A data free neural operator enabling fast inference of 2D and 3D Navier Stokes equations

Abstract: Ensemble simulations of high-dimensional flow models (e.g., Navier Stokes type PDEs) are computationally prohibitive for real time applications. Neural operators enable fast inference but are limited by costly data requirements and poor generalization to 3D flows. We present a data-free operator network for the Navier Stokes equations that eliminates the need for paired solution data and enables robust, real time inference for large ensemble forecasting. The physics-grounded architecture takes initial and boundary conditions as well as forcing functions, yielding solutions robust to high variability and perturbations. Across 2D benchmarks and 3D test cases, the method surpasses prior neural operators in accuracy and, for ensembles, achieves greater efficiency than conventional numerical solvers. Notably, it delivers accurate solutions of the three dimensional Navier Stokes equations, a regime not previously demonstrated for data free neural operators. By uniting a numerically grounded architecture with the scalability of machine learning, this approach establishes a practical pathway toward data free, high fidelity PDE surrogates for end to end scientific simulation and prediction.