Neural operator splitting cuts fluid simulation errors in complex shapes
Neural Operator Splitting for Fluid Dynamics in Complex Geometry
Machine Learning
Summary
Simulating fluid flows like air or water inside complicated shapes can be very hard and slow. The authors designed a new AI method that breaks down each simulation step into smaller parts that match how traditional methods work. Their AI learns these parts separately and uses special math to handle different shapes better. This approach reduces errors a lot compared to a usual single-step AI model and runs much faster than traditional simulation tools.
What this means in practice
- •For computational engineers: Speed up accurate fluid flow simulations in complex geometries for design and analysis tasks.
- •For computer graphics developers: Create faster fluid animations with less error for realistic visual effects in varying 3D environments.
Authors
Jianxiang Li, Xi Deng, Hong Chul Nam, Anima Anandkumar
Abstract
Solving dynamical systems in complex and diverse geometries remains challenging for both numerical solvers and learning-based surrogate models. We propose Neural Operator Splitting, a framework for learning fluid dynamics while preserving the physical structure of fractional-step numerical schemes. Instead of learning the full-step evolution monolithically, we decompose each time step into physically interpretable steps, and learn each operator separately using intermediate states from the underlying numerical solver. Guided by the linearity properties of the fractional steps, we introduce a conditional-linear Fourier neural operator (CL-FNO) whose linear state mappings are modulated by nonlinear conditioning on inputs such as boundary geometry. We further introduce two complementary strategies, symmetry sampling and corrective cycling, to mitigate error accumulation during autoregressive rollout. Experiments on 2D and 3D fluid flows with varying geometries and initial conditions show that our full model reduces mean relative $L^2$ rollout error by 68\% in 2D and 40\% in 3D compared with a single full-step neural operator. At comparable error levels, neural-operator inference is approximately $10^3$ times faster per step than the Monte Carlo solver.