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

2025-10-27

AI Summary

Real-time ensemble simulation of high-dimensional Navier–Stokes equations suffers from prohibitive computational cost, while existing neural operators rely heavily on large paired datasets and exhibit weak generalization to 3D domains. Method: We propose a data-free, physics-driven neural operator that directly encodes initial/boundary conditions and forcing functions as inputs. Leveraging a physics-embedded architecture, automatic differentiation, and a residual PDE loss, it enables end-to-end differentiable solving without ground-truth labels or training data. Contribution/Results: To our knowledge, this is the first unsupervised method achieving high-fidelity, robust 3D Navier–Stokes inference. Experiments demonstrate superior accuracy over state-of-the-art neural operators on both 2D and 3D benchmarks, significantly higher ensemble simulation efficiency than traditional numerical solvers, and strong guarantees of physical consistency, massive parallelizability, and cross-dimensional generalization.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Eliminates need for paired data in neural operator training
• Enables real-time ensemble forecasting for Navier-Stokes equations
• Achieves accurate 3D flow solutions without training data

Innovation

• Data-free neural operator eliminates paired solution data
• Physics-grounded architecture handles initial boundary conditions
• Achieves accurate 3D Navier-Stokes solutions without training data