Algorithmic differentiation and hull-consistency enforcing using C++ template meta-programming

Algorithmic differentiation is a tool used in several branches of computational science, both in conjunction with the interval calculus, and apart of it. This paper presents the ADHC library [ 14 ] developed by the author, and identified as package “na60” by Numerical Algorithms journal. This librar...

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Bibliographic Details
Published in:Numerical algorithms Vol. 94; no. 4; pp. 1673 - 1704
Main Author: Kubica, Bartłomiej Jacek
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2023
Springer Nature B.V
Subjects:
Algebra
Algorithms
C plus plus
C++ (programming language)
Calculus
Computer Science
Differentiation
Libraries
Machine learning
Mathematical analysis
Neural networks
Nonlinear systems
Numbers
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Textbooks
Theory of Computation
Interval calculus
C++ template meta-programming
Algorithmic differentiation
Hull-consistency
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:Algorithmic differentiation is a tool used in several branches of computational science, both in conjunction with the interval calculus, and apart of it. This paper presents the ADHC library [ 14 ] developed by the author, and identified as package “na60” by Numerical Algorithms journal. This library makes intensive use of the C++ template meta-programming, and it has several unique features. ADHC seems particularly useful for interval-related applications. The library has been used by some solvers, also developed by the author, including HIBA_USNE. The paper describes the library, presenting its features, focusing on the new ones, added in version 2.0; in particular, we describe bounding subdifferentials of non-smooth functions and computing derivatives over various datatypes. Efficiency comparison with respect to other packages is also presented. Then some examples of ADHC applications are given, involving the use of HIBA_USNE and standard benchmark problems for solving nonlinear systems. A particular emphasis is put on examples related to modern machine learning, but not limited to them. Planned extensions and possible directions for future development of ADHC are also outlined and discussed.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-023-01551-8