Continuous-time (CT) modeling has proven to provide improved sample efficiency and interpretability in learning the dynamical behavior of physical systems compared to discrete-time (DT) models. However, even with numerous recent developments, the CT nonlinear state-space (NL-SS) model identification problem remains to be solved in full, considering common experimental aspects such as the presence of external inputs, measurement noise, latent states, and general robustness. This paper presents a novel estimation method that addresses all these aspects and that can obtain state-of-the-art results on multiple benchmarks with compact fully connected neural networks capturing the CT dynamics. The proposed estimation method called the subspace encoder approach (SUBNET) ascertains these results by efficiently approximating the complete simulation loss by evaluating short simulations on subsections of the data, by using an encoder function to estimate the initial state for each subsection and a novel state-derivative normalization to ensure stability and good numerical conditioning of the training process. We prove that the use of subsections increases cost function smoothness together with the necessary requirements for the existence of the encoder function and we show that the proposed state-derivative normalization is essential for reliable estimation of CT NL-SS models.
翻译:连续时间(CT)建模证明在学习物理系统与离散时间(DT)模型相比的动态行为方面提高了抽样效率和解释性,但是,即使最近取得了许多发展,CT非线性状态(NL-SS)建模模型识别问题仍待完全解决,考虑到外部投入的存在、测量噪音、潜在状态和总体稳健性等共同实验方面,本文件提出了一个新的估计方法,涉及所有这些方面,并能够取得与收集CT动态的紧凑、完全连通的神经网络的多个基准的最先进的结果。拟议的估算方法称为子空间编码器方法(SUBNET),通过对数据分节的短模拟进行评估,有效地接近模拟损失的完全确定这些结果,为此使用一种编码器功能来估计每个分节的初始状态,以及一种新的状态衍生正常化,以确保培训过程的稳定性和良好的数字调节。我们证明,分节的使用提高了成本功能的平稳性,同时增加了存在编码器模型正常性的必要要求。我们证明,拟议的状态模型是用于可靠的NCIV模型正常性估算的基本要求。