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Background and Objectives. Modern ecological forecasting tasks require models that combine accuracy, robustness to incomplete data, and compliance with fundamental physical laws. While statistical methods, particularly neural networks, offer flexibility, they often neglect physical plausibility. Conversely, physics-based models ensure interpretability and adherence to conservation laws but are computationally demanding and sensitive to uncertain inputs. The objective of this study is to develop a hybrid neural network architecture that incorporates physical constraints for eco-statistical prediction tasks. Materials and methods. The proposed model embeds a physical constraint based on the advection–diffusion equation into the training process of a neural network. It minimizes both prediction error and the violation of physical laws by optimizing a combined loss function that includes a physics-based regularization term. The model is trained on heterogeneous data sources, including climate variables, emission monitoring, and satellite imagery. Performance was evaluated on real-world tasks of air pollution forecasting and biodiversity classification. Results. The hybrid model reduced mean squared error (MSE) by 18% compared to an LSTM network and by 9% relative to the CALPUFF physical model. In biodiversity classification, the model improved accuracy by 14%. It also maintained physical consistency and stable performance in the presence of up to 30% missing input data, demonstrating enhanced interpretability and resilience. Conclusions. The developed approach effectively integrates the strengths of physics-based and data-driven models. It is particularly suitable for applied ecological modeling tasks that require reliable, interpretable forecasts, including air quality monitoring, climate impact modeling, and sustainable resource management.
Keywords:physics-informed learning, hybrid models, ecological forecasting, neural networks, sustainable development.
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