An optimization-driven hierarchical deep learning approach using the Gray Langurs algorithm for data-driven seismic...

The statistical prediction of seismic activity patterns from historical earthquake catalog data remains a major challenge in data-centered seismic hazard analysis because seismic time series are non-stationary, multi-scale, and clustered in nature. Existing data-driven seismic prediction pipelines often emphasize architectural innovation while giving less attention to systematic hyperparameter optimization, which is essential for achieving strong predictive performance. This work is motivated by the need for an integrated and computationally efficient data-driven time-series modeling framework. Accordingly, a hierarchical deep learning-metaheuristic optimization paradigm is proposed based on the Neural Hierarchical Interpolation for Time Series Forecasting (N-HITS) algorithm and the Gray Langurs Optimizer (GLO). We conduct a systematic benchmarking of N-HITS against state-of-the-art deep time-series prediction models trained under identical preprocessing and training conditions, followed by adaptive hyperparameter optimization. Baseline analysis showed that N-HITS, with a coefficient of determination ([Formula: see text]) of 0.921 and a Mean Squared Error (MSE) of 0.00234, was the strongest standalone model. Following GLO-based hyperparameter optimization, performance improved to an [Formula: see text] of [Formula: see text] and an MSE of 7.980e-05 ± 7.980e-07, indicating substantial error reduction and higher convergence stability. These results highlight the importance of optimization intelligence in catalog-based statistical seismic activity prediction and position hierarchical deep learning with adaptive metaheuristic search as a scalable architecture for seismic trend monitoring. However, the proposed model relies only on historical seismic catalog patterns and does not incorporate tectonic processes or geophysical drivers; therefore, its outputs should be interpreted as statistical trend estimates rather than physically reliable earthquake predictions.