Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows
This addresses the computational bottleneck for incompressible flow simulations in engineering and physics, offering a more accurate and efficient surrogate model.
The paper tackled the problem of efficiently modeling incompressible flows with physical property preservation, achieving up to six orders of magnitude lower errors and five orders of magnitude faster training compared to neural operators.
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.