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Machine-learning-based models in particle-in-cell codes for advanced physics extensions

Part of: Machine Learning for Plasma Physics and Fusion Energy

Published online by Cambridge University Press:  07 December 2022

Chiara Badiali Open the ORCID record for Chiara Badiali [Opens in a new window] ,
Pablo J. Bilbao Open the ORCID record for Pablo J. Bilbao [Opens in a new window] ,
Fábio Cruz Open the ORCID record for Fábio Cruz [Opens in a new window]  and
Luís O. Silva Open the ORCID record for Luís O. Silva [Opens in a new window]
Chiara Badiali*
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal
Pablo J. Bilbao
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal
Fábio Cruz
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal Inductiva Research Labs, Rua da Prata 80, 1100-420 Lisboa, Portugal
Luís O. Silva*
Affiliation:
GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

In this paper we propose a methodology for the efficient implementation of machine learning (ML)-based methods in particle-in-cell (PIC) codes, with a focus on Monte Carlo or statistical extensions to the PIC algorithm. The presented approach allows for neural networks to be developed in a Python environment, where advanced ML tools are readily available to proficiently train and test them. Those models are then efficiently deployed within highly scalable and fully parallelized PIC simulations during runtime. We demonstrate this methodology with a proof-of-concept implementation within the PIC code OSIRIS, where a fully connected neural network is used to replace a section of a Compton scattering module. We demonstrate that the ML-based method reproduces the results obtained with the conventional method and achieves better computational performance. These results offer a promising avenue for future applications of ML-based methods in PIC, particularly for physics extensions where a ML-based approach can provide a higher performance increase.

Keywords

plasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 88 , Issue 6 , December 2022 , 895880602
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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Footnotes

‡

C. Badiali and P.J. Bilbao contributed equally to this work.

References

REFERENCES

Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., Devin, M., et al. 2015 TensorFlow: Large-scale machine learning on heterogeneous systems. Software available from tensorflow.org.Google Scholar
Aguilar, X. & Markidis, S. 2021 A deep learning-based particle-in-cell method for plasma simulations. In 2021 IEEE International Conference on Cluster Computing (CLUSTER), pp. 692–697. IEEE.CrossRefGoogle Scholar
Arber, T.D., Bennett, K., Brady, C.S., Lawrence-Douglas, A., Ramsay, M.G., Sircombe, N.J., Gillies, P., Evans, R.G., Schmitz, H., Bell, A.R., et al. 2015 Contemporary particle-in-cell approach to laser-plasma modelling. Plasma Phys. Control. Fusion 57 (11), 113001.CrossRefGoogle Scholar
Arrowsmith, C.D., Shukla, N., Charitonidis, N., Boni, R., Chen, H., Davenne, T., Dyson, A., Froula, D.H., Gudmundsson, J.T., Huffman, B.T., et al. 2021 Generating ultradense pair beams using 400 GeV/c protons. Phys. Rev. Res. 3 (2), 023103.CrossRefGoogle Scholar
Bacchini, F., Ripperda, B., Chen, A.Y. & Sironi, L. 2018 Generalized, energy-conserving numerical simulations of particles in general relativity. I. Time-like and null geodesics. Astrophys. J. Suppl. Ser. 237 (1), 6.CrossRefGoogle Scholar
Bello, F.A.D., Shlomi, J., Badiali, C., Frattari, G., Gross, E., Ippolito, V. & Kado, M. 2021 Efficiency parameterization with neural networks. Comput. Softw. Big Sci. 5 (1), 1–12.CrossRefGoogle Scholar
Bird, G.A. 1989 Perception of numerical methods in rarefied gasdynamics. Prog. Astronaut. Aeronaut. 117, 211–226.Google Scholar
Blumenthal, G.R. & Gould, R.J. 1970 Bremsstrahlung, synchrotron radiation, and compton scattering of high-energy electrons traversing dilute gases. Rev. Mod. Phys. 42 (2), 237.CrossRefGoogle Scholar
Buneman, O. 1993 Tristan. Computer Space Plasma Physics: Simulation Techniques and Softwares.Google Scholar
Chollet, F. 2017 Deep Learning with Python. Simon and Schuster.Google Scholar
Chollet, F. 2018 Keras: The Python Deep Learning Library. Astrophysics Source Code Library. ascl–1806.Google Scholar
Compton, A.H. 1923 A quantum theory of the scattering of x-rays by light elements. Phys. Rev. 21 (5), 483.CrossRefGoogle Scholar
Curcic, M. 2019 A parallel Fortran framework for neural networks and deep learning. In Acm sigplan fortran forum (Vol. 38, No. 1, pp. 421). New York, NY, USA: ACM.CrossRefGoogle Scholar
Dawson, J.M. 1983 Particle simulation of plasmas. Rev. Mod. Phys. 55 (2), 403.CrossRefGoogle Scholar
Decyk, V.K. 2007 Upic: a framework for massively parallel particle-in-cell codes. Comput. Phys. Commun. 177 (1–2), 95–97.CrossRefGoogle Scholar
Del Gaudio, F., Grismayer, T., Fonseca, R.A. & Silva, L.O. 2020 Compton scattering in particle-in-cell codes. J. Plasma Phys. 86 (5).CrossRefGoogle Scholar
Fonseca, R.A., Martins, S.F., Silva, L.O., Tonge, J.W., Tsung, F.S. & Mori, W.B. 2008 One-to-one direct modeling of experiments and astrophysical scenarios: pushing the envelope on kinetic plasma simulations. Plasma Phys. Control. Fusion 50 (12), 124034.CrossRefGoogle Scholar
Fonseca, R.A., Silva, L.O., Tsung, F.S., Decyk, V.K., Lu, W., Ren, C., Mori, W.B., Deng, S., Lee, S., Katsouleas, T., et al. 2002 OSIRIS: a three-dimensional, fully relativistic particle in cell code for modeling plasma based accelerators. In International Conference on Computational Science, pp. 342–351. Springer.CrossRefGoogle Scholar
Fukushima, K. 1969 Visual feature extraction by a multilayered network of analog threshold elements. IEEE Trans. Syst. Sci. Cybern. 5 (4), 322–333.CrossRefGoogle Scholar
Grismayer, T., Torres, R., Carneiro, P., Cruz, F., Fonseca, R.A. & Silva, L.O. 2021 Quantum electrodynamics vacuum polarization solver. New J. Phys. 23 (9), 095005.CrossRefGoogle Scholar
Han, J. & Moraga, C. 1995 The influence of the sigmoid function parameters on the speed of backpropagation learning. In International Workshop on Artificial Neural Networks, pp. 195–201. Springer.CrossRefGoogle Scholar
Higginson, D.P. 2017 A full-angle Monte-Carlo scattering technique including cumulative and single-event Rutherford scattering in plasmas. J. Comput. Phys. 349, 589–603.CrossRefGoogle Scholar
Hockney, R.W. & Eastwood, J.W. 1988 Computer Simulation Using Particles. CRC Press.CrossRefGoogle Scholar
Kemp, A.J, Pfund, R.E.W. & Meyer-ter Vehn, J. 2004 Modeling ultrafast laser-driven ionization dynamics with monte carlo collisional particle-in-cell simulations. Phys. Plasmas 11 (12), 5648–5657.Google Scholar
Kingma, D.P. & Ba, J. 2014 Adam: a method for stochastic optimization. arXiv:1412.6980.Google Scholar
Kirkpatrick, J., Pascanu, R., Rabinowitz, N., Veness, J., Desjardins, G., Rusu, A.A., Milan, K., Quan, J., Ramalho, T., Grabska-Barwinska, A., et al. 2017 Overcoming catastrophic forgetting in neural networks. Proc. Natl Acad. Sci. 114 (13), 3521–3526.CrossRefGoogle ScholarPubMed
Kube, R., Churchill, R.M. & Sturdevant, B. 2021 Machine learning accelerated particle-in-cell plasma simulations. arXiv preprint arXiv:2110.12444.Google Scholar
Miller, R.H. & Combi, M.R. 1994 A Coulomb collision algorithm for weighted particle simulations. Geophys. Res. Lett. 21 (16), 1735–1738.CrossRefGoogle Scholar
Nanbu, K. 1997 Theory of cumulative small-angle collisions in plasmas. Phys. Rev. E 55 (4), 4642.CrossRefGoogle Scholar
Ott, J., Pritchard, M., Best, N., Linstead, E., Curcic, M. & Baldi, P. 2020 A fortran-keras deep learning bridge for scientific computing. Scientific Programming, 2020.Google Scholar
Parfrey, K., Philippov, A. & Cerutti, B. 2019 First-principles plasma simulations of black-hole jet launching. Phys. Rev. Lett. 122 (3), 035101.CrossRefGoogle ScholarPubMed
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., et al. 2019 Pytorch: an imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems 32, pp. 8024–8035. Curran Associates.Google Scholar
Sherlock, M. 2008 A Monte-Carlo method for Coulomb collisions in hybrid plasma models. J. Comput. Phys. 227 (4), 2286–2292.CrossRefGoogle Scholar
Shukla, N., Schoeffler, K., Boella, E., Vieira, J., Fonseca, R. & Silva, L.O. 2020 Interplay between the Weibel instability and the Biermann battery in realistic laser-solid interactions. Phys. Rev. Res. 2 (2), 023129.CrossRefGoogle Scholar
Takizuka, T. & Abe, H. 1977 A binary collision model for plasma simulation with a particle code. J. Comput. Phys. 25 (3), 205–219.CrossRefGoogle Scholar
Tan, C., Sun, F., Kong, T., Zhang, W., Yang, C. & Liu, C. 2018 A survey on deep transfer learning. In International Conference on Artificial Neural Networks, pp. 270–279. Springer.CrossRefGoogle Scholar
Vranic, M., Grismayer, T., Fonseca, R.A. & Silva, L.O. 2016 a Quantum radiation reaction in head-on laser-electron beam interaction. New J. Phys. 18 (7), 073035.CrossRefGoogle Scholar
Vranic, M., Martins, J.L., Fonseca, R.A. & Silva, L.O. 2016 b Classical radiation reaction in particle-in-cell simulations. Comput. Phys. Commun. 204, 141–151.CrossRefGoogle Scholar