Automatic differentiation of codes in nuclear engineering applications.

Alexe, Mihai; Roderick, Oleg; Utke, Jean; Anitescu, Mihai; Hovland, Paul; Fanning, T. H.

doi:10.2172/971984

Cited by 3 publications

(4 citation statements)

References 22 publications

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“…Specifically, we have shown that components of the gradient can be used as additional fitting conditions in multivariate regression techniques and stochastic processesbased machine learning; the result was that surrogate response to uncertainty, which would normally require many code evaluations, could be constructed by using outputs and gradients at <10 points in the parameter space. In Figure 1, we provide an illustration from recently published research on gradient-enhanced kriging techniques: a confidence interval for order statistics of a complex simulation model (SAS subset MATWS) is correctly placed using a total of 8 model runs [11,4]. Normally, this task would require hundreds of code evaluations.…”

Section: Motivation For Automatic Differentiation Of Simulation Modelsmentioning

confidence: 99%

Derivative-based uncertainty quantification: automatic differentiation tools for SAS.

Roderick¹,

Anitescu²,

Utke³

2012

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Automatic differentiation, or more properly algorithmic differentiation (AD), is a technique for efficiently computing accurate derivatives for numerical models. It is based on augmenting the code with partial derivatives of elementary mathematical operations on important variables and retracing the calculation flow (in forward or reverse direction) to assemble derivatives by chain rule. The relative computational overhead associated with AD is bounded, independent of dimension, and is largely independent of the mathematical model.In our larger body of work on advanced uncertainty analysis of simulation models of nuclear engineering, AD serves as the driving element behind such methods as polynomial regression with derivatives, gradient-enhanced universal kriging, and sensitivity-based dimensionality reduction of the uncertainty space. In fact, the main alternative to using AD to get sensitivity information is hand coding of direct and adjoint derivatives, which is always a significant development effort and often cannot be expected from the developers.In this report, we discuss the findings and intermediate benefits of the latest effort to enable algorithmic differentiation of the SHARP safety code SAS. This effort was planned as an exercise to demonstrate the effectiveness of AD on simulations of professional interest. The subject is a legacy code comprising 120,000 lines of uncommented Fortran 77 code; it thus presents significant challenges for manual analysis. An intermediate outcome of the preparation work required for AD is a semiautomatically generated code annotation, with identification and characterization of code features in the context of AD.While no principal, mathematical model-related reason prevents algorithmic differentiation for SAS, certain features in model implementation pose steep technical hurdles. We report the categories of the problematic features found in SAS and recommend possible remedies, amounting to a future effort in code rewriting.Because the full capability for differentiation of SAS was not achieved, we redirected the effort to differentiation of the SHARP component neutronics code UNIC. We report on the outcome-differentiation in forward mode achieved-and outline other capabilities that can now be acquired and verified.

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Section: Motivation For Automatic Differentiation Of Simulation Modelsmentioning

confidence: 99%

Derivative-based uncertainty quantification: automatic differentiation tools for SAS.

Roderick¹,

Anitescu²,

Utke³

2012

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“…There are several checks that need to be made [61,4,39]. First, at any level of the code, the development of the discrete adjoint model can be checked by appling the following identity…”

Section: Checking the Correctness Of The Implementationmentioning

confidence: 99%

“…Within this framework one may imagine a situation where Greeks are computed (using AD techniques) in real time to provide hedging with respect to various risk factors: interest rate, counterparty credit, correlation, model parameters etc. Due to complexity of quant libraries, AD tools and special techniques of memory management, checkpointing etc can prove extremely useful, potentially leveraging knowledge acquired during AD applications to large software packages in other areas: meteorology, computational fluid dynamics etc where such techniques were employed [43,25,45,4,39,15,8] 9.1 Block architecture for Greeks [10] presents a "Block architecture for Greeks" , using calculators and allocators. Sensitivities are computed for each block component, including root-finding and optimization routines, trees and latices.…”

Section: Calibrationmentioning

confidence: 99%

Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance

Homescu¹

2011

SSRN Journal

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Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic differentiation (AD), also known as algorithmic differentiation, techniques to calculate these sensitivities. When compared to finite difference approximation, this approach can potentially reduce the computational cost by several orders of magnitude, with sensitivities accurate up to machine precision. Examples and a literature survey are also provided. *

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“…2 In the nuclear engineering field, the complex-step method was applied to verify first derivatives computed with other methods in MATWS, a code that "combines the point-kinetics module from the SAS4A/SASSYS computer code with a simplified representation of a reactor heatremoval system." 6 More recently, Ref. 7 implemented the complex-step method in the neutron transport equation to obtain first-order derivatives of the k-eigenvalue with respect to nuclear cross sections.…”

Section: Introductionmentioning

confidence: 99%

Multidual Sensitivity Method in Ray-Tracing Transport Simulations

Balcer

Millwater

Favorite

2021

Nuclear Science and Engineering

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The multidual differentiation method has been implemented in a ray-tracing transport simulation for the purpose of calculating arbitrary-order sensitivities of the uncollided particle leakage. This method extends dual number differentiation by perturbing variables along multiple nonreal axes to calculate arbitrary-order derivatives. Numerical results of first-through third-order multidual sensitivities of the uncollided particle leakage with respect to isotope densities, microscopic cross sections, source emission rates, and material interface locations (including the outer boundary) are shown for a two-region sphere. The relative error of first and second partial derivatives with respect to isotopic parameters and first partial derivatives of the leakage with respect to interface locations are within 9.8E−10% of existing adjoint-based sensitivities. Higher-order multidual-based derivatives that are not available with the adjoint method are in excellent agreement with central difference approximations.

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Automatic differentiation of codes in nuclear engineering applications.

Abstract: The Laboratory's main facility is outside Chicago, at 9700 South Cass Avenue, Argonne, Illinois 60439. For information about Argonne and its pioneering science and technology programs, see www.anl.gov.

Cited by 3 publications

References 22 publications

Derivative-based uncertainty quantification: automatic differentiation tools for SAS.

Derivative-based uncertainty quantification: automatic differentiation tools for SAS.

Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance

Multidual Sensitivity Method in Ray-Tracing Transport Simulations

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