Multi-timescale time encoding for CNN prediction of Fenna-Matthews-Olson energy-transfer dynamics

TL;DR

The paper tackles the challenge of predicting long-time open quantum dynamics for the FMO complex without recursive error accumulation. It introduces a non-recursive CNN fed by a redundant, multi-timescale time encoding and physics-informed labels, trained on short 0–7 ps Lindblad trajectories to forecast 0–100 ps EET dynamics. Key innovations include a time-encoding scheme that stabilizes temporal inputs across regimes and labels enforcing population conservation and inter-site consistency, enabling stable extrapolation with ARE < 0.05 beyond 20 ps. The approach yields data-efficient, accurate long-time predictions and holds promise for aiding design of light-harvesting materials and extending to other pigment–protein systems.

Abstract

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.

Figures (5)

• Figure 1: Redundant time-functions $f_{k}(t_{n})$ for $k=0,\dots,99$. (a) Encoding of Ref. Ullah20 (inset: $k \in [0,5]$), which achieves normalization only after $k\geq 3$. (b) Present encoding, exhibiting stable normalization and improved discrimination across short-, intermediate-, and long-time regimes.
• Figure 2: (a) Seven bacteriochlorophyll (BChl) pigments in an FMO monomer. (b) Dominant excitation energy transfer (EET) pathway: baseplate $\rightarrow$ BChl 1 $\rightarrow$ 2 $\rightarrow$ 3 $\rightarrow$ 4, with the initial excitation at BChl 1.
• Figure 3: Population dynamics of the seven chlorophyll sites with green solid lines being theoretical values and black dashed lines being predicted values in the FMO complex within 7 $ps$. Other parameters are $\lambda$=15 $\mathrm{cm^{-1}}$, $\gamma$=275 $\mathrm{cm^{-1}}$, $T$=155 $\mathrm{K}$.
• Figure 4: Extended population dynamics over 0$\sim$100 $ps$. Green solid lines: theoretical values; black dotted lines: CNN predictions. Insets use logarithmic scales. Parameters: $\lambda=30~\mathrm{cm^{-1}}, \gamma=286~\mathrm{cm^{-1}}, T=166~\mathrm{K}$.
• Figure 5: Absolute relative error (ARE) and loss function (inset) for seven-site populations over 7$\sim$100 $ps$ (logarithmic scale). Parameters identical to Fig. \ref{['Fig4']}.