贝叶斯盆地追踪：多稳态动力系统的高效全局延拓
Bayesian Basin Tracking: Efficient Global Continuation of Multistable Dynamical Systems
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中文总结 AI 辅助
研究高维多稳态动力系统全局相空间绘制难题，提出贝叶斯盆地追踪框架，利用盆地边界持续性及概率建模，结合对数贝叶斯因子检测结构变化，经多模型验证，能克服维度缩放问题，实现计算加速并保留误差界限。
中文摘要 AI 辅助
绘制高维多稳态动力系统的全局相空间在计算上是 prohibitive 的，因为传统方法需要大量数值积分。本文介绍了贝叶斯盆地追踪（BBT），这是一种自适应贝叶斯框架，利用盆地边界在参数延拓下的持续性，仅用传统方法所需模拟的一小部分来重建全局相空间结构。通过对采样初始条件收敛到特定吸引子的概率建模，该方法通过狄利克雷-多项分布模型表示在给定参数值处建立的相空间几何。在附近参数值处，通过用新采样数据更新先验分布来估计这些概率。为自动检测边界危机和分岔，使用对数贝叶斯因子作为信息理论传感器，仅在结构变化使历史先验在统计上不合理时触发密集重采样。用离散 Hénon 映射、连续时间 Duffing 振子和 300 维耦合 Rössler 振子网络验证了该框架。BBT 通过将计算要求最高的计算集中在结构易变区域，克服了确定性网格细分的限制性维度缩放。在高维同步景观中，它实现了近六倍的计算加速，同时保留了理论推导的误差界限。
英文摘要
Mapping the global phase space of high-dimensional multistable dynamical systems is computationally prohibitive because conventional approaches require extensive numerical integration. Here, we introduce Bayesian Basin Tracking (BBT), an adaptive Bayesian framework that exploits the persistence of basin boundaries under parameter continuation to reconstruct global phase-space structure using only a fraction of the simulations required by conventional methods. By modeling the probability that a sampled initial condition converges to a particular attractor, the method represents the phase-space geometry established at a given parameter value through a Dirichlet-multinomial model. At a nearby parameter value, these probabilities are estimated by updating the prior distribution with newly sampled data. To detect boundary crises and bifurcations autonomously, we use the log Bayes factor as an information-theoretic sensor that triggers dense resampling only when structural changes render the historical prior statistically implausible. We validate the framework using the discrete Hénon map, the continuous-time Duffing oscillator, and a 300-dimensional network of coupled Rössler oscillators. BBT overcomes the restrictive dimensional scaling of deterministic grid tessellations by concentrating the most computationally demanding calculations in structurally volatile regions. In high-dimensional synchronization landscapes, it achieves an almost sixfold computational speed-up while retaining theoretically derived error bounds.
