publication . Preprint . 2016

Density functionals from deep learning

McMahon, Jeffrey M.;
Open Access English
  • Published: 01 Aug 2016
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep learning is developed to approximate this functional. Deep learning allows computational models that are capable of naturally discovering intricate structure in large and/or high-dimensional data sets, with multiple levels of abstraction. As no assumptions are made as to the form of this structure, this approach is much more powerful and flexible than traditional approaches. As an example application, the model is shown to perform...
free text keywords: Physics - Computational Physics, Physics - Chemical Physics
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36 references, page 1 of 3

8 C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988).

9 J. C. Snyder, M. Rupp, K. Hansen, K.-R. Muller, and K. Burke, Phys. Rev. Lett. 108, 253002 (2012).

10 R. O. Duda and P. E. Hart, Pattern Classi cation and Scene Analysis (Wiley, 1973).

11 J. C. Snyder, M. Rupp, K. Hansen, L. Blooston, K.-R. Mller, and K. Burke, The Journal of Chemical Physics 139, 224104 (2013).

12 B. Scholkopf and A. J. Smola, Learning with Kernels (The MIT Press, 2001).

13 L. Li, J. C. Snyder, I. M. Pelaschier, J. Huang, U.-N. Niranjan, P. Duncan, M. Rupp, K.-R. Mller, and K. Burke, International Journal of Quantum Chemistry 116, 819 (2016).

14 Y. Bengio, O. Delalleau, and N. L. Roux, in In Advances in Neural Information Processing Systems 18 (MIT Press, 2006) p. 2006.

15 Y. LeCun, Y. Bengio, and G. Hinton, Nature 521, 436 (2015).

16 D. Erhan, A. Courville, and Y. Bengio, Understanding Representations Learned in Deep Architectures, Tech. Rep. 1355 (Universite de Montreal/DIRO, 2010).

17 I. Goodfellow, H. Lee, Q. V. Le, A. Saxe, and A. Y. Ng, in Advances in Neural Information Processing Systems 22 , edited by Y. Bengio, D. Schuurmans, J. La erty, C. Williams, and A. Culotta (Curran Associates, Inc., 2009) pp. 646{654.

18 L. Deng, APSIPA Transactions on Signal and Information Processing 3 (2014), 10.1017/atsip.2013.9.

19 In this work, the input data v is continuous. Therefore, p(v) corresponds to a probability density function. The notation was chosen to be consistent with that commonly used.

20 D. McQuarrie, Statistical Mechanics (University Science Books, 2000).

21 J. J. Hop eld, Proceedings of the National Academy of Sciences 79, 2554 (1982),

22 S. R. Hanna and D. W. Heinold, Development and Application of a Simple Method for Evaluating Air Quality Models, Tech. Rep. API Publication No. 4409 (American Petroleum Institute, Washington, DC, 1985).

36 references, page 1 of 3
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