{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/k-2-vae-a-koopman-kalman-enhanced-variational","title":"$K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting","arxiv_id":"2505.23017","date":"2025-05-29","proceeding":null,"authors":["Xingjian Wu","Xiangfei Qiu","Hongfan Gao","Jilin Hu","Bin Yang","Chenjuan Guo"],"abstract":"Probabilistic Time Series Forecasting (PTSF) plays a crucial role in decision-making across various fields, including economics, energy, and transportation. Most existing methods excell at short-term forecasting, while overlooking the hurdles of Long-term Probabilistic Time Series Forecasting (LPTSF). As the forecast horizon extends, the inherent nonlinear dynamics have a significant adverse effect on prediction accuracy, and make generative models inefficient by increasing the cost of each iteration. To overcome these limitations, we introduce $K^2$VAE, an efficient VAE-based generative model that leverages a KoopmanNet to transform nonlinear time series into a linear dynamical system, and devises a KalmanNet to refine predictions and model uncertainty in such linear system, which reduces error accumulation in long-term forecasting. Extensive experiments demonstrate that $K^2$VAE outperforms state-of-the-art methods in both short- and long-term PTSF, providing a more efficient and accurate solution.","url_abs":"https://arxiv.org/abs/2505.23017v1","url_pdf":"https://arxiv.org/pdf/2505.23017v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"k-2-vae-a-koopman-kalman-enhanced-variational","repo_url":"https://github.com/decisionintelligence/k2vae","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"decision-making","task_name":"Decision Making"},{"task_slug":"probabilistic-time-series-forecasting","task_name":"Probabilistic Time Series Forecasting"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series-forecasting","task_name":"Time Series Forecasting"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2505.23017","atlas_url":"https://app.syntology.ai/?focus=2505.23017","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2505.23017"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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