Semisupervised Deep State-Space Model for Plant Growth Modeling

The optimal control of sugar content and its associated technology is important for producing high-quality crops more stably and efficiently. Model-based reinforcement learning (RL) indicates a desirable action depending on the type of situation based on trial-and-error calculations conducted by an environmental model. In this paper, we address plant growth modeling as an environmental model for the optimal control of sugar content. In the growth process, fruiting plants generate sugar depending on their state and evolve via various external stimuli; however, sugar content data are sparse because appropriate remote sensing technology is yet to be developed, and thus, sugar content is measured manually. We propose a semisupervised deep state-space model (SDSSM) where semisupervised learning is introduced into a sequential deep generative model. SDSSM achieves a high generalization performance by optimizing the parameters while inferring unobserved data and using training data efficiently, even if some categories of training data are sparse. We designed an appropriate model combined with model-based RL for the optimal control of sugar content using SDSSM for plant growth modeling. We evaluated the performance of SDSSM using tomato greenhouse cultivation data and applied cross-validation to the comparative evaluation method. The SDSSM was trained using approximately 500 sugar content data of appropriately inferred plant states and reduced the mean absolute error by approximately 38% compared with other supervised learning algorithms. The results demonstrate that SDSSM has good potential to estimate time-series sugar content variation and validate uncertainty for the optimal control of high-quality fruit cultivation using model-based RL.