mlsanityData to 7 Oct 2026

Operator inference with roll outs for learning reduced models from scarce and low-quality data

arXiv 2212.01418 ↗First posted 2 Dec 2022cs.LG cs.NA math.NAcited by 11

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Abstract (arXiv)

Data-driven modeling has become a key building block in computational science and engineering. However, data that are available in science and engineering are typically scarce, often polluted with noise and affected by measurement errors and other perturbations, which makes learning the dynamics of systems challenging. In this work, we propose to combine data-driven modeling via operator inference with the dynamic training via roll outs of neural ordinary differential equations. Operator inference with roll outs inherits interpretability, scalability, and structure preservation of traditional operator inference while leveraging the dynamic training via roll outs over multiple time steps to increase stability and robustness for learning from low-quality and noisy data. Numerical experiments with data describing shallow water waves and surface quasi-geostrophic dynamics demonstrate that operator inference with roll outs provides predictive models from training trajectories even if data are sampled sparsely in time and polluted with noise of up to 10%.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 28 of its 85 references that are in the map. First posted on arXiv 2 Dec 2022.

Builds on

28 of 85 references.

References · 28

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16 more
  1. 2021Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inferencecited by 23
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Cited by year

Citing papers per year: 2023: 4; 2024: 4; 2025: 3.

11 papers.

  1. 2023Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inferencecited by 10
  2. 2024Scientific Machine Learning Based Reduced-Order Models for Plasma Turbulence Simulationscited by 6
  3. 2023Gaussian process learning of nonlinear dynamicscited by 5
  4. 2025Nested Operator Inference for Adaptive Data-Driven Learning of Reduced-order Modelscited by 3
  5. 2025Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reductioncited by 2
  6. 2024Learning Noise-Robust Stable Koopman Operator for Control with Hankel DMDcited by 1
  7. 2024A parametric framework for kernel-based dynamic mode decomposition using deep learningcited by 1
  8. 2025Causal Multi-fidelity Surrogate Forward and Inverse Models for ICF Implosionscited by 1
  9. 2023Inference of Continuous Linear Systems from Data with Guaranteed Stabilitycited by 0
  10. 2023Small-data Reduced Order Modeling of Chaotic Dynamics through SyCo-AE: Synthetically Constrained Autoencoderscited by 0
  11. 2024Stability-Certified Learning of Control Systems with Quadratic Nonlinearitiescited by 0