In this contribution, we propose a data-driven procedure to fit quadratic-bilinear surrogate models from data. Although the dynamics characterizing the original model are strongly nonlinear, we rely on lifting techniques to embed the original model into a quadratic-bilinear format. Here, data represent generalized transfer function values. This method is an extension of methods that do bilinear, or quadratic inference, separately. It is based on first fitting a linear model with the classical Loewner framework, and then on inferring the best supplementing nonlinear operators, in a least-squares sense. The application scope of this method is given by electrical circuits with nonlinear components (such as diodes). We propose various test cases to illustrate the performance of the method.
翻译:在这一贡献中,我们提出了一个数据驱动程序,以适应数据中的二次等离子体代谢模型。虽然原型模型的动态特征非线性很强,但我们依靠提升技术将原型模型嵌入二次等离子体格式。在这里,数据代表了通用的转移函数值。这种方法是双线或二次等离子推断方法的延伸。它基于首先将线性模型与古典Lewner框架相匹配,然后从最小的意义上推断出最佳的补充非线性非线性操作者。这种方法的应用范围由非线性部件的电路(例如二极)提供。我们提出了各种测试案例来说明该方法的性能。