Automatic Differentiation Of Fortran Research Articles

Efficient sensitivity/uncertainty analysis using the combined stochastic response surface method and automated differentiation: application to environmental and biological systems.

Estimation of uncertainties associated with model predictions is an important component of the application of environmental and biological models. "Traditional" methods for propagating uncertainty, such as standard Monte Carlo and Latin Hypercube Sampling, however, often require performing a prohibitive number of model simulations, especially for complex, computationally intensive models. Here, a computationally efficient method for uncertainty propagation, the Stochastic Response Surface Method (SRSM) is coupled with another method, the Automatic Differentiation of FORTRAN (ADIFOR). The SRSM is based on series expansions of model inputs and outputs in terms of a set of "well-behaved" standard random variables. The ADIFOR method is used to transform the model code into one that calculates the derivatives of the model outputs with respect to inputs or transformed inputs. The calculated model outputs and the derivatives at a set of sample points are used to approximate the unknown coefficients in the series expansions of outputs. A framework for the coupling of the SRSM and ADIFOR is developed and presented here. Two case studies are presented, involving (1) a physiologically based pharmacokinetic model for perchloroethylene for humans, and (2) an atmospheric photochemical model, the Reactive Plume Model. The results obtained agree closely with those of traditional Monte Carlo and Latin hypercube sampling methods, while reducing the required number of model simulations by about two orders of magnitude.

Application of an automatic differentiation tool in the development of a compositional reservoir simulator

Automatic differentiation is an approach to numerically compute derivatives both accurately and efficiently. This can be quite valuable, for example, in the fully implicit solution of compositional reservoir equations. We describe the procedures necessary to apply the ADIFOR (Automatic Differentiation of Fortran) tool to the IPARS (Integrated Parallel Accurate Reservoir Simulator) compositional reservoir simulator and the approaches used to exploit the sparsity in the required Jacobian matrix. Values and execution times of the ADIFOR-generated derivatives are compared with a handwritten code that implements analytically derived expressions for the derivatives. Copyright © 1999 John Wiley & Sons, Ltd.

Application of an automatic differentiation tool in the development of a compositional reservoir simulator

Automatic differentiation is an approach to numerically compute derivatives both accurately and efficiently. This can be quite valuable, for example, in the fully implicit solution of compositional reservoir equations. We describe the procedures necessary to apply the ADIFOR (Automatic Differentiation of Fortran) tool to the IPARS (Integrated Parallel Accurate Reservoir Simulator) compositional reservoir simulator and the approaches used to exploit the sparsity in the required Jacobian matrix. Values and execution times of the ADIFOR-generated derivatives are compared with a handwritten code that implements analytically derived expressions for the derivatives. Copyright © 1999 John Wiley & Sons, Ltd.

Application of Automatic Differentiation to Reservoir Design Models

Automatic differentiation is a technique for computing derivatives accurately and efficiently with minimal human effort. The calculation of derivatives of numerical models is necessary for gradient-based op­ timization of reservoir systems to determine optimal sizes for reservoirs. The writers report on the use of automatic differentiation and divided difference approaches for computing derivatives for a single- and multiple­ reservoir yield model. In the experiments, the AD1FOR (Automatic Differentiation of Fortran) tool is employed. The results show that, for both the single- and the multiple-reservoir model, automatic differentiation computes derivatives exactly and more efficiently than the divided difference implementation. Postoptimization of the ADIFOR-generated derivative code by exploiting the model structure is also discussed. The writers observe that the availability of exact derivatives significantly benefits the convergence of the optimization algorithm: the solution of the muItireservoir problem, which took 10.5 hours with divided difference derivatives, is decreased to less than two hours with ADIFOR out of the box derivatives, and to less than an hour using the postop­ timized ADIFOR derivative code.

Efficient Derivative Codes through Automatic Differentiation and Interface Contraction: An Application in Biostatistics

Developing code for computing the first- and higher-order derivatives of a function by hand can be very time consuming and is prone to errors. Automatic differentiation has proven capable of producing derivative codes with very little effort on the part of the user. Automatic differentiation avoids the truncation errors characteristic of divided difference approximations. However, the derivative code produced by automatic differentiation can be significantly less efficient than one produced by hand. This shortcoming may be overcome by utilizing insight into the high-level structure of a computation. This paper focuses on how to take advantage of the fact that the number of variables passed between subroutines frequently is small compared with the number of variables with respect to which one wishes to differentiate. Such an "interface contraction," coupled with the associativity of the chain rule for differentiation, allows one to apply automatic differentiation in a more judicious fashion, resulting in much more efficient code for the computation of derivatives. A case study involving the ADIFOR (Automatic Differentiation of Fortran) tool and a program for maximizing a logistic-normal likelihood function developed from a problem in nutritional epidemiology is examined, and performance figures are presented.

Computing Gradients in Large-Scale Optimization Using Automatic Differentiation

The accurate and efficient computation of gradients for partially separable functions is central to the solution of large-scale optimization problems, because these functions are ubiquitous in large-scale problems. We describe two approaches for computing gradients of partially separable functions via automatic differentiation. In our experiments we employ the ADIFOR (automatic differentiation of Fortran) tool and the SparsLinC (sparse linear combination) library. We use applications from the MINPACK-2 test problem collection to compare the numerical reliability and computational efficiency of these approaches with hand-coded derivatives and approximations based on differences of function values. Our conclusion is that automatic differentiation is the method of choice, providing code for the efficient computation of the gradient without the need for tedious hand-coding.

ADIFOR–Generating Derivative Codes from Fortran Programs

The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of a function f Rn→Rm. Both the accuracy and the computational requirements of the derivative computation are usually of critical importance for the robustness and speed of the numerical solution. Automatic Differentiation of FORtran (ADIFOR) is a source transformation tool that accepts Fortran 77 code for the computation of a function and writes portable Fortran 77 code for the computation of the derivatives. In contrast to previous approaches, ADIFOR views automatic differentiation as a source transformation problem. ADIFOR employs the data analysis capabilities of the ParaScope Parallel Programming Environment, which enable us to handle arbitrary Fortran 77 codes and to exploit the computational context in the computation of derivatives. Experimental results show that ADIFOR can handle real‐life codes and that ADIFOR‐generated codes are competitive with divided‐difference approximations of derivatives. In addition, studies suggest that the source transformation approach to automatic differentiation may improve the time to compute derivatives by orders of magnitude.