用贝叶斯方法从数据中自动发现带延迟的微分方程
A Bayesian Approach for Discovering Time- Delayed Differential Equation from Data
- 基于贝叶斯推断与稀疏先验，自动识别时间延迟项
- 可准确识别任意大的延迟值，精度取决于数据分辨率
- 适合处理含噪声数据的复杂动态系统建模
时滞微分方程（TDDEs）广泛用于建模未来状态依赖过去状态的复杂动态系统。然而，由于真实系统中存在非线性、不确定性与噪声，从观测数据中推断底层TDDE仍具挑战性。传统方程发现方法在处理大时滞时表现受限，多依赖确定性技术或优化方法，存在可扩展性与鲁棒性不足的问题。本文提出BayTiDe——一种基于贝叶斯推断的时滞微分方程发现方法，结合稀疏促进的不连续尖峰-平滑先验，能够以与输入数据分辨率成正比的精度，准确识别任意大小的时间延迟。该方法有效缩小搜索空间，实现显著计算节省。通过多种数值实验验证，BayTiDe在含噪声数据下仍能可靠恢复时滞微分方程。
原文摘要 · Abstract (English)
Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem due to the inherent nonlinearity, uncertainty, and noise in real-world systems. Conventional equation discovery methods often exhibit limitations when dealing with large time delays, relying on deterministic techniques or optimization-based approaches that may struggle with scalability and robustness. In this paper, we present BayTiDe - Bayesian Approach for Discovering Time-Delayed Differential Equations from Data, that is capable of identifying arbitrarily large values of time delay to an accuracy that is directly proportional to the resolution of the data input to it. BayTiDe leverages Bayesian inference combined with a sparsity-promoting discontinuous spike-and-slab prior to accurately identify time-delayed differential equations. The approach accommodates arbitrarily large time delays with accuracy proportional to the input data resolution, while efficiently narrowing the search space to achieve significant computational savings. We demonstrate the efficiency and robustness of BayTiDe through a range of numerical examples, validating its ability to recover delayed differential equations from noisy data.
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。