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Inference and De-noising of Non-gaussian Particle Distribution Functions: A Generative Modeling Approach

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Machine Learning, Optimization, and Data Science (LOD 2021)

Abstract

The particle-in-cell numerical method of plasma physics balances a trade-off between computational cost and intrinsic noise. Inference on data produced by these simulations generally consists of binning the data to recover the particle distribution function, from which physical processes may be investigated. In addition to containing noise, the distribution function is temporally dynamic and can be non-gaussian and multi-modal, making the task of modeling it difficult. Here we demonstrate the use of normalizing flows to learn a smooth, tractable approximation to the noisy particle distribution function. We demonstrate that the resulting data driven likelihood conserves relevant physics and may be extended to encapsulate the temporal evolution of the distribution function.

Partially Supported by Department of Energy Grant 17-SC-20-SC.

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References

  1. Agostinelli, F., Anderson, M.R., Lee, H.: Adaptive multi-column deep neural networks with application to robust image denoising. In: Proceedings of the 26th International Conference on Neural Information Processing Systems, NIPS 2013, vol. 1, pp. 1493–1501. Curran Associates Inc., Red Hook (2013)

    Google Scholar 

  2. Bigdeli, S.A., Lin, G., Portenier, T., Dunbar, L.A., Zwicker, M.: Learning generative models using denoising density estimators (2020)

    Google Scholar 

  3. Block, A., Mroueh, Y., Rakhlin, A.: Generative modeling with denoising auto-encoders and Langevin sampling (2020)

    Google Scholar 

  4. Cho, K.: Simple sparsification improves sparse denoising autoencoders in denoising highly noisy images. In: 30th International Conference on Machine Learning, ICML 2013, 16 June 2013–21 June 2013, pp. 1469–1477 (2013)

    Google Scholar 

  5. Choi, J.Y., et al.: Coupling exascale multiphysics applications: methods and lessons learned, pp. 442–452 (2018). https://doi.org/10.1109/eScience.2018.00133

  6. Dilokthanakul, N., et al.: Deep unsupervised clustering with Gaussian mixture variational autoencoders (2017)

    Google Scholar 

  7. Dinh, L., Krueger, D., Bengio, Y.: NICE: non-linear independent components estimation (2015)

    Google Scholar 

  8. Dinh, L., Sohl-Dickstein, J., Bengio, S.: Density estimation using real NVP (2017)

    Google Scholar 

  9. Dominski, J., et al.: Spatial coupling of gyrokinetic simulations, a generalized scheme based on first-principles. Phys. Plasmas 28(2) (2021). https://doi.org/10.1063/5.0027160

  10. Dominski, J., et al.: A tight-coupling scheme sharing minimum information across a spatial interface between gyrokinetic turbulence codes. Phys. Plasmas 25(7), 072308 (2018). https://doi.org/10.1063/1.5044707

  11. Durkan, C., Bekasov, A., Murray, I., Papamakarios, G.: nflows: normalizing flows in PyTorch (November 2020). https://doi.org/10.5281/zenodo.4296287

  12. Germaschewski, K., et al.: The plasma simulation code: a modern particle-in-cell code with patch-based load-balancing. J. Comput. Phys. 318, 305–326 (2016). https://doi.org/10.1016/j.jcp.2016.05.013. https://www.sciencedirect.com/science/article/pii/S0021999116301413

  13. Goodfellow, I.J., et al.: Generative adversarial networks (2014)

    Google Scholar 

  14. Kingma, D.P., Dhariwal, P.: Glow: generative flow with invertible 1 \(\times \) 1 convolutions (2018)

    Google Scholar 

  15. Kingma, D.P., Welling, M.: Auto-encoding variational Bayes (2014)

    Google Scholar 

  16. Lezhnin, K.V., et al.: Kinetic simulations of electron pre-energization by magnetized collisionless shocks in expanding laboratory plasmas. Astrophys. J. 908(2), L52 (2021). https://doi.org/10.3847/2041-8213/abe407

  17. Merlo, G., et al.: First coupled GENE–XGC microturbulence simulations. Phys. Plasmas 28(1), 012303 (2021). https://doi.org/10.1063/5.0026661

  18. Papamakarios, G., Pavlakou, T., Murray, I.: Masked autoregressive flow for density estimation (2018)

    Google Scholar 

  19. Rezende, D.J., Mohamed, S.: Variational inference with normalizing flows (2016)

    Google Scholar 

  20. Rivero, A.D., Dvorkin, C.: Flow-based likelihoods for non-gaussian inference. Phys. Rev. D 102(10) (2020). https://doi.org/10.1103/physrevd.102.103507

  21. Xie, J., Xu, L., Chen, E.: Image denoising and inpainting with deep neural networks. In: Advances in Neural Information Processing Systems, vol. 25. Curran Associates, Inc. (2012). https://proceedings.neurips.cc/paper/2012/file/6cdd60ea0045eb7a6ec44c54d29ed402-Paper.pdf

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Correspondence to John Donaghy .

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Donaghy, J., Germaschewski, K. (2022). Inference and De-noising of Non-gaussian Particle Distribution Functions: A Generative Modeling Approach. In: Nicosia, G., et al. Machine Learning, Optimization, and Data Science. LOD 2021. Lecture Notes in Computer Science(), vol 13163. Springer, Cham. https://doi.org/10.1007/978-3-030-95467-3_25

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  • DOI: https://doi.org/10.1007/978-3-030-95467-3_25

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-030-95467-3

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