从实验数据中学习离散模型
Learning Discrepancy Models From Experimental Data
摘要：
物理系统的第一性原理建模导致了所有科学分支的重大技术进步。然而，对于非线性系统，小的建模误差可能导致与真实测量行为的显著偏差。即使在机械系统中，其中的方程被假定为众所周知的，往往有模型的差异对应于非线性摩擦，风阻力等发现这些差异的模型仍然是一个开放的挑战，许多复杂的系统。在这项工作中，我们使用稀疏识别的非线性动力学（SINDy）算法来发现一个模型的简化模型和测量数据之间的差异。特别是，我们假设模型不匹配可以稀疏地表示在候选模型项的库中。我们证明了我们的方法的有效性的几个例子，包括实验数据从一个双摆推车。我们进一步设计并实作一前馈控制器于模拟中，显示出差异模型的改善。
英文摘要：
First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured behavior. Even in mechanical systems, where the equations are assumed to be well-known, there are often model discrepancies corresponding to nonlinear friction, wind resistance, etc. Discovering models for these discrepancies remains an open challenge for many complex systems. In this work, we use the sparse identification of nonlinear dynamics (SINDy) algorithm to discover a model for the discrepancy between a simplified model and measurement data. In particular, we assume that the model mismatch can be sparsely represented in a library of candidate model terms. We demonstrate the efficacy of our approach on several examples including experimental data from a double pendulum on a cart. We further design and implement a feed-forward controller in simulations, showing improvement with a discrepancy model.
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