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Time-series generation has crucial practical significance for decision-making under uncertainty. Existing methods have various limitations like accumulating errors over time, significantly impacting downstream tasks. We develop a novel generation method, DT-VAE, that incorporates generalizable domain knowledge, is mathematically justified, and significantly outperforms existing methods by mitigating error accumulation through a cumulative difference learning mechanism. We evaluate the performance of DT-VAE on several downstream tasks using both semi-synthetic and real time-series datasets, including benchmark datasets and our newly curated COVID-19 hospitalization datasets. The COVID-19 datasets enrich existing resources for time-series analysis. Additionally, we introduce Diverse Trend Preserving (DTP), a time-series clustering-based evaluation for direct and interpretable assessments of generated samples, serving as a valuable tool for evaluating time-series generative models. 

Abstract The high instantaneous luminosity of the CERN Large Hadron Collider leads to multiple proton–proton interactions in the same or nearby bunch crossings (pileup). Advanced pileup mitigation algorithms are designed to remove this noise from pileup particles and improve the performance of crucial physics observables. This study implements a semi-supervised graph neural network for particle-level pileup noise removal, by identifying individual particles produced from pileup. The graph neural network is firstly trained on charged particles with known labels, which can be obtained from detector measurements on data or simulation, and then inferred on neutral particles for which such labels are missing. This semi-supervised approach does not depend on the neutral particle pileup label information from simulation, and thus allows us to perform training directly on experimental data. The performance of this approach is found to be consistently better than widely-used domain algorithms and comparable to the fully-supervised training using simulation truth information. The study serves as the first attempt at applying semi-supervised learning techniques to pileup mitigation, and opens up a new direction of fully data-driven machine learning pileup mitigation studies.