meerkat ASKAP
33 Radio Interferometry Visibilities Correlated voltages of two Antennas Visibilities Interferometer baseline coordinates Fourier domain of the sky Sky Brightness Flat sky coordinates
34 Data model known unknown covariances: unknown known response known
35 Data model known unknown covariances: unknown known response known
36 Radio Interferometry Junklewitz et al. (arxiv: ) low noise, 40% uv-coverage
37 Radio Interferometry Junklewitz et al. (arxiv: ) low noise, 40% uv-coverage
38 Radio Interferometry Junklewitz et al. (arxiv: ) simulated signal
39 Radio Interferometry Junklewitz et al. (arxiv: ) low noise, 40% uv-coverage
40 Radio Interferometry Junklewitz et al. (arxiv: ) high noise, 40% uv-coverage
41 Radio Interferometry Junklewitz et al. (in prep.) low noise, 10% uv-coverage
42 Abell 8415 MHz data by Valentina Vacca
43 Abell 8415 MHz CLEAN map by Valentina Vacca
44 Abell 8415 MHz fast-resolve map by Maksim Greiner
45 Abell 8415 MHz fast-resolve uncertainty map by Maksim Greiner
46 Denoising, Deconvolving, and Decomposing Photon Observations Selig et al. (2014) / \ (oo ) \=/ / \ // /o\ \\ // \ / \ / (' \ / ') [] [] /_] [_\
47 3 D PO challenges & assumptions Selig & Enßlin (2014) arxiv: signal fields diffuse point-like superposition photon flux instrument response functions photon counts Poissonian shot noise data
48 3 D PO challenges & assumptions log-normal Selig & Enßlin (2014) arxiv: power spectrum diffuse point-like photon flux photon counts data likelihood
49 3 D PO challenges & assumptions Selig & Enßlin (2014) arxiv: model parameters smoothness prior log-normal independent inverse-gamma power spectrum diffuse point-like photon flux photon counts data likelihood
50 3 D PO challenges & assumptions Selig & Enßlin (2014) arxiv: model parameters smoothness prior log-normal independent inverse-gamma power spectrum diffuse point-like photon flux photon counts data likelihood
51 3 D PO challenges & assumptions Selig & Enßlin (2014) arxiv:
52 3 D PO 1D scenario
53 D3PO a guided demo The Response operator
54 D3PO a guided demo raw input data D1PO denoised observations
55 D3PO a guided demo demasked flux D2PO denoised observations
56 D3PO a guided demo demasked flux D2PO deconvolved flux
57 D3PO a guided demo reconvolved point sources D2PO deconvolved flux
58 D3PO a guided demo reconvolved point sources D3PO diffuse flux
59 γ-ray sky
60 photon data relative residuals diffuse flux relative difference point-liketoflux Fermi map
61
62
63
64
65 γ-ray sky
66
67
68
69 energy
70 log-data denoised deconvolved decomposed
71 log-data denoised deconvolved decomposed
72 log-data denoised deconvolved decomposed
73 log-data denoised deconvolved decomposed
74 log-data denoised deconvolved decomposed
75 Selig, Vacca, Oppermann, Enßlin (2015) log-data denoised deconvolved decomposed
76 First D³PO Fermi Point Source Candidates Catalog (1DF) catalog with 3106 candidates, 1897 of them known in 3FGL
77 Diffuse gamma-ray sky
78 Diffuse gamma-ray sky bulge -like bubble -like cloud -like
79 Spectra of diffuse components mix of hadronic + leptonic? hadronic? π0 decay Inverse Compton leptonic? Inverse Compton
80 diffuse flux superposition cloud -like bubble -like
81 cloud -like
82 Planck dust map
83
84
85
86
87 cloud -like = cold/dense ISM
88 bubble-like Photon spectral index: 2.4 Inverse Compton?
89 30GHz (Planck 2013) Photon spectral index: 2.56 Synchrotron?
90 bubble-like
91 Planck 2013 low frequency component Free-free and synchrotron emission tracing hot ISM
92 buble -like = hot/dilute ISM
93 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
94 Online resources Online material (info/codes/docu/data/maps): IFT: NIFTy: D³PO: Data:
95 Thank you!
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