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<p>Predictive modeling of complex systems frequently encounters inadequate processing capabilities for multi-scale heterogeneous data, as conventional methods grapple with the effective integration of such data. This study contributes to existing approaches by addressing multi-scale heterogeneous data fusion. We hereby propose a methodology that integrates reparameterized heterogeneous convolution and capsule networks. A dynamic parameterization mechanism adjusts the convolution kernel's weights and biases according to the input data's multi-scale and heterogeneous features. The capsule network's resilience to spatial transformations is enhanced through the application of a transformation matrix, thereby enabling each capsule's output to mirror alterations in features under various spatial transformations. The dynamic routing algorithm optimizes the information transmission path between capsule units, adapting to spatial transformation changes and enhancing the model's ability to handle complex data spatial relationships. The experimental results obtained demonstrate the model's effectiveness. In the context of traffic flow prediction, our method attains mean-square errors (MSE) of 45.6, 42.1, and 38.4 vehicles per hour for predictions spanning one hour, six hours, and 24&#xa0;h, respectively, thereby demonstrating superior performance in comparison to alternative methodologies. For the purpose of meteorological change prediction, the average Brier score remains around 0.08, indicating low error and high stability. In the context of economic trend prediction, the directional accuracy for GDP growth rate and unemployment rate is 94.17% and 95.35%, respectively, with inflection point detection deviations of only 0.9 and 1.2 quarters. The model demonstrates notable generalization and robustness in ecological environment change prediction. The findings underscore the model's notable strengths in managing multi-scale heterogeneous data and forecasting complex systems, thereby providing a novel approach for interdisciplinary complex system predictive modeling.</p>

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Application of capsule networks based on reparameterized heterogeneous convolution in multi-scale heterogeneous environment matrix in predictive modeling of interdisciplinary complex systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月4日

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  • Shuya Liu,
  • Xiaoli Zhang

摘要

Predictive modeling of complex systems frequently encounters inadequate processing capabilities for multi-scale heterogeneous data, as conventional methods grapple with the effective integration of such data. This study contributes to existing approaches by addressing multi-scale heterogeneous data fusion. We hereby propose a methodology that integrates reparameterized heterogeneous convolution and capsule networks. A dynamic parameterization mechanism adjusts the convolution kernel's weights and biases according to the input data's multi-scale and heterogeneous features. The capsule network's resilience to spatial transformations is enhanced through the application of a transformation matrix, thereby enabling each capsule's output to mirror alterations in features under various spatial transformations. The dynamic routing algorithm optimizes the information transmission path between capsule units, adapting to spatial transformation changes and enhancing the model's ability to handle complex data spatial relationships. The experimental results obtained demonstrate the model's effectiveness. In the context of traffic flow prediction, our method attains mean-square errors (MSE) of 45.6, 42.1, and 38.4 vehicles per hour for predictions spanning one hour, six hours, and 24 h, respectively, thereby demonstrating superior performance in comparison to alternative methodologies. For the purpose of meteorological change prediction, the average Brier score remains around 0.08, indicating low error and high stability. In the context of economic trend prediction, the directional accuracy for GDP growth rate and unemployment rate is 94.17% and 95.35%, respectively, with inflection point detection deviations of only 0.9 and 1.2 quarters. The model demonstrates notable generalization and robustness in ecological environment change prediction. The findings underscore the model's notable strengths in managing multi-scale heterogeneous data and forecasting complex systems, thereby providing a novel approach for interdisciplinary complex system predictive modeling.