Generative Models of Multichannel Data from a Single Example—Application to Dust Emission

Blancard, Bruno Régaldo-Saint; Allys, Erwan; Auclair, Constant; Boulanger, F.; Eickenberg, Michael; Levrier, F.; Vacher, L.; Zhang, Sixin

doi:10.3847/1538-4357/aca538

Cited by 5 publications

(2 citation statements)

References 62 publications

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“…( 23 , 24 ), involving extensions to the modeling of cross-regularities when multiple channels are available, e.g. ( 22 ).…”

Section: Discussionmentioning

confidence: 99%

Scattering spectra models for physics

Cheng,

Morel,

Allys

et al. 2024

PNAS Nexus

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Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the number of samples is limited. In this paper, we introduce scattering spectra models for stationary fields and we show that they provide accurate and robust statistical descriptions of a wide range of fields encountered in physics. These models are based on covariances of scattering coefficients, i.e. wavelet decomposition of a field coupled with a pointwise modulus. After introducing useful dimension reductions taking advantage of the regularity of a field under rotation and scaling, we validate these models on various multiscale physical fields and demonstrate that they reproduce standard statistics, including spatial moments up to 4th order. The scattering spectra provide us with a low-dimensional structured representation that captures key properties encountered in a wide range of physical fields. These generic models can be used for data exploration, classification, parameter inference, symmetry detection, and component separation.

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“…( 23 , 24 ), involving extensions to the modeling of cross-regularities when multiple channels are available, e.g. ( 22 ).…”

Section: Discussionmentioning

confidence: 99%

Scattering spectra models for physics

Cheng,

Morel,

Allys

et al. 2024

PNAS Nexus

Self Cite

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“…Where the forward WPH transform takes less than a second, the inverse transform may take more than an hour. Even with these deficiencies, this transformation has been used with great success, most notably to analyze cosmological simulations [19,20].…”

Section: Mallat Scattering Transformation (Mst) and Wavelet Phase Har...mentioning

confidence: 99%

Mallat Scattering Transformation based surrogate for Magnetohydrodynamics

Glinsky¹,

Maupin

2023

Comput Mech

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A Machine and Deep Learning (MLDL) methodology is developed and applied to give a high fidelity, fast surrogate for 2D resistive MagnetoHydroDynamic (MHD) simulations of Magnetic Liner Inertial Fusion (MagLIF) implosions. The resistive MHD code is used to generate an ensemble of implosions with different liner aspect ratios, initial gas preheat temperatures (that is, different adiabats), and different liner perturbations. The liner density and magnetic field as functions of x, y, and z were generated. The Mallat Scattering Transformation (MST) is taken of the logarithm of both fields and a Principal Components Analysis (PCA) is done on the logarithm of the MST of both fields. The fields are projected onto the PCA vectors and a small number of these PCA vector components are kept. Singular Value Decompositions of the cross correlation of the input parameters to the output logarithm of the MST of the fields, and of the cross correlation of the SVD vector components to the PCA vector components are done. This allows the identification of the PCA vectors vis-a-vis the input parameters. Finally, a Multi Layer Perceptron (MLP) neural network with ReLU activation and a simple three layer encoder/decoder architecture is trained on this dataset to predict the PCA vector components of the fields as a function of time. Details of the implosion, stagnation, and the disassembly are well captured. Examination of the PCA vectors and a permutation importance analysis of the MLP show definitive evidence of an inverse turbulent cascade into a dipole emergent behavior. The orientation of the dipole is set by the initial liner perturbation. The analysis is repeated with a version of the MST which includes phase, called Wavelet Phase Harmonics (WPH). While WPH do not give the physical insight of the MST, they can and are inverted to give field configurations as a function of time, including field-to-field correlations.

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Separation of dust emission from the cosmic infrared background in Herschel observations with wavelet phase harmonics

Auclair,

Allys,

Boulanger

et al. 2023

A&A

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The low-brightness dust emission at high Galactic latitudes is of interest with respect to studying the interplay among the physical processes involved in shaping the structure of the interstellar medium (ISM), as well as in statistical characterizations of the dust emission as a foreground to the cosmic microwave background (CMB). Progress in this avenue of research has been hampered by the difficulty related to separating the dust emission from the cosmic infrared background (CIB). We demonstrate that the dust and CIB may be effectively separated based on their different structure on the sky and we use the separation to characterize the structure of diffuse dust emission on angular scales, where the CIB is a significant component in terms of power. We used scattering transform statistics, wavelet phase harmonics (WPH) to perform a statistical component separation using Herschel SPIRE observations. This component separation is done only from observational data using non-Gaussian properties as a lever arm and is done at a single $250\ frequency. This method, which we validated on mock data, gives us access to non-Gaussian statistics of the interstellar dust and an output dust map that is essentially free from CIB contamination. Our statistical modeling characterizes the non-Gaussian structure of the diffuse ISM down to the smallest scales observed by Herschel. We recovered the power law shape of the dust power spectrum up to $k = 2 \ arcmin $, where the dust signal represents $2 <!PCT!>$ of the total power. Going beyond the standard power spectra analysis, we show that the non-Gaussian properties of the dust emission are not scale-invariant. The output dust map reveals coherent structures at the smallest scales, which had been hidden by the CIB anisotropies. This aspect opens up new observational perspectives on the formation of structure in the diffuse ISM, which we discuss here in reference to a previous work. We have succeeded in performing a statistical separation from the observational data at a single frequency by using non-Gaussian statistics.

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Generative Models of Multichannel Data from a Single Example—Application to Dust Emission

Cited by 5 publications

References 62 publications

Scattering spectra models for physics

Scattering spectra models for physics

Mallat Scattering Transformation based surrogate for Magnetohydrodynamics

Separation of dust emission from the cosmic infrared background in Herschel observations with wavelet phase harmonics

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