Differential Sensitivity Theory applied to the MESA2D code for multi-material problems

Henninger, R.J.; Maudlin, P.J.; Harstad, E. N.

doi:10.1063/1.50795

Cited by 3 publications

(3 citation statements)

References 6 publications

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“…An important issue when choosing whether to use a forward or adjoint method to determine sensitivities is the amount of computer time that each method requires. As mentioned in previous work (1,2,3), the number of parameters versus the number of responses plays a key role in this decision. For this problem we have chosen only one response.…”

Section: ;)mentioning

confidence: 94%

Code differentiation for hydrodynamic model optimization

Henninger¹,

Maudlin²

2000

AIP Conference Proceedings

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Section: ;)mentioning

confidence: 94%

Code differentiation for hydrodynamic model optimization

Henninger¹,

Maudlin²

2000

AIP Conference Proceedings

Self Cite

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“…The distinctive feature of ADICT is that a separate computer code is used to compute the adjoint derivatives and that code is based on the simulation code with the explicit intent to "differentiate" the forward calculation or numerical algorithm. For optimization of a functional based on computation, it is desirable to have the gradient of the computation, not of the physics equations that the computation is supposed to approximate [6,7]. The ADICT principle can produce more accurate derivatives [8].…”

Section: Inversion Based On Simulationsmentioning

confidence: 99%

Maximum Entropy and Bayesian Methods

Skilling¹,

Sibisi²

1996

170

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Abstract.A standard approach to solving inversion problems that involve many parameters uses gradient-based optimization to find the parameters that best match the data. We will discuss enabling techniques that facilitate application of this approach to large-scale computational simulations, which are the only way to investigate many complex physical phenomena. Such simulations may not seem to lend themselves to calculation of the gradient with respect to numerous parameters. However, adjoint differentiation allows one to efficiently compute the gradient of an objective function with respect to all the variables of a simulation. When combined with advanced gradient-based optimization algorithms, adjoint differentiation permits one to solve very large problems of optimization or parameter estimation. These techniques will be illustrated through the simulation of the time-dependent diffusion of infrared light through tissue, which has been used to perform optical tomography. The techniques discussed have a wide range of applicability to modeling including the optimization of models to achieve a desired design goal.Key words: simulation, inversion, reconstruction, adjoint differentiation, sensitivity analysis, optimization, model validation INTRODUCTION TO THE GENERAL PROBLEMFrequently a physical situation can only be described fully by a computational model. We wish to address the general problem of finding the values of the parameters in such a model that best match a given set of data. This problem in often referred to as that of inversion. In data matching the objective function to be minimized is often the negative logarithm of the likelihood of the data given their predicted values, which yields the maximum likelihood (ML) solution. Alternative approaches include regularized versions of maximum likelihood and Bayesian methods, in which the objective function is the minus-log-posterior, yielding the maximum a posteriori (MAP) estimate.We confine ourselves to objective functions that depend on the parameters in a continuous and differentiable fashion. We do not necessarily avoid problems for which the objective function possesses multiple minima. However, because the techniques that we present make use of gradients in the optimization process, they will work effectively only when one can easily find the basin of attraction for the global minimum, for example, by multiscale or multiresolution optimization.

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“…The DST results were then improved by means of "compatible" finite difference operators (6,7). We have seen, however, that DST techniques do not produce accurate values for sensitivities to all of the parameters of interest and for problems with discontinuities such as a multi-material problem (8). To obtain accurate sensitivities for arbitrary numerical resolution a more code-based approach was then tried.…”

Section: Introductionmentioning

confidence: 99%

Sensitivities for Taylor-Test Model Parameters

Henninger¹

2002

AIP Conference Proceedings

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Abstract. The Taylor-Cylinder test has long been used to calibrate equation-of-state and materialstrength models. The process consists of impacting a cylinder of material on a rigid anvil and adjusting the model parameters to predict the resultant shape. Here we discuss the use of Automatic Differentiation (AD) of an Eulerian hydrodynamics model to provide sensitivities that are used as a gradient in the parameter fitting process. We apply AD in the forward and adjoint modes. For comparison, the gradient is also determined by finite differences. We find that adjoint methods provide the most efficient use of computational resources when there are 9 or more parameters.

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Differential Sensitivity Theory applied to the MESA2D code for multi-material problems

Cited by 3 publications

References 6 publications

Code differentiation for hydrodynamic model optimization

Code differentiation for hydrodynamic model optimization

Maximum Entropy and Bayesian Methods

Sensitivities for Taylor-Test Model Parameters

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