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Landau: language for dynamical systems with automatic differentiation
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 485 (2019), pp. 78-89 Cet article a éte moissonné depuis la source Math-Net.Ru

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Most numerical solvers used to determine free variables of dynamical systems rely on first-order derivatives of the state of the system w.r.t. the free variables. The number of the free variables can be fairly large. One of the approaches of obtaining those derivatives is the integration of the derivatives simultaneously with the dynamical equations, which is best done with the automatic differentiation technique. Even though there exist many automatic differentiation tools, none have been found to be scalable and usable for practical purposes of dynamic systems modelling. Landau is a Turing incomplete statically typed domain-specific language aimed to fill this gap. The Turing incompleteness provides the ability of sophisticated source code analysis and, as a result, a highly optimized compiled code. Among other things, the language syntax supports functions, compile-time ranged for loops, if/else branching constructions, real variables and arrays, and the ability to manually discard calculation where the automatic derivatives values are expected to be negligibly small. In spite of reasonable restrictions, the language is rich enough to express and differentiate any cumbersome paper-equation with practically no effort. 
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I. Dolgakov; D. Pavlov. Landau: language for dynamical systems with automatic differentiation. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 485 (2019), pp. 78-89. http://geodesic.mathdoc.fr/item/ZNSL_2019_485_a4/

[1] A. Abad, R. Barrio, M. Marco-Buzunariz, M. Rodríguez, “Automatic implementation of the numerical Taylor series method”, Appl. Math. Comput., 268 (2015), 227–245 | Zbl

[2] “Automatic implementation of the numerical Taylor series method: A Mathematica and Sage approach”, Appl. Math. Comput., 268 (2015), 227–245 | Zbl

[3] Ch. Bischof, A. Carle, G. Corliss, A. Griewank, P. Hovland, “ADIFOR–generating derivative codes from Fortran programs”, Scientific Programming, 1:1 (1992), 11–29 | DOI

[4] Ch. Bischof, L. Roh, A. J. Mauer-Oats, “ADIC: an extensible automatic differentiation tool for ANSI-C”, Software: Practice and Experience, 27:12 (1997), 1427–1456 | 3.0.CO;2-Q class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[5] F. C. Botelho, R. Pagh, N. Ziviani, “Simple and space-efficient minimal perfect hash functions”, Workshop on Algorithms and Data Structures, 2007, 139–150 | Zbl

[6] T. F. Coleman, A. Verma, “ADMAT: An automatic differentiation toolbox for MATLAB”, Proceedings of the SIAM Workshop on Object Oriented Methods for Inter-Operable Scientific and Engineering Computing, v. 2, SIAM, Philadelphia, PA, 1998 | Zbl

[7] M. Felleisen, R. B. Findler, M. Flatt, Sh. Krishnamurthi, E. Barzilay, J. McCarthy, S. Tobin-Hochstadt, “A Programmable Programming Language”, Commun. ACM, 61:3 (2018), 62–71 | DOI

[8] A. Griewank, D. Juedes, J. Utke, “Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++”, ACM Transactions on Mathematical Software (TOMS), 22:2 (1996), 131–167 | DOI | Zbl

[9] À. Jorba, M. Zou, “A Software Package for the Numerical Integration of ODEs by Means of High-Order Taylor Methods”, Experimental Mathematics, 14:1 (2005), 99–117 | DOI | MR | Zbl

[10] J. M. Siskind, B. A. Pearlmutter, “Nesting forward-mode AD in a functional framework”, Higher-Order and Symbolic Computation, 21:4 (2008), 361–376 | DOI | Zbl

[11] J. M. Siskind, B, A. Pearlmutter, “Efficient Implementation of a Higher-Order Language with Built-In AD”, AD2016 – 7th International Conference on Algorithmic Differentiation (Oxford, UK, 2016)

[12] M. Tadjouddine, Sjh. A. Forth, J. D. Pryce, “AD tools and prospects for optimal AD in CFD flux Jacobian calculations”, Automatic differentiation of algorithms, 2002, 255–261 | DOI