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

6

7

8 An information field theory is defined over continuous space, But calculations can be performed in sufficiently fine discretized spaces.

9

10

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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