We introduce Coarse-Grained Nonlinear Dynamics, an efficient and universal parameterization of nonlinear system dynamics based on the Volterra series expansion. These models require a number of parameters only quasilinear in the system's memory regardless of the order at which the Volterra expansion is truncated; this is a superpolynomial reduction in the number of parameters as the order becomes large. This efficient parameterization is achieved by coarse-graining parts of the system dynamics that depend on the product of temporally distant input samples; this is conceptually similar to the coarse-graining that the fast multipole method uses to achieve $\mathcal{O}(n)$ simulation of n-body dynamics. Our efficient parameterization of nonlinear dynamics can be used for regularization, leading to Coarse-Grained Nonlinear System Identification, a technique which requires very little experimental data to identify accurate nonlinear dynamic models. We demonstrate the properties of this approach on a simple synthetic problem. We also demonstrate this approach experimentally, showing that it identifies an accurate model of the nonlinear voltage to luminosity dynamics of a tungsten filament with less than a second of experimental data.
翻译:我们引入了Coarse-Graine 的非线性动态,这是基于Volterra系列扩展的非线性系统动态的有效和普遍的参数化。 这些模型要求系统记忆中的若干参数仅是准线性参数,而不论伏尔特拉扩展变速的顺序如何; 这是随着顺序变大而使参数数量的超极极性减少。 这种高效参数化是通过系统动态中依赖时间遥远的输入样本的产物的粗毛性微粒化部分来实现的; 这在概念上类似于快速多极方法用于实现 n体动态的模拟的粗皮质加分。 我们的非线性动态的高效参数化可用于正规化, 导致非线性非线性系统识别, 这种方法需要极少的实验数据来识别准确的非线性动态模型。 我们在一个简单的合成问题上展示了这种方法的特性。 我们还实验性地展示了这一方法, 表明它识别了非线性实验性模型的精确模型, 而不是光性数据动态的二线性。