Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows

• URL: http://arxiv.org/abs/2602.15472v1
• Date: Tue, 17 Feb 2026 10:20:46 GMT
• Title: Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows
• Authors: Ramansh Sharma, Matthew Lowery, Houman Owhadi, Varun Shankar,
• Abstract summary: We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier-Stokes equations.
• Score: 3.8498574327875947
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier-Stokes equations. Traditional numerical solvers incur significant computational costs to respect incompressibility. Operator learning offers efficient surrogate models, but current neural operators fail to exactly enforce physical properties such as incompressibility, periodicity, and turbulence. Our method maps input functions to expansion coefficients of output functions in a property-preserving kernel basis, ensuring that predicted velocity fields analytically and simultaneously preserve the aforementioned physical properties. We evaluate the method on challenging 2D and 3D, laminar and turbulent, incompressible flow problems. Our method achieves up to six orders of magnitude lower relative $\ell_2$ errors upon generalization and trains up to five orders of magnitude faster compared to neural operators. Moreover, while our method enforces incompressibility analytically, neural operators exhibit very large deviations. Our results show that our method provides an accurate and efficient surrogate for incompressible flows.

Related papers

• Efficient temporal prediction of compressible flows in irregular domains using Fourier neural operators [0.3819617852128932]
  This paper investigates the temporal evolution of high-speed compressible fluids in irregular flow fields using the Fourier Operator (FNO)<n>We reconstruct the irregular flow field point set into sequential format compatible with FNO input requirements, and then embed temporal bundling technique within a recurrent neural network (RNN) for multi-step prediction.
  arXiv  Detail & Related papers  (2026-01-05T09:12:35Z)
• Flow matching Operators for Residual-Augmented Probabilistic Learning of Partial Differential Equations [0.5729426778193397]
  We formulate flow matching in an infinite-dimensional function space to learn a probabilistic transport.<n>We develop a conditional neural operator architecture based on feature-wise linear modulation for flow matching vector fields.<n>We show that the proposed method can accurately learn solution operators across different resolutions and fidelities.
  arXiv  Detail & Related papers  (2025-12-14T16:06:10Z)
• Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching [60.37045080890305]
  We provide the first analysis of the sample complexity for flow-matching based generative models.<n>We decompose the velocity field estimation error into neural-network approximation error, statistical error due to the finite sample size, and optimization error due to the finite number of optimization steps for estimating the velocity field.
  arXiv  Detail & Related papers  (2025-12-01T05:14:25Z)
• NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers [1.8117099374299037]
  Partial differential equations (PDEs) underpin quantitative descriptions across the physical sciences and engineering.<n>Data-driven surrogates can be strikingly fast but are often unreliable when applied outside their training distribution.<n>Here we introduce Neural Operator Warm Starts (NOWS), a hybrid strategy that harnesses learned solution operators to accelerate classical iterative solvers.
  arXiv  Detail & Related papers  (2025-11-04T11:12:27Z)
• A reduced-order derivative-informed neural operator for subsurface fluid-flow [0.21585047554218337]
  We propose a reduced-order, derivative-informed training framework for neural operators.<n>DeFINO captures sensitivity information directly informed by observational data.<n>We demonstrate improvements in gradient accuracy while maintaining robust forward predictions of underlying fluid dynamics.
  arXiv  Detail & Related papers  (2025-09-17T01:30:44Z)
• Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systems [51.54065545849027]
  The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems.<n>VAMPnet and DPNet have been proposed to learn the leading singular subspaces of the Koopman operator.<n>We propose a scalable and conceptually simple method for learning the top-$k$ singular functions of the Koopman operator.
  arXiv  Detail & Related papers  (2025-07-09T18:55:48Z)
• Neural Operators with Localized Integral and Differential Kernels [77.76991758980003]
  We present a principled approach to operator learning that can capture local features under two frameworks. We prove that we obtain differential operators under an appropriate scaling of the kernel values of CNNs. To obtain local integral operators, we utilize suitable basis representations for the kernels based on discrete-continuous convolutions.
  arXiv  Detail & Related papers  (2024-02-26T18:59:31Z)
• Guaranteed Approximation Bounds for Mixed-Precision Neural Operators [83.64404557466528]
  We build on intuition that neural operator learning inherently induces an approximation error. We show that our approach reduces GPU memory usage by up to 50% and improves throughput by 58% with little or no reduction in accuracy.
  arXiv  Detail & Related papers  (2023-07-27T17:42:06Z)
• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers.<n>We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles.<n>Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• Forecasting subcritical cylinder wakes with Fourier Neural Operators [58.68996255635669]
  We apply a state-of-the-art operator learning technique to forecast the temporal evolution of experimentally measured velocity fields. We find that FNOs are capable of accurately predicting the evolution of experimental velocity fields throughout the range of Reynolds numbers tested.
  arXiv  Detail & Related papers  (2023-01-19T20:04:36Z)
• Neural Operator: Learning Maps Between Function Spaces [75.93843876663128]
  We propose a generalization of neural networks to learn operators, termed neural operators, that map between infinite dimensional function spaces. We prove a universal approximation theorem for our proposed neural operator, showing that it can approximate any given nonlinear continuous operator. An important application for neural operators is learning surrogate maps for the solution operators of partial differential equations.
  arXiv  Detail & Related papers  (2021-08-19T03:56:49Z)
• Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows [5.756349331930218]
  We suggest a new approach to learning structured low-order models for incompressible flow from data. We show that learning dynamics of the velocity and pressure can be decoupled, thus leading to an efficient operator inference approach.
  arXiv  Detail & Related papers  (2020-10-13T21:26:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.