Abstract:

[Objective] The gas exchange method is the most widely applied and most direct quantitative measurement technique in plant photosynthesis research. Plant photosynthetic measurement systems based on the gas exchange method usually rely on the "steady-state paradigm" to determine the photosynthetic rate and other physiological parameters. During the measurement process, the system needs to wait until the CO₂ concentration reaches a steady state. However, this process is affected by factors such as plant physiology, leaf chamber volume, and sensor response characteristics, which severely restricts measurement efficiency. To this end, a new method is proposed that predicts the steady-state CO₂ concentration in advance based on the dynamic response sequence of the sensor and adaptively determines the measurement termination time using predictive uncertainty. [Methods] A dual-branch encoding network, DBE-TSNet (Dual-Branch Encoder for Time-Series Network), was constructed. The overall architecture of the network consisted of dual feature encoders and an aggregation encoder. The dual feature encoders adopted a structurally symmetric and parameter-independent branch design. They combined differential enhancement, cross-channel convolution–linear channel transformation, and global average pooling to model the dynamic response processes of the CO₂ concentration decrease and increase stages perceived by the system, respectively. After concatenating the features of the two branches, the aggregation encoder generated a four-dimensional output vector through a two-layer multilayer perceptron decoder: predicted decrease value (t̂₁), predicted decrease uncertainty (σ̂₁²), predicted increase value (t̂₂), and predicted increase uncertainty (σ̂₂²). During training, a Gaussian negative log-likelihood loss function was adopted to simultaneously learn the steady-state prediction together with its associated predictive uncertainty, while sample weights were adaptively adjusted accordingly. By setting uncertainty thresholds, adaptive truncation of the input sequence was realized, enabling determination of the prediction timing and the steady-state value, thereby improving measurement efficiency. A photosynthetic measurement system was built based on a single CO₂ sensor, using a time-shared differential measurement mode. Gas exchange data was collected from eight plant species (corn, potato, radish, bok choy, lettuce, loquat, orange tree, and paper mulberry) under three light intensity levels (low, medium, and high) for model training and validation. [Results and Discussion] By comparison with six typical time-series prediction models, including one-dimensional convolutional neural network (1D-CNN) and recurrent neural network (RNN), the DBE-TSNet model achieved the best performance in the steady-state prediction task: the MAE of the decreasing stage was 1.22 μmol/mol, and that of the increasing stage was 2.07 μmol/mol; the R² values reached 0.996 and 0.984, respectively. To evaluate the relationship between model predictive reliability and output uncertainty, all test samples were divided into ten intervals according to the uncertainty output by the model, and the relationships between each interval and MAE, RMSE, MAPE, and the input segment ratio were counted. The results showed that as uncertainty gradually increased, the prediction error gradually increased, resulting in a significant decline in model predictive reliability. Based on this analysis, the uncertainty thresholds of the decreasing stage and increasing stage were determined to be 0.026 7 and 0.014 6, respectively. Early prediction experiments based on the set thresholds showed that under the premise of maintaining the error below 1 μmol/mol, the model saved about 128.87 s of measurement time on average, shortened the measurement cycle by about 51%, and significantly improved measurement efficiency. [Conclusions] DBE-TSNet integrated dual-branch encoding and uncertainty estimation mechanisms to achieve accurate and early prediction of steady-state CO₂ concentration in plant photosynthetic measurement, effectively solving the problem of long steady-state measurement time in the gas exchange method and transforming the traditional "waiting for steady state" process into a data-driven decision-making process of "dynamic steady-state prediction". The model showed stable performance under multiple plant species and multiple light conditions, with good generalization ability, and could provide key technical support for improving the efficiency of plant photosynthetic measurement systems based on the gas exchange method.

Key words: CO₂ gas exchange, time-series prediction model, uncertainty estimation, steady-state prediction