发表机构
Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS)（南里奥格兰德联邦大学物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
用机器学习聚类短时模拟数据，绘制一维非线性薛定谔方程在准周期无序和静电场下的输运相图，识别五个区域并预测长时行为。
AI 中文摘要
我们绘制了在一维离散非线性薛定谔（Gross-Pitaevskii）方程下，具有准周期Aubry-André势和静（Stark）场的波包输运区域图，该图作为自相互作用$g$、场$F$和准周期强度$\lambda$的函数，针对两种初始态（delta和Gaussian）而构建。我们不是对每个网格点进行一次昂贵的长时模拟，而是运行3600次短时模拟，将每次模拟简化为八个动力学特征，并使用高斯混合模型对参数空间进行聚类。聚类在无监督情况下找到各区域之间的边界；随后通过手工校准规则为每个聚类命名，消融实验表明聚类可测量地平滑了这些边界，而不仅仅是重新标记它们。所得五个区域（弹道、局域、振荡-局域、次扩散和自俘获）在比短时扫描大八倍的晶格上通过100次长时运行进行验证，因此即使对于最快扩散的区域，验证窗口也比训练窗口长。短时聚类预测了长时渐近扩散指数（弹道$\alpha_\infty = 2.01\pm0.07$，次扩散$0.28\pm0.16$，与弱混沌预测$\alpha=1/3$一致），并独立地预测了自俘获聚类的长时保留率$\Pi_0=0.72\pm0.32$，而仅靠指数无法诊断该聚类。初始态对比显著：delta态发展出宽阔的自俘获楔形区（在$\lambda=0$时起始于$g=3.907\pm0.017$），随着$g$增大而侵入弹道和局域区域，而Gaussian态则无自俘获，反而沿Aubry-André临界线开辟出随$g$增宽的次扩散走廊。该方案在几分钟内即可生成完整的$15\times15$相图切片，而直接渐近模拟（每点$t\gtrsim10^6$）则不可行。
英文摘要
We map the transport regimes of a wave packet evolving under the one-dimensional discrete nonlinear Schrödinger (Gross-Pitaevskii) equation with a quasiperiodic Aubry-André potential and a static (Stark) field, as a function of self-interaction $g$, field $F$, and quasiperiodic strength $λ$, for two initial states (delta and Gaussian). Instead of one expensive long-time simulation per grid point, we run 3600 short simulations, reduce each to eight dynamical features, and cluster parameter space with a Gaussian mixture model. Clustering finds the boundaries between regimes unsupervised; each cluster's name is then assigned by a hand-calibrated rule, and an ablation shows clustering measurably smooths those boundaries rather than merely relabeling them. The five resulting regimes (ballistic, localized, oscillatory-localized, subdiffusive, and self-trapped) are validated against 100 long runs on a lattice eight times larger than the short sweep, so the validation window is longer than the training window even for the fastest-spreading regime. The short-time clusters predict the long-time asymptotic spreading exponent ($α_\infty = 2.01\pm0.07$ ballistic, $0.28\pm0.16$ subdiffusive, consistent with the weak-chaos prediction $α=1/3$) and, independently, a long-time retention $Π_0=0.72\pm0.32$ for the self-trapped cluster, whose exponent alone is not diagnostic. The initial-state contrast is striking: the delta state develops a broad self-trapping wedge (onset at $g=3.907\pm0.017$ at $λ=0$) that invades the ballistic and localized regions as $g$ grows, while the Gaussian state shows no self-trapping, instead opening a subdiffusive corridor along the Aubry-André critical line that widens with $g$. The scheme yields a full $15\times15$ phase map in minutes per slice, where direct asymptotic simulation ($t\gtrsim10^6$ per point) is prohibitive.
