Adjoint algorithmic differentiation tool support for typical numerical patterns in computational finance

Naumann, Uwe; Toit, Jacques du

doi:10.21314/jcf.2018.339

Cited by 15 publications

(8 citation statements)

References 19 publications

(16 reference statements)

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“…But for higher-dimensional problems (e.g. Partial Differential Equations or Monte Carlo simulation) we recommend accelerating derivative computation using adjoint AD [NAG, 2020;Naumann and du Toit, 2018]. The software presented enables users to implement and benchmark all these alternatives so that the most appropriate methods for a given problem can be chosen.…”

Section: Discussionmentioning

confidence: 99%

MCMC for Bayesian uncertainty quantification from time-series data

Maybank,

Peltzer,

Naumann

et al. 2020

Preprint

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Many problems in science and engineering require uncertainty quantification that accounts for observed data. For example, in computational neuroscience, Neural Population Models (NPMs) are mechanistic models that describe brain physiology in a range of different states. Within computational neuroscience there is growing interest in the inverse problem of inferring NPM parameters from recordings such as the EEG (Electroencephalogram). Uncertainty quantification is essential in this application area in order to infer the mechanistic effect of interventions such as anaesthesia.This paper presents C++ software for Bayesian uncertainty quantification in the parameters of NPMs from approximately stationary data using Markov Chain Monte Carlo (MCMC). Modern MCMC methods require first order (and in some cases higher order) derivatives of the posterior density. The software presented offers two distinct methods of evaluating derivatives: finite differences and exact derivatives obtained through Algorithmic Differentiation (AD). For AD, two different implementations are used: the open source Stan Math Library and the commercially licenced dco/c++ tool distributed by NAG (Numerical Algorithms Group).The use of derivative information in MCMC sampling is demonstrated through a simple example, the noise-driven harmonic oscillator. And different methods for computing derivatives are compared. The software is written in a modular object-oriented way such that it can be extended to derivative based MCMC for other scientific domains.

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Section: Discussionmentioning

confidence: 99%

MCMC for Bayesian uncertainty quantification from time-series data

Maybank,

Peltzer,

Naumann

et al. 2020

Preprint

Self Cite

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“…The set of elemental functions including all built-in arithmetic operators and intrinsic functions is overloaded for the active (for example, first-order tangent) data type. dco/c++ has been applied successfully to numerous practically relevant applications in Computational Science, Engineering, and Finance; see, for example, [50][51][52].…”

Section: Methodsmentioning

confidence: 99%

Algorithmic differentiation of hyperbolic flow problems

Herty,

Hüser,

Naumann

et al. 2020

Preprint

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We are interested in the development of an algorithmic differentiation framework for computing approximations to tangent vectors to scalar and systems of hyperbolic partial differential equations. The main difficulty of such a numerical method is the presence of shock waves that are resolved by proposing a numerical discretization of the calculus introduced in Bressan and Marson [Rend. Sem. Mat. Univ. Padova, 94:79-94, 1995]. Numerical results are presented for the one-dimensional Burgers equation and the Euler equations. Using the essential routines of a state-of-the-art code for computational fluid dynamics (CFD) as a starting point, three modifications are required to apply the introduced calculus. First, the CFD code is modified to solve an additional equation for the shock location. Second, we customize the computation of the corresponding tangent to the shock location. Finally, the modified method is enhanced by algorithmic differentiation. Applying the introduced calculus to problems of the Burgers equation and the Euler equations, it is found that correct sensitivities can be computed, whereas the application of black-box algorithmic differentiation fails.

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“…But for higher-dimensional problems (e.g. Partial Differential Equations or Monte Carlo simulation) we recommend accelerating derivative computation using adjoint AD [19,21]. The software presented enables users to implement and benchmark all these alternatives so that the most appropriate methods for a given problem can be chosen.…”

Section: Actualmentioning

confidence: 99%

MCMC for Bayesian Uncertainty Quantification from Time-Series Data

Maybank

Peltzer

Naumann

et al. 2020

Lecture Notes in Computer Science

Self Cite

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In computational neuroscience, Neural Population Models (NPMs) are mechanistic models that describe brain physiology in a range of different states. Within computational neuroscience there is growing interest in the inverse problem of inferring NPM parameters from recordings such as the EEG (Electroencephalogram). Uncertainty quantification is essential in this application area in order to infer the mechanistic effect of interventions such as anaesthesia.This paper presents C++ software for Bayesian uncertainty quantification in the parameters of NPMs from approximately stationary data using Markov Chain Monte Carlo (MCMC). Modern MCMC methods require first order (and in some cases higher order) derivatives of the posterior density. The software presented offers two distinct methods of evaluating derivatives: finite differences and exact derivatives obtained through Algorithmic Differentiation (AD). For AD, two different implementations are used: the open source Stan Math Library and the commercially licenced dco/c++ tool distributed by NAG (Numerical Algorithms Group). The use of derivative information in MCMC sampling is demonstrated through a simple example, the noise-driven harmonic oscillator. And different methods for computing derivatives are compared. The software is written in a modular object-oriented way such that it can be extended to derivative based MCMC for other scientific domains.

show abstract

Adjoint algorithmic differentiation tool support for typical numerical patterns in computational finance

Cited by 15 publications

References 19 publications

MCMC for Bayesian uncertainty quantification from time-series data

MCMC for Bayesian uncertainty quantification from time-series data

Algorithmic differentiation of hyperbolic flow problems

MCMC for Bayesian Uncertainty Quantification from Time-Series Data

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