Sentence examples for by the automatic differentiation from inspiring English sources
The gradient information is supplied by the automatic differentiation tool Adifor by Argonne National Laboratory.
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 automatic differentiation technique is used to obtain the consistent tangent operator.
The tool uses a combination of the Adjoint method, the chain rule for differentiation, and the automatic differentiation to compute the sensitivities.
The mini-array allows for the automatic differentiation between the tumors with and those without a specific characteristic.
The derivatives computed by automatic differentiation are compared with approximations based on divided differences.
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 correction step is replaced by the mere integration of an ordinary differential equation with the help of automatic differentiation (see, e.g., [5, 29]).
