Neural Operator Splitting for Fluid Dynamics in Complex Geometry

Key points

• Solving dynamical systems in complex and diverse geometries remains challenging for both numerical solvers and learning-based surrogate models.1
• 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.1
• 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.1
• 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.1

Sources (1)

• [1]Neural Operator Splitting for Fluid Dynamics in Complex Geometry
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 05:37 AM

  We propose Neural Operator Splitting, a framework for learning fluid dynamics while preserving the physical structure of fractional-step numerical schemes.

  Solving dynamical systems in complex and diverse geometries remains challenging for both numerical solvers and learning-based surrogate models.

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