Title: From Noise to Laws: Regularized Time-Series Forecasting via Denoised Dynamic Graphs
Primary area: learning on time series and dynamical systems
Keywords: Dynamic correlation-thresholded graphs, Physics-informed regularization, Reaction–diffusion stability, Score-based diffusion denoising, Time-series forecasting

Abstract: Long-horizon multivariate time-series forecasting is hard because realistic predictions must (i) denoise heterogeneous signals, (ii) track time-varying cross-series dependencies, and (iii) remain stable and physically plausible over long rollout horizons. We present PRISM, which couples a score-based diffusion preconditioner with a dynamic, correlation-thresholded graph encoder and a forecast head regularized by generic physics penalties. We prove contraction of the induced horizon dynamics under mild conditions and derive Lipschitz bounds for graph blocks, explaining the model’s robustness. On six standard benchmarks (Electricity, Traffic, Weather, ILI, Exchange Rate, ETT), PRISM achieves consistent SOTA with good MSE and MAE gains. Frequency-domain analysis shows fundamentals preserved and high-frequency noise attenuated, while ablations attribute improvements to (i) denoise-aware topology, (ii) adaptivity of the graph, (iii) reaction--diffusion stabilization, and (iv) tail control via kinematic constraints. Together, these results indicate that denoising, dynamic relational reasoning, and physics-aware regularization are complementary and necessary for reliable long-horizon forecasting.