mlsanityData to 7 Oct 2026

Non-intrusive reduced-order models for parametric partial differential equations via data-driven operator inference

arXiv 2110.07653 ↗First posted 14 Oct 2021cs.CE cs.NA math.NAcited by 23

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Abstract (arXiv)

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning and physics-based modeling. The parametric structure of the governing equations is embedded directly into the reduced-order model, and parameterized reduced-order operators are learned via a data-driven linear regression problem. The result is a reduced-order model that can be solved rapidly to map parameter values to approximate PDE solutions. Such parameterized reduced-order models may be used as physics-based surrogates for uncertainty quantification and inverse problems that require many forward solves of parametric PDEs. Numerical issues such as well-posedness and the need for appropriate regularization in the learning problem are considered, and an algorithm for hyperparameter selection is presented. The method is illustrated for a parametric heat equation and demonstrated for the FitzHugh-Nagumo neuron model.

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Oct 2021.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 2; 2024: 3; 2025: 8; 2026: 7.

23 papers.

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  1. 2022gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identificationcited by 30
  2. 2022Operator inference with roll outs for learning reduced models from scarce and low-quality datacited by 11
  3. 2023Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inferencecited by 10
  4. 2024Domain Decomposition-based coupling of Operator Inference reduced order models via the Schwarz alternating methodcited by 5
  5. 2022Certified data-driven physics-informed greedy auto-encoder simulatorcited by 4
  6. 2023Solving High-Dimensional Inverse Problems with Auxiliary Uncertainty via Operator Learning with Limited Datacited by 4
  7. 2026OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inferencecited by 4
  8. 2025Nested Operator Inference for Adaptive Data-Driven Learning of Reduced-order Modelscited by 3
  9. 2026Toward Adaptive Non-Intrusive Reduced-Order Models: Design and Challengescited by 3
  10. 2025Physically consistent predictive reduced-order modeling by enhancing Operator Inference with state constraintscited by 2
  11. 2025Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reductioncited by 2
  12. 2025Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decompositioncited by 2
11 more
  1. 2024Stabilizing and Solving Unique Continuation Problems by Parameterizing Data and Learning Finite Element Solution Operatorscited by 1
  2. 2025Reduced-Basis Deep Operator Learning for Parametric PDEs with Independently Varying Boundary and Source Datacited by 1
  3. 2026NN-OpInf: an operator inference approach using structure-preserving composable neural networkscited by 1
  4. 2026Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagatorscited by 1
  5. 2024Learning reduced-order Quadratic-Linear models in Process Engineering using Operator Inferencecited by 0
  6. 2025Subspace-Distance-Enabled Active Learning for Efficient Data-Driven Model Reduction of Parametric Dynamical Systemscited by 0
  7. 2025ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marchingcited by 0
  8. 2025Active learning for data-driven reduced models of parametric differential systems with Bayesian operator inferencecited by 0
  9. 2026Data-driven stochastic reduced-order modeling of parametrized dynamical systemscited by 0
  10. 2026WGFINNs: Weak formulation-based GENERIC formalism informed neural networkscited by 0
  11. 2026Conformal risk control for model-form uncertainty in parametric non-intrusive reduced-order modelscited by 0