PhyTM: A Physics-Informed Tri-Modal Transformer-Mamba Framework for Time Series Forecasting

With the growing volume of time series data across real-world applications, accurate forecasting has become essential for understanding temporal dynamics and predicting future trends. However, existing approaches often overlook the physical processes underlying observed time series, resulting in limited incorporation of physical dynamics under noisy observations, weak temporal-physical awareness in attention-based components, and insufficient dynamical constraints in State-Space Models (SSMs) that may lead to spectral drift and structural distortion over long forecasting horizons. To address these challenges, PhyTM is proposed as a physics-informed tri-modal forecasting framework that incorporates physical priors into multimodal temporal modeling and improves long-term forecasting stability. First, a Dynamic Mode Decomposition (DMD)-based representation module is introduced to embed time series into a delayed state space and extract spectrally consistent dynamical modes for temporal evolution modeling. Second, a physics-informed dual-stream attention Transformer is designed for textual temporal representations by integrating semantic attention with DMD-derived physical priors to enhance temporal-physical awareness beyond conventional positional encoding. Third, a physics-structured SSM is developed for visual temporal representations to enforce physically consistent state transitions and patch-level evolution while maintaining linear-time efficiency. Finally, extensive experiments on long-term and short-term forecasting benchmarks verify the effectiveness of PhyTM, which achieves a 23.4% Mean Squared Error (MSE) reduction on Exchange at $H=720$ and a 12.7% Overall Weighted Average (OWA) reduction on M4-Others. Code and data are available at https://anonymous.4open.science/r/PhyTM-2026-E33D.