ROMAN: Reduced-Order Modeling with Artificial Neurons

11/13/2018
by   Alvin J. K. Chua, et al.
NASA
0

Gravitational-wave data analysis is rapidly absorbing techniques from deep learning, with a focus on convolutional networks and related methods that treat noisy time series as images. We pursue an alternative approach, in which waveforms are first represented as weighted sums over reduced bases (reduced-order modeling); we then train artificial neural networks to map gravitational-wave source parameters into basis coefficients. Statistical inference proceeds directly in coefficient space, where it is theoretically straightforward and computationally efficient. The neural networks also provide analytic waveform derivatives, which are useful for gradient-based sampling schemes. We demonstrate fast and accurate coefficient interpolation for the case of a four-dimensional binary-inspiral waveform family, and discuss promising applications of our framework in parameter estimation.

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References

  • [1] B. F. Schutz. Gravitational Wave Data Analysis. Springer Netherlands, 2012.
  • [2] P. Jaranowski and A. Królak. Analysis of Gravitational-wave Data. Cambridge University Press, 2009.
  • [3] B. P. Abbott et al. GW150914: First results from the search for binary black hole coalescence with Advanced LIGO. Phys. Rev. D, 93(12):122003, June 2016.
  • [4] B. P. Abbott et al. Properties of the Binary Black Hole Merger GW150914. Physical Review Letters, 116(24):241102, June 2016.
  • [5] S. E. Field, C. R. Galley, F. Herrmann, J. S. Hesthaven, E. Ochsner, and M. Tiglio. Reduced Basis Catalogs for Gravitational Wave Templates. Phys. Rev. Lett., 106:221102, Jun 2011.
  • [6] K. G. Arun, A. Buonanno, G. Faye, and E. Ochsner. Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational waveforms. Phys. Rev. D, 79:104023, May 2009.
  • [7] S. E. Field, C. R. Galley, J. S. Hesthaven, J. Kaye, and M. Tiglio. Fast Prediction and Evaluation of Gravitational Waveforms Using Surrogate Models. Phys. Rev. X, 4:031006, Jul 2014.
  • [8] J. Blackman, S. E. Field, C. R. Galley, B. Szilágyi, M. A. Scheel, M. Tiglio, and D. A. Hemberger. Fast and Accurate Prediction of Numerical Relativity Waveforms from Binary Black Hole Coalescences Using Surrogate Models. Phys. Rev. Lett., 115:121102, Sep 2015.
  • [9] J. Blackman, S. E. Field, M. A. Scheel, C. R. Galley, D. A. Hemberger, P. Schmidt, and R. Smith. A surrogate model of gravitational waveforms from numerical relativity simulations of precessing binary black hole mergers. Phys. Rev. D, 95:104023, May 2017.
  • [10] B. D. Lackey, S. Bernuzzi, C. R. Galley, J. Meidam, and C. Van Den Broeck. Effective-one-body waveforms for binary neutron stars using surrogate models. Phys. Rev. D, 95:104036, May 2017.
  • [11] J. Blackman, S. E. Field, M. A. Scheel, C. R. Galley, C. D. Ott, M. Boyle, L. E. Kidder, H. P. Pfeiffer, and B. Szilágyi. Numerical relativity waveform surrogate model for generically precessing binary black hole mergers. Phys. Rev. D, 96:024058, Jul 2017.
  • [12] W. Schilders, H. Van der Vorst, and J. Rommes. Model Order Reduction: Theory, Research Aspects and Applications, volume 13. Springer, 2008.
  • [13] J. Blackman, B. Szilagyi, C. R. Galley, and M. Tiglio. Sparse Representations of Gravitational Waves from Precessing Compact Binaries. Phys. Rev. Lett., 113:021101, Jul 2014.
  • [14] V. N. Temlyakov. Greedy approximation. Acta Numerica, 17:235–409, 2008.
  • [15] P. Cañizares, S. E. Field, J. R. Gair, and M. Tiglio. Gravitational wave parameter estimation with compressed likelihood evaluations. Phys. Rev. D, 87:124005, 2013.
  • [16] P. Cañizares, S. E. Field, J. R. Gair, V. Raymond, R. Smith, and M. Tiglio. Accelerated Gravitational Wave Parameter Estimation with Reduced Order Modeling. Phys. Rev. Lett., 114:071104, Feb 2015.
  • [17] M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera.

    An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations.

    Comptes Rendus Mathematique, 339(9):667–672, 2004.
  • [18] I. Goodfellow, Y. Bengio, and A. Courville. Deep Learning. MIT Press, 2016.
  • [19] S. J. Russell and P. Norvig. Artificial Intelligence: A Modern Approach. Prentice Hall, 2010.
  • [20] T. Gebhard, N. Kilbertus, G. Parascandolo, I. Harry, and B. Schölkopf. ConvWave: Searching for Gravitational Waves with Fully Convolutional Neural Nets. In Workshop on Deep Learning for Physical Sciences (DLPS) at the 31st Conference on Neural Information Processing Systems (NIPS), December 2017.
  • [21] D. George and E. A. Huerta. Deep neural networks to enable real-time multimessenger astrophysics. Phys. Rev. D, 97:044039, Feb 2018.
  • [22] D. George and E.A. Huerta. Deep Learning for real-time gravitational wave detection and parameter estimation: Results with Advanced LIGO data. Physics Letters B, 778:64 – 70, 2018.
  • [23] M. Razzano and E. Cuoco. Image-based deep learning for classification of noise transients in gravitational wave detectors. Class. Quantum Grav., 35(9):095016, 2018.
  • [24] H. Gabbard, M. Williams, F. Hayes, and C. Messenger. Matching Matched Filtering with Deep Networks for Gravitational-Wave Astronomy. Phys. Rev. Lett., 120:141103, Apr 2018.
  • [25] D. George, H. Shen, and E. A. Huerta.

    Classification and unsupervised clustering of LIGO data with Deep Transfer Learning.

    Phys. Rev. D, 97:101501, May 2018.
  • [26] A. Rebei, E. A. Huerta, S. Wang, S. Habib, R. Haas, D. Johnson, and D. George. Fusing numerical relativity and deep learning to detect higher-order multipole waveforms from eccentric binary black hole mergers. ArXiv e-prints, July 2018.
  • [27] G. Cybenko.

    Approximation by superpositions of a sigmoidal function.

    Mathematics of Control, Signals and Systems, 2(4):303–314, Dec 1989.
  • [28] Y. LeCun and Y. Bengio. Convolutional networks for images, speech, and time series. In M. A. Arbib, editor, The Handbook of Brain Theory and Neural Networks, pages 255–258. MIT Press, Cambridge, MA, USA, 1998.
  • [29] N. Sebe, I. Cohen, A. Garg, and T. S. Huang. Machine Learning in Computer Vision. Springer Netherlands, 2005.
  • [30] Y. Goldberg. A Primer on Neural Network Models for Natural Language Processing. J. Artif. Int. Res., 57(1):345–420, September 2016.
  • [31] R. Fergus, M. D. Zeiler, G. W. Taylor, and D. Krishnan. Deconvolutional networks. In

    2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition(CVPR)

    , volume 00, pages 2528–2535, 06 2010.
  • [32] A. Cichocki. Era of Big Data Processing: A New Approach via Tensor Networks and Tensor Decompositions. ArXiv e-prints, March 2014.
  • [33] S. S. Haykin. Neural Networks: A Comprehensive Foundation. Prentice Hall, 1999.
  • [34] D. E. Rumelhart, G. E. Hinton, and R. J. Williams. Learning internal representations by error propagation. In D. E. Rumelhart, J. L. McClelland, and PDP Research Group, editors, Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1, pages 318–362. MIT Press, Cambridge, MA, USA, 1986.
  • [35] A. Buonanno, Y. Chen, and M. Vallisneri. Detection template families for gravitational waves from the final stages of binary black-hole inspirals: Nonspinning case. Phys. Rev. D, 67(2):024016, January 2003.
  • [36] K. Danzmann et al. Laser Interferometer Space Antenna. ArXiv e-prints, February 2017.
  • [37] C. J. Cutler and É. E. Flanagan. Gravitational waves from merging compact binaries: How accurately can one extract the binary’s parameters from the inspiral waveform? Phys. Rev. D, 49:2658–2697, Mar 1994.
  • [38] C. R. Galley. In prep.
  • [39] M. Abadi et al. TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems, 2015.
  • [40] A. Y. Ng A. L. Maas, A. Y. Hannun. Rectifier Nonlinearities Improve Neural Network Acoustic Models. In Proceedings of the 30th International Conference on Machine Learning, 2013.
  • [41] X. Glorot, A. Bordes, and Y. Bengio. Deep sparse rectifier neural networks. In G. Gordon, D. Dunson, and M. Dudík, editors, Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, volume 15 of Proceedings of Machine Learning Research, pages 315–323, Apr 2011.
  • [42] Y. A. LeCun, L. Bottou, G. B. Orr, and K.-R. Müller. Efficient BackProp. In G. Montavon, G. B. Orr, and K.-R. Müller, editors, Neural Networks: Tricks of the Trade: Second Edition, pages 9–48. Springer Berlin Heidelberg, Berlin, Heidelberg, 2012.
  • [43] D. P. Kingma and J. Ba. Adam: A Method for Stochastic Optimization. ArXiv e-prints, December 2014.
  • [44] M. Vallisneri. Use and abuse of the Fisher information matrix in the assessment of gravitational-wave parameter-estimation prospects. Phys. Rev. D, 77:042001, Feb 2008.
  • [45] E. Sellentin, M. Quartin, and L. Amendola. Breaking the spell of Gaussianity: forecasting with higher order Fisher matrices. Monthly Notices of the Royal Astronomical Society, 441(2):1831–1840, 2014.
  • [46] G. O. Roberts and J. S. Rosenthal. Optimal scaling of discrete approximations to Langevin diffusions. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 60(1):255–268, 1998.
  • [47] M. Girolami and B. Calderhead. Riemann manifold Langevin and Hamiltonian Monte Carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(2):123–214, 2011.
  • [48] S. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth. Hybrid Monte Carlo. Physics Letters B, 195(2):216 – 222, 1987.
  • [49] Y.-A. Ma, T. Chen, and E. B. Fox. A Complete Recipe for Stochastic Gradient MCMC. In Proceedings of the 28th International Conference on Neural Information Processing Systems - Volume 2, NIPS’15, pages 2917–2925, Cambridge, MA, USA, 2015. MIT Press.
  • [50] A. J. K. Chua. Sampling from manifold-restricted distributions using tangent bundle projections. In review.