基于柯尔莫哥洛夫对称性的高斯过程，提升动态系统预测与表征的可靠性。
Koopman-Equivariant Gaussian Processes
- 利用轨迹等变性构建线性时不变响应的高斯过程模型
- 可同时量化预测与表征不确定性，且在大规模回归中表现优于核方法
- 适合需要可信动态系统建模的研究者，如机器人、气候模拟领域
可信的动态系统预测与表征学习对可靠决策至关重要。我们提出一类高斯过程（GP）模型，适用于具有线性时不变响应、仅初始条件非线性的动态系统。该线性结构使轨迹分布的不确定性可解析计算，显著缓解了基于GP的动态系统轨迹分布计算难题，并支持对柯尔莫哥洛夫算子表示的全新概率化学习方式。通过引入基于轨迹的等变性（称为“柯尔莫哥洛夫等变性”），模型具备更强的泛化能力。为实现大规模回归，框架采用基于合适诱导点的变分推断。实验表明，该方法在动态系统学习中的预测性能与核方法相当，且经常更优。
原文摘要 · Abstract (English)
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear time-invariant responses, which are nonlinear only in initial conditions. This linearity allows us to tractably quantify forecasting and representational uncertainty, simultaneously alleviating the challenge of computing the distribution of trajectories from a GP-based dynamical system and enabling a new probabilistic treatment of learning Koopman operator representations. Using a trajectory-based equivariance -- which we refer to as \textit{Koopman equivariance} -- we obtain a GP model with enhanced generalization capabilities. To allow for large-scale regression, we equip our framework with variational inference based on suitable inducing points. Experiments demonstrate on-par and often better forecasting performance compared to kernel-based methods for learning dynamical systems.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。