Can a machine learn about multiple scattering?

Artur Gower (The University of Manchester)

ATB Frank Adams 1,

Most mathematical models of wave propagation assumes a continuous medium, like a sound wave travelling in the air, that is only occasionally interpreted by some discontinuity, like a wall. However, the wave is not fond of this assumption for very short wavelengths. The smaller the wavelength, the more the wave starts to see the details of its host material, and realise that it is actually travelling in a discrete medium (possibly made up of molecules or cells or atoms or stars! Depends on the kind of wave.). More often, the medium will appear to be semi-discrete, as one of its components will likely be larger than all the rest.  Faced with an uncountable number of small objects, the wave will scatter from each of them, and then this scattered wave will re-scatter again and again and so on. This is called multiple scattering. It is a phenomena that appears in acoustics, optics, electromagnetics, quantum mechanics and gravity waves, when the wavelength, compared to the medium, is small enough. The question we pose is what can we learn about the small objects by measuring waves after they have been multiply scattered by this semi-discrete medium?  The multiply scattered waves are often complex and difficult to model analytically. So we turn to machine learning to see if we can figure out the size of the small objects and their quantity, per unit area, from these waves.

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