Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques respectively to achieve their goals. This paper introduces improvements to these mathematical methods to then improve the convergence behaviour of the overarching models when used in highly non-linear systems. The performance of the new techniques is examined in detail and compared to that of the standard methods. The improved techniques are also tested with FEM models to show their practical application. Depending on the specific configuration of the problem, the improved models yielded larger convergence basins and/or took fewer steps to converge.

翻译：正向模型和逆向模型广泛应用于不同工程领域，用于预测和理解系统行为，并从一组观测数据中找出参数。这些模型分别采用求根法和最小化技术来实现其目标。本文针对这些数学方法进行改进，以提升高度非线性系统中整体模型的收敛性能。详细分析了新技术的性能，并与标准方法进行了对比。改进后的技术还通过有限元模型进行测试，以展示其实际应用。根据问题的具体配置，改进后的模型生成了更大的收敛盆地，并且/或收敛所需的步骤更少。