A Novel Bayesian Probabilistic Approach for Debris Flow Accumulation Volume Prediction Using Bayesian Neural Networks with Synthetic and Real-World Data Integration

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Abstract
Debris flow events are complex natural phenomena that are challenging to predict, especially when data are limited or uncertain. This study presents a novel Bayesian probabilistic approach using Bayesian Neural Networks (BNNs) to predict possible volumes of debris flow accumulation by integrating both synthetic and real-world data. Synthetic datasets are created based on statistical distributions informed by geomorphological and hydrological knowledge, allowing the model to learn typical behaviors even with limited real data. BNNs provide uncertainty quantification by modeling neural weights as probability distributions. The models resulting from validation on synthetic data and two real datasets from China and South Korea show strong predictive performance (R² > 0.99) and close alignment between predicted and observed volumes, even in the presence of outliers. Our framework for generating synthetic data allows for the creation of context-specific datasets, calibrating the statistical parameters of debris flows for each territory. These specific datasets allow for the creation of specific predictive models; however, some models can be transferred between regions similar in geological, climatic and geomorphological characteristics, even with the absence or scarcity of data. The key strength of this integrated approach lies in its integration of synthetic data generation, real data augmentation based on Bootstrapping, expert knowledge and Bayesian deep learning to overcome limitations of traditional statistical models, improving debris flow forecasting and enabling more informed and resilient risk management strategies.
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