Publication: Implementación de diferenciación automática en solver no lineales
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Date
2023-12
Authors
Jiménez Meza, Valerie Alexandra Eugenia
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Abstract
Uno de los desafíos más significativos radica en la resolución de sistemas de
ecuaciones no lineales sobredeterminados, principalmente debido a los altos requisitos
computacionales y de memoria asociados a la obtención de la matriz Jacobiana. En este
trabajo, se propone la implementación de la diferenciación automática a través de las
funciones de Jacobian-Vector Product (jvp) y Vector-Jacobian Product (vjp). Además, se
plantea una estrategia para obtener una aproximación de la matriz Jacobiana ˜ J con la
particularidad de ser una versión dispersa, lo que resulta fundamental para el manejo
eficiente del producto ˜ JT w. Todo ello con el fin de implementar una versión alternativa
del método nsLSQR que pueda obtener resultados satisfactorios sin requerir recursos
computacionales excesivos
One of the most significant challenges lies in solving overdetermined nonlinear systems of equations, primarily due to the high computational and memory requirements associated with obtaining the Jacobian matrix. In this work, the implementation of automatic differentiation through the Jacobian-Vector Product (jvp) and Vector-Jacobian Product (vjp) functions is proposed. Additionally, a strategy is introduced to obtain an approximation of the Jacobian matrix ˜ J with the particularity of being a sparse version, which is crucial for the efficient handling of the ˜ JT w product. All of this is aimed at developing an alternative version of the nsLSQR method that can achieve satisfactory results without demanding excessive computational resources.
One of the most significant challenges lies in solving overdetermined nonlinear systems of equations, primarily due to the high computational and memory requirements associated with obtaining the Jacobian matrix. In this work, the implementation of automatic differentiation through the Jacobian-Vector Product (jvp) and Vector-Jacobian Product (vjp) functions is proposed. Additionally, a strategy is introduced to obtain an approximation of the Jacobian matrix ˜ J with the particularity of being a sparse version, which is crucial for the efficient handling of the ˜ JT w product. All of this is aimed at developing an alternative version of the nsLSQR method that can achieve satisfactory results without demanding excessive computational resources.
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Keywords
Sistemas de ecuaciones no lineales , Matriz Jacobiana , Métodos de resolución , Diferenciación automática