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Machine learning S-wave scattering phase shifts bypassing the radial Schrödinger equation

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Abstract

We present a proof of concept machine learning model resting on a convolutional neural network capable of yielding accurate scattering s-wave phase shifts caused by different three-dimensional spherically symmetric potentials at fixed collision energy thereby bypassing the radial Schrödinger equation. In our work, we discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor. The good performance, even in presence of bound states in the data sets, exhibited by our model that accordingly is trained on the Hamiltonian through each scattering potential, demonstrates the feasibility of this proof of principle.

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Data availability

This manuscript has associated data in a data repository. [Authors comment: The data are publicly released on author‘s (a) GitHub (https://github.com/aleromualdi/quantum-phase-shift-cnn).]

Notes

  1. Note that in this case, using the same model hyperparameters as in the previous cases, resulted in higher variability in validation loss during training. We regularized the model by reducing the learning rate of the Adam optimizer to \(10^{-6}\) and the training epochs to 5000.

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Acknowledgements

We thank professor Ravi Rau for pointing out important works regarding the phase amplitude equation and dr. Jan Hermann and dr. Peter Šušnjar for valuable comments and suggestions. This work was supported by the EU through the European Regional Development Fund CoE program TK133 “The Dark Side of the Universe”.

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Authors and Affiliations

  1. Berlin, Germany

    Alessandro Romualdi

  2. Departament de Física de la Matèria Condensada, Universitat de Barcelona, Carrer Martí i Franquès 1, 08028, Barcelona, Spain

    Gionni Marchetti

  3. National Institute of Chemical Physics and Biophysics, Rävala 10, 10143, Tallinn, Estonia

    Gionni Marchetti

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  1. Alessandro Romualdi
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  2. Gionni Marchetti
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Both authors contributed equally to this study.

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Romualdi, A., Marchetti, G. Machine learning S-wave scattering phase shifts bypassing the radial Schrödinger equation. Eur. Phys. J. B 94, 249 (2021). https://doi.org/10.1140/epjb/s10051-021-00261-1

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