Sentence examples for by an automatic differentiation from inspiring English sources

Analytical expressions for sensitivities are obtained by an automatic differentiation tool.

The discrete adjoint solver is obtained with the aid of an automatic differentiation tool, TAPENADE.

First- and second-order sensitivity coefficients of the thermal and mechanical response quantities (derivatives with respect to various thermomechanical parameters) are evaluated using a direct differentiation approach in conjunction with an automatic differentiation software facility.

Expressions of the potential and kinetic energies are then introduced in a suitable finite element software that can perform an automatic differentiation to solve the problem.

This paper discusses the development and implementation of an automatic differentiation based nonlinear reduced order model for unsteady separated flows.

The discretized equation system is solved by a modified Newton's method, in which the Jacobian matrix is computed by the automatic differentiation (AD) technique.

The gradient information is supplied by the automatic differentiation tool Adifor by Argonne National Laboratory.

By applying automatic differentiation to these micromechanics incremental schemes, the first order and high order sensitivities of the effective material properties can be easily computed in the same analysis.

This can be done efficiently by using automatic differentiation techniques (see details in [32]).

According to this formulation, procedural components of implementing the required matrix-vector products are generated by means of automatic differentiation (AD) in a structured and modular manner.

The derivatives computed by automatic differentiation are compared with approximations based on divided differences.