Rapid and precise forecasting of dynamical systems is critical to ensuring safe aerospace missions. Previous forecasting research has primarily concentrated on global trend analysis using full-scale inputs. However, time series arising from real-world applications such as aerospace propulsion, exhibit a distinct dynamical periodicity over a limited timeframe. Here we develop a deep learning model, TimeWaves, to capture both global trends and local variations, through 3D spectrum-oriented interval extraction from an integrated viewpoint of biological perceptions. Specifically, a shared parameter fusion algorithm is employed to effectively integrate Fourier and Wavelet analyses, providing full and sliced 1D sequences to form 2D tensors that can be seamlessly processed by parameter-efficient inception blocks. Additionally, a dual-way learning workflow using TwinBlock, inspired by the cooperative behavior of visual cells, is implemented to enhance perception of dynamical multi-scale features at a reduced computational cost. TimeWaves demonstrates reliable and robust performance in predicting rocket combustion instability, a key challenge in the aerospace industry.
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