Melanie Schaller

Melanie Schaller, Nick Janssen, Bodo Rosenhahn

This paper presents Naga, a deep State Space Model (SSM) encoding approach inspired by structural concepts from Vedic mathematics. The proposed method introduces a bidirectional representation for time series by jointly processing forward and time-reversed input sequences. These representations are then combined through an element-wise (Hadamard) interaction, resulting in a Vedic-inspired encoding that enhances the model's ability to capture temporal dependencies across distant time steps. We evaluate Naga on multiple long-term time series forecasting (LTSF) benchmarks, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, Traffic, and ILI. The experimental results show that Naga outperforms 28 current state of the art models and demonstrates improved efficiency compared to existing deep SSM-based approaches. The findings suggest that incorporating structured, Vedic-inspired decomposition can provide an interpretable and computationally efficient alternative for long-range sequence modeling.

Melanie Schaller, Daniel Schlör, Andreas Hotho

External influences such as traffic and environmental factors induce vibrations in structures, leading to material degradation over time. These vibrations result in cracks due to the material's lack of plasticity compromising structural integrity. Detecting such damage requires the installation of vibration sensors to capture the internal dynamics. However, distinguishing relevant eigenmodes from external noise necessitates the use of Deep Learning models. The detection of changes in eigenmodes can be used to anticipate these shifts in material properties and to discern between normal and anomalous structural behavior. Eigenmodes, representing characteristic vibration patterns, provide insights into structural dynamics and deviations from expected states. Thus, we propose ModeConv to automatically capture and analyze changes in eigenmodes, facilitating effective anomaly detection in structures and material properties. In the conducted experiments, ModeConv demonstrates computational efficiency improvements, resulting in reduced runtime for model calculations. The novel ModeConv neural network layer is tailored for temporal graph neural networks, in which every node represents one sensor. ModeConv employs a singular value decomposition based convolutional filter design for complex numbers and leverages modal transformation in lieu of Fourier or Laplace transformations in spectral graph convolutions. We include a mathematical complexity analysis illustrating the runtime reduction.