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Relevant bibliographies by topics / Forward Mode Automatic Differentiation

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Academic literature on the topic 'Forward Mode Automatic Differentiation'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Forward Mode Automatic Differentiation"

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Vassilev, Vassil, Aleksandr Efremov, and Oksana Shadura. "Automatic Differentiation in ROOT." EPJ Web of Conferences 245 (2020): 02015. http://dx.doi.org/10.1051/epjconf/202024502015.

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In mathematics and computer algebra, automatic differentiation (AD) is a set of techniques to evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.), elementary functions (exp, log, sin, cos, etc.) and control flow statements. AD takes source code of a function as input and produces source code of the derived function. By applying the chain rule repeatedly to these operations, derivatives of

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Forth, Shaun A. "An efficient overloaded implementation of forward mode automatic differentiation in MATLAB." ACM Transactions on Mathematical Software 32, no. 2 (2006): 195–222. http://dx.doi.org/10.1145/1141885.1141888.

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Khan, Kamil A., and Paul I. Barton. "A vector forward mode of automatic differentiation for generalized derivative evaluation." Optimization Methods and Software 30, no. 6 (2015): 1185–212. http://dx.doi.org/10.1080/10556788.2015.1025400.

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Toivanen, Jukka I., and Raino A. E. Mäkinen. "Implementation of sparse forward mode automatic differentiation with application to electromagnetic shape optimization." Optimization Methods and Software 26, no. 4-5 (2011): 601–16. http://dx.doi.org/10.1080/10556781003642305.

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Hascoët, L., J. Utke, and U. Naumann. "Cheaper Adjoints by Reversing Address Computations." Scientific Programming 16, no. 1 (2008): 81–92. http://dx.doi.org/10.1155/2008/375243.

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The reverse mode of automatic differentiation is widely used in science and engineering. A severe bottleneck for the performance of the reverse mode, however, is the necessity to recover certain intermediate values of the program in reverse order. Among these values are computed addresses, which traditionally are recovered through forward recomputation and storage in memory. We propose an alternative approach for recovery that uses inverse computation based on dependency information. Address storage constitutes a significant portion of the overall storage requirements. An example illustrates s

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DeGroot, Christopher. "Convergence and error analysis of an automatically differentiated finite volume based heat conduction code." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 7 (2019): 2389–406. http://dx.doi.org/10.1108/hff-09-2018-0489.

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Purpose This paper aims to investigate the convergence and error properties of a finite volume-based heat conduction code that uses automatic differentiation to evaluate derivatives of solutions outputs with respect to arbitrary solution input(s). A problem involving conduction in a plane wall with convection at its surfaces is used as a test problem, as it has an analytical solution, and the error can be evaluated directly. Design/methodology/approach The finite volume method is used to discretize the transient heat diffusion equation with constant thermophysical properties. The discretized p

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Belikov, Dmitry A., Shamil Maksyutov, Alexey Yaremchuk, et al. "Adjoint of the global Eulerian–Lagrangian coupled atmospheric transport model (A-GELCA v1.0): development and validation." Geoscientific Model Development 9, no. 2 (2016): 749–64. http://dx.doi.org/10.5194/gmd-9-749-2016.

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Abstract. We present the development of the Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt

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Rios, O., W. Jahn, and G. Rein. "Forecasting wind-driven wildfires using an inverse modelling approach." Natural Hazards and Earth System Sciences Discussions 1, no. 6 (2013): 6923–59. http://dx.doi.org/10.5194/nhessd-1-6923-2013.

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Abstract. A technology able to rapidly forecast wildlfire dynamics would lead to a paradigm shift in the response to emergencies, providing the Fire Service with essential information about the on-going fire. The article at hand presents and explores a novel methodology to forecast wildfire dynamics in wind-driven conditions, using real time data assimilation and inverse modelling. The forecasting algorithm combines Rothermel's rate of spread theory with a perimeter expansion model based on Huygens principle and solves the optimisation problem with a tangent linear approach and a forward autom

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Belikov, D. A., S. Maksyutov, A. Yaremchuk, et al. "Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric transport model (A-GELCA v1.0): development and validation." Geoscientific Model Development Discussions 8, no. 7 (2015): 5983–6019. http://dx.doi.org/10.5194/gmdd-8-5983-2015.

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Abstract. We present the development of the Adjoint of the Global Eulerian–Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian plume diffusion model (LPDM). The tangent and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com), with additio

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Xu, J., F. Schreier, P. Vogt, A. Doicu, and T. Trautmann. "A sensitivity study for far infrared balloon-borne limb emission sounding of stratospheric trace gases." Geoscientific Instrumentation, Methods and Data Systems Discussions 3, no. 1 (2013): 251–303. http://dx.doi.org/10.5194/gid-3-251-2013.

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Abstract. This paper presents a sensitivity study performed for trace gases retrieval from synthetic observations by TELIS (TErahertz and submillimeter LImb Sounder) which is a stratospheric balloon-borne cryogenic heterodyne spectrometer. Issues pertaining to hydroxyl radical (OH) retrieval from the far infrared measurements by the 1.8 THz channel are addressed. The study is conducted by a retrieval code PILS (Profile Inversion for Limb Sounding) developed to solve the nonlinear inverse problems arising in the analysis of infrared/microwave limb sounding measurements. PILS combines a line-by-

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Dissertations / Theses on the topic "Forward Mode Automatic Differentiation"

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Kang, Yixiu. "Implementation of Forward and Reverse Mode Automatic Differentiation for GNU Octave Applications." Ohio University / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1049467867.

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Walter, Sebastian. "Structured higher-order algorithmic differentiation in the forward and reverse mode with application in optimum experimental design." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2012. http://dx.doi.org/10.18452/16514.

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In dieser Arbeit werden Techniken beschrieben, die es erlauben (höhere) Ableitungen und Taylorapproximationen solcher Computerprogramme effizient zu berechnen. Auch inbesondere dann, wenn die Programme Algorithmen der numerischen linearen Algebra (NLA) enthalten. Im Gegensatz zur traditionellen algorithmischen Differentiation (AD), bei der die zugrunde liegenden Algorithmen um zusätzliche Befehlere erweitert werden, sind in dieser Arbeit die Zerlegungen durch definierende Gleichungen charakterisiert. Basierend auf den definierenden Gleichungen werden Strukturausnutzende Algorithmen hergeleit

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Hjelmberg, David, and Björn Lagerström. "Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation." Thesis, Linköpings universitet, Produktionsekonomi, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-110875.

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In this master thesis we have examined the possibility of pricing multiple American options, on an underlying asset with discrete dividends, with a finite difference method. We have found a good and stable way to price one American option by solving the BSM PDE backwards, while also calculating the Greeks of the option with automatic differentiation. The list of Greeks for an option is quite extensive since we have been using a local volatility surface. We have also tried to find a way to price several American options simultaneously by solving a forward PDE. Unfortunately, we haven't found an

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Willkomm, Johannes [Verfasser]. "The reverse mode of automatic differentiation applied to the MATLAB language - advanced methods for adjoint code generation / Johannes Willkomm." München : Verlag Dr. Hut, 2021. http://d-nb.info/1238423108/34.

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Walter, Sebastian F. [Verfasser], Andreas [Akademischer Betreuer] Griewank, Hans Georg [Akademischer Betreuer] Bock, and Richard D. [Akademischer Betreuer] Neidinger. "Structured higher-order algorithmic differentiation in the forward and reverse mode with application in optimum experimental design / Sebastian Walter. Gutachter: Andreas Griewank ; Hans Georg Bock ; Richard D. Neidinger." Berlin : Humboldt Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2012. http://d-nb.info/1023079682/34.

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Xiong, Xin. "Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation." Thesis, 2014. http://hdl.handle.net/10012/8197.

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This thesis is concerned with the efficient computation of Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of two directed edge separator methods, the weighted minimum separator and natural order separator methods, to exploit the structure of the computational graph of the nonlinear system.This allows for the efficient determination of the Jacobian matrix using AD software. We will illustrate the promise of this approach with computational experiments.

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Book chapters on the topic "Forward Mode Automatic Differentiation"

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Aubert, Pierre, and Nicolas Di Césaré. "Expression Templates and Forward Mode Automatic Differentiation." In Automatic Differentiation of Algorithms. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0075-5_37.

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Giles, Mike B. "Collected Matrix Derivative Results for Forward and Reverse Mode Algorithmic Differentiation." In Advances in Automatic Differentiation. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-68942-3_4.

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Ulbrich, Michael, and Stefan Ulbrich. "Automatic Differentiation: A Structure-Exploiting Forward Mode with Almost Optimal Complexity for Kantorovič Trees." In Applied Mathematics and Parallel Computing. Physica-Verlag HD, 1996. http://dx.doi.org/10.1007/978-3-642-99789-1_24.

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Huot, Mathieu, Sam Staton, and Matthijs Vákár. "Correctness of Automatic Differentiation via Diffeologies and Categorical Gluing." In Lecture Notes in Computer Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45231-5_17.

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AbstractWe present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Finally, we sketch how the analysis extends to other AD methods by considering a continuation-based method.

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Vákár, Matthijs. "Reverse AD at Higher Types: Pure, Principled and Denotationally Correct." In Programming Languages and Systems. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72019-3_22.

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AbstractWe show how to define forward- and reverse-mode automatic differentiation source-code transformations or on a standard higher-order functional language. The transformations generate purely functional code, and they are principled in the sense that their definition arises from a categorical universal property. We give a semantic proof of correctness of the transformations. In their most elegant formulation, the transformations generate code with linear types. However, we demonstrate how the transformations can be implemented in a standard functional language without sacrificing correctness. To do so, we make use of abstract data types to represent the required linear types, e.g. through the use of a basic module system.

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Giering, Ralf, and Thomas Kaminski. "Recomputations in Reverse Mode AD." In Automatic Differentiation of Algorithms. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0075-5_33.

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Bischof, Christian, Niels Guertler, Andreas Kowarz, and Andrea Walther. "Parallel Reverse Mode Automatic Differentiation for OpenMP Programs with ADOL-C." In Advances in Automatic Differentiation. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-68942-3_15.

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Kaler, Tim, Tao B. Schardl, Brian Xie, et al. "PARAD: A Work-Efficient Parallel Algorithm for Reverse-Mode Automatic Differentiation." In Symposium on Algorithmic Principles of Computer Systems (APOCS). Society for Industrial and Applied Mathematics, 2021. http://dx.doi.org/10.1137/1.9781611976489.11.

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Naumann, Uwe. "Reducing the Memory Requirement in Reverse Mode Automatic Differentiation by Solving TBR Flow Equations." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-46080-2_109.

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Barthe, Gilles, Raphaëlle Crubillé, Ugo Dal Lago, and Francesco Gavazzo. "On the Versatility of Open Logical Relations." In Programming Languages and Systems. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44914-8_3.

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AbstractLogical relations are one among the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be immediately proved by means of logical relations, for instance program continuity and differentiability in higher-order languages extended with real-valued functions. Informally, the problem stems from the fact that these properties are naturally expressed on terms of non-ground type (or, equivalently, on open terms of base type), and there is no apparent good definition for a base case (i.e. for closed terms of ground types). To overcome this issue, we study a generalization of the concept of a logical relation, called open logical relation, and prove that it can be fruitfully applied in several contexts in which the property of interest is about expressions of first-order type. Our setting is a simply-typed $$\lambda $$ λ -calculus enriched with real numbers and real-valued first-order functions from a given set, such as the one of continuous or differentiable functions. We first prove a containment theorem stating that for any collection of real-valued first-order functions including projection functions and closed under function composition, any well-typed term of first-order type denotes a function belonging to that collection. Then, we show by way of open logical relations the correctness of the core of a recently published algorithm for forward automatic differentiation. Finally, we define a refinement-based type system for local continuity in an extension of our calculus with conditionals, and prove the soundness of the type system using open logical relations.

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Conference papers on the topic "Forward Mode Automatic Differentiation"

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Hückelheim, Jan, Michel Schanen, Sri Hari Krishna Narayanan, and Paul Hovland. "Vector Forward Mode Automatic Differentiation on SIMD/SIMT architectures." In ICPP '20: 49th International Conference on Parallel Processing. ACM, 2020. http://dx.doi.org/10.1145/3404397.3404470.

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Lauser, A., A. F. Rasmussen, T. H. Sandve, and H. M. Nilsen. "Local Forward-Mode Automatic Differentiation For High Performance Parallel Pilot-Level Reservoir Simulation." In ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery. EAGE Publications BV, 2018. http://dx.doi.org/10.3997/2214-4609.201802153.

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Mathur, Sanjay R., Aarti Chigullapalli, and Jayathi Y. Murthy. "A Unified Unintrusive Discrete Approach to Sensitivity Analysis and Uncertainty Propagation in Fluid Flow Simulations." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-37789.

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In recent years, there has been growing interest in making computational fluid dynamics (CFD) predictions with quantifiable uncertainty. Tangent-mode sensitivity analysis and uncertainty propagation are integral components of the uncertainty quantification process. Generalized polynomial chaos (gPC) is a viable candidate for uncertainty propagation, and involves representing the dependant variables in the governing partial differential equations (pdes) as expansions in an orthogonal polynomial basis in the random variables. Deterministic coupled non-linear pdes are derived for the coefficients

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Mohammadi, Bijan, and Bijan Mohammadi. "Optimal shape design, reverse mode of automatic differentiation and turbulence." In 35th Aerospace Sciences Meeting and Exhibit. American Institute of Aeronautics and Astronautics, 1997. http://dx.doi.org/10.2514/6.1997-99.

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Zhang, Wei, Dingxi Wang, Xiuquan Huang, Tianxiao Yang, Hong Yan, and Jianling Li. "On the Use of the Automatic Differentiation for Developing a Linear Harmonic Solver." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-76004.

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The linear and nonlinear harmonic methods are efficient frequency domain methods for analyzing time periodic unsteady flow fields. They have been widely used in both academia and industry. But the cost and complexity of developing a linear harmonic solver has been limiting its wider applications. On the other hand, the automatic differentiation (AD) has long been used in the CFD community with a focus on generating adjoint codes in a reverse mode. All those AD tools can do a much better job in generating linearized codes in a tangent mode, but so far very little, if any, attention is paid to u

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Ramos Gurjao, Kildare George, Eduardo Gildin, Richard Gibson, and Mark Everett. "Mechanistic Modeling of Distributed Strain Sensing DSS and Distributed Acoustic Sensing DAS to Assist Machine Learning Schemes Interpreting Unconventional Reservoir Datasets." In SPE Annual Technical Conference and Exhibition. SPE, 2021. http://dx.doi.org/10.2118/206049-ms.

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Abstract The use of fiber optics in reservoir surveillance is bringing valuable insights to fracture geometry and fracture-hit identification, stage communication and perforation cluster fluid distribution in many hydraulic fracturing processes. However, given the complexity associated with field data, its interpretation is a major challenge faced by engineers and geoscientists. In this work, we propose to generate Distributed Strain/Acoustic Sensing (DSS/DAS) synthetic data of a cross-well fiber deployment that incorporate the physics governing hydraulic fracturing treatments. Our forward mod

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Gao, Yuefen, Guohua Shi, and Songling Wang. "Study on Operating Condition in Solar-Absorption Refrigerating System in Summer." In ASME 2007 Energy Sustainability Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/es2007-36062.

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A solar-absorption refrigerating system using the solar energy as the driving power is an energy efficiency system, which is also friendly to the environment. However, as the solar radiation varies with the season, the day and night and the climate, the solar energy supplying to the system is unsteady, which affects the security and the stability of the system. Here a typical solar-absorption refrigerating system is put forward to. Then the operating conditions in summer and their operating performance are discussed. Different operating modes are chosen according to the cooling loads and the w

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Tai, W. C., and I. Y. Shen. "Experimental Verification of Ground-Based Response of a Spinning, Cyclic Symmetric, Rotor Assembled to a Flexible Stationary Housing via Multiple Bearings." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34749.

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This paper is to present an experimental study that measures ground-based response of a spinning, cyclic, symmetric rotor-bearing-housing system. In particular, the study focuses on rotor-housing coupled modes that are significantly dominated by housing deformation. In the experiments, a ball-bearing spindle motor, carrying a disk with four evenly spaced slots (i.e., the rotor), is mounted onto a stationary housing. The housing is a square plate supported with steel spacers at four corners and fixed to the ground. Two different ways are used to excite the rotor-housing system to measure freque

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Sviridov, Mikhail, Anton Mosin, Sergey Lebedev, and Ron Thompson. "VENDOR-NEUTRAL STOCHASTIC INVERSION OF LWD DEEP AZIMUTHAL RESISTIVITY DATA AS A STEP TOWARD EFFICIENCY STANDARDIZATION OF GEOSTEERING SERVICES." In 2021 SPWLA 62nd Annual Logging Symposium Online. Society of Petrophysicists and Well Log Analysts, 2021. http://dx.doi.org/10.30632/spwla-2021-0103.

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While proactive geosteering, special inversion algorithms are used to process the readings of logging-while-drilling resistivity tools in real-time and provide oil field operators with formation models to make informed steering decisions. Currently, there is no industry standard for inversion deliverables and corresponding quality indicators because major tool vendors develop their own device-specific algorithms and use them internally. This paper presents the first implementation of vendor-neutral inversion approach applicable for any induction resistivity tool and enabling operators to stand

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