mlsanityData to 14 Oct 2026

Universal Functional Regression with Neural Operator Flows

arXiv 2404.02986 ↗First posted 3 Apr 2024cs.LG stat.MLcited by 9

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Abstract (arXiv)

Regression on function spaces is typically limited to models with Gaussian process priors. We introduce the notion of universal functional regression, in which we aim to learn a prior distribution over non-Gaussian function spaces that remains mathematically tractable for functional regression. To do this, we develop Neural Operator Flows (OpFlow), an infinite-dimensional extension of normalizing flows. OpFlow is an invertible operator that maps the (potentially unknown) data function space into a Gaussian process, allowing for exact likelihood estimation of functional point evaluations. OpFlow enables robust and accurate uncertainty quantification via drawing posterior samples of the Gaussian process and subsequently mapping them into the data function space. We empirically study the performance of OpFlow on regression and generation tasks with data generated from Gaussian processes with known posterior forms and non-Gaussian processes, as well as real-world earthquake seismograms with an unknown closed-form distribution.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 48 of its 79 references that are in the map. First posted on arXiv 3 Apr 2024.

Builds on

48 of 79 references.

References · 48

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36 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 5; 2026: 3.

9 papers.

  1. 2025Guided Diffusion Sampling on Function Spaces with Applications to PDEscited by 36
  2. 2025Stochastic Process Learning via Operator Flow Matchingcited by 14
  3. 2025Mesh-Informed Neural Operator : A Transformer Generative Approachcited by 11
  4. 2024FUSE: Fast Unified Simulation and Estimation for PDEscited by 8
  5. 2025Reframing Generative Models for Physical Systems using Stochastic Interpolantscited by 2
  6. 2025FuncGenFoil: Airfoil Generation and Editing Model in Function Spacecited by 0
  7. 2026Large-Scale 3D Ground-Motion Synthesis with Physics-Inspired Latent Operator Flow Matchingcited by 0
  8. 2026Flow Annealing Posterior Sampling for Function-Space Regression and Inverse Problemscited by 0
  9. 2026Orca: Neural Operators for Causal Reasoning in Continuous Timecited by 0