Machine Learning-Based Diffusion Processes for the Estimation of Stand Volume Yield and Growth Dynamics in Mixed-Age and Mixed-Species Forest Ecosystems

This investigation examines diffusion processes for predicting whole-stand volume, incorporating the variability and uncertainty inherent in regional, operational, and environmental factors. The distribution and spatial organization of trees within a specified forest region, alongside dynamic fluctuations and intricate uncertainties, are modeled by a set of nonsymmetric stochastic differential equations of a sigmoidal nature. The study introduces a three-dimensional system of stochastic differential equations (SDEs) with mixed-effect parameters, designed to quantify the dynamics of the three-dimensional distribution of tree-size components—namely diameter (diameter at breast height), potentially occupied area, and height—with respect to the age of a tree. This research significantly contributes by translating the analysis of tree size variables, specifically height, occupied area, and diameter, into stochastic processes. This transformation facilitates the representation of stand volume changes over time. Crucially, the estimation of model parameters is based exclusively on measurements of tree diameter, occupied area, and height, avoiding the need for direct tree volume assessments. The newly developed model has proven capable of accurately predicting, tracking, and elucidating the dynamics of stand volume yield and growth as trees mature. An empirical dataset composed of mixed-species, uneven-aged permanent experimental plots in Lithuania serves to substantiate the theoretical findings. According to the dataset under examination, the model-based estimates of stand volume per hectare in this region exhibited satisfactory goodness-of-fit statistics. Specifically, the root mean square error (and corresponding relative root mean square error) for the living trees of mixed, pine, spruce, and birch tree species were 68.814 m3 (20.4%), 20.778 m3 (7.8%), 32.776 m3 (37.3%), and 4.825 m3 (26.3%), respectively. The model is executed within Maple, a symbolic algebra system.