engleski

Application of self-adapting regularization, machine learning tools and limits in Levenberg– Marquardt algorithm to solve CNLS problem

The Electrochemical Spectroscopy Impedance (EIS) data are usually analyzed by solving different Complex Nonlinear Least Squares (CNLS) problems. These problems are generally solved by using the Levenberg–Marquardt algorithm (LMA), which is a self-adaptive regularization technique that applies the first derivatives values stored in the Jacobian matrix. The LMA convergence can be amplified by the application of both the limit tactics and the exact first derivative values. These exact values can be obtained by using the automatic differentiation (AD) algorithm embedded in PyTorch, which is an open-source machine learning framework. However, the joint application of AD, self-adapting regularization, and the limits has not been reported as a part of CNLS strategy yet. Herein, we have designed and developed a new CNLS strategy that applies the limits tactics, AD, and self-adapting regularization. Also, we claim that the new strategy can be straightforwardly employed as the exact first derivative values can be obtained by EEC and AD, which simplifies developing tasks. The results in this work clearly reveal that the LMA convergence is boosted when using the exact Jacobian matrix constructed by both the limits and AD. In addition to that, the new strategy decreases the impact of the poor starting parameters. The tests in this work, conducted by analyzing ZARCs and FRACs synthetic data, show a superior performance of the newly developed CNLS strategy.

Levenberg–Marquardt algorithm ; CNLS ; Limits ; EEC ; Jacobian matrix ; Automatic differentiation

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