用时间编码的CNN直接预测光合复合物能量传递，避免误差累积。
Multi-timescale time encoding for CNN prediction of Fenna-Matthews-Olson energy-transfer dynamics
- 用冗余时间编码+物理约束函数，直接映射参数到能量分布
- 仅用0~7皮秒数据训练，准确预测0~100皮秒动态，误差低于5%
- 适合研究光合材料设计与长时量子耗散系统建模
机器学习模拟开放量子动力学常依赖递归预测器，导致误差累积。本文提出一种非递归卷积神经网络（CNN），将系统参数与冗余时间编码直接映射至Fenna-Matthews-Olson复合物中的激发态能量转移分布。通过编码修正的逻辑斯蒂加tanh函数对时间归一化，可分辨快速过渡与准稳态阶段；物理信息标签强制守恒与位点一致性。模型仅在QuTiP中用Lindblad模型生成的0~7皮秒参考轨迹训练，即可准确预测0~100皮秒内多种重组能、浴态速率与温度下的动力学。超过20皮秒后，绝对相对误差始终低于0.05，展现稳定长时外推能力。该方法通过避免逐步递归，抑制了误差积累，并实现跨时间尺度泛化。结果表明，冗余时间编码可实现数据高效推理真实色素-蛋白复合物中的长时量子耗散动力学，有望助力光捕获材料的数据驱动设计。
原文摘要 · Abstract (English)
Machine learning simulations of open quantum dynamics often rely on recursive predictors that accumulate error. We develop a non-recursive convolutional neural networks (CNNs) that maps system parameters and a redundant time encoding directly to excitation-energy-transfer populations in the Fenna-Matthews-Olson complex. The encoding-modified logistic plus $\tanh$ functions-normalizes time and resolves fast, transitional, and quasi-steady regimes, while physics-informed labels enforce population conservation and inter-site consistency. Trained only on $0\sim 7 ps$ reference trajectories generated with a Lindblad model in QuTiP, the network accurately predicts $0\sim100 ps$ dynamics across a range of reorganization energies, bath rates, and temperatures. Beyond $20 ps$, the absolute relative error remains below 0.05, demonstrating stable long-time extrapolation. By avoiding step-by-step recursion, the method suppresses error accumulation and generalizes across timescales. These results show that redundant time encoding enables data-efficient inference of long-time quantum dissipative dynamics in realistic pigment-protein complexes, and may aid the data-driven design of light-harvesting materials.
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