Learning Latent Representations for Long-Term Chaotic Forecasting

Long-term autonomous forecasting of chaotic dynamical systems is challenging because small errors can progressively influence subsequent evolution under chaotic dynamics. Latent-space prediction has become an important paradigm for modeling complex dynamical systems. However, achieving long-term chaotic forecasting in latent space remains an open problem: models often struggle to preserve long-term attractor structure and dynamical characteristics during sustained autonomous rollout. Forecasting performance depends not only on the learned representation itself, but also on whether that representation can support sustained autonomous evolution under a downstream prediction model. We therefore propose Latent Chaotic Time Series Forecasting (LatentCTSF), a two-stage latent forecasting framework for chaotic systems. In the first stage, LatentCTSF constructs a Robust–Residual latent representation from multi-scale histories. Future prediction and autonomous rollout are used to improve its forecastability. We further introduce finite-horizon relative dynamics with gradient protection to capture the sensitivity of chaotic systems while limiting conflicts with the primary objectives. In the second stage, the encoder and decoder are frozen. We integrate various time-series forecasting backbones into a unified incremental forecasting framework within the latent space. For high-dimensional systems, cross-variable and spatial dependencies are further modeled explicitly. Experiments on representative chaotic systems show that LatentCTSF consistently improves short-term prediction accuracy, substantially extends the valid prediction time across different forecasting backbones, and better preserves long-term dynamical statistics.