Multi-Task Learning of Conditional Mean Operators: applications to dynamical systems and uncertainty quantification

arXiv:2609.35429 · stat.ML, cs.LG · Submitted 2026-09-28 · Read on arXiv

stat.ML, cs.LG

Submitted: 2026-09-28

Updated: 2026-09-28

Code: https://github.com/gyselax/tokam2d

Terminology

• Uncertainty Quantification — 17× in this paper · explained in 8 episodes
• Conditional Mean Operator — 13× in this paper
• Representation Learning — 11× in this paper · explained in 2 episodes
• Regularization — 10× in this paper · explained in 3 episodes
• Transfer Learning — 10× in this paper · explained in 10 episodes
• Hilbert Space — 9× in this paper · explained in 2 episodes
• Reconstruction Error — 9× in this paper · explained in 2 episodes
• Adaptation — 8× in this paper · explained in 1 episode
• Embeddings — 6× in this paper · explained in 2 episodes
• Langevin Dynamics — 6× in this paper · explained in 2 episodes
• Neural Conditional Probability — 5× in this paper
• Benchmark — 4× in this paper · explained in 2 episodes
• Mixture Density Network — 4× in this paper
• Meta-learning — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Flow Matching — 2× in this paper · explained in 8 episodes
• Neural Spline Flow — 2× in this paper
• Activation Function — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Conditional Flow Matching — 1× in this paper
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Elias — 1× in this paper · explained in 2 episodes
• Exchangeability — 1× in this paper · explained in 2 episodes
• Few-Shot Learning — 1× in this paper · explained in 4 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Latent Representation — 1× in this paper · explained in 2 episodes
• Latent Space — 1× in this paper · explained in 7 episodes
• Reproducible Kernel Hilbert Space — 1× in this paper
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes
• Spectral Geometry — 1× in this paper · explained in 2 episodes
• Wasserstein Distance — 1× in this paper · explained in 4 episodes

Sources

• Verifiable Regularity Criterion for Conditional Expectation Operators and Conditional Mean Embeddings with Applications to Nonparametric Regression, Bayesian Inverse Problems, and Koopman Operators
• Meta-Learning for Koopman Spectral Analysis with Short Time-series
• Nonparametric approximation of conditional expectation operators

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