Physics-Informed Fine-Tuned Neural Operator for Flow Field Modeling

Modeling flow field evolution accurately is important for numerous natural and engineering applications, such as pollutant dispersion in the ocean and atmosphere, yet remains challenging because of the highly nonlinear, multi-physics, and high-dimensional features of flow systems. While traditional equation-based numerical methods suffer from high computational costs, data-driven neural networks struggle with insufficient data and lack physical explainability. The physics-informed neural operator (PINO) addresses this by combining physics and data losses but faces a fundamental gradient imbalance problem. This work proposes a physics-informed fine-tuned neural operator for high-dimensional flow field modeling that decouples the optimization of physics and data losses. Our method first trains the neural network using data loss and then fine-tunes it with physics loss before inference, enabling the model to adapt to evaluation data while respecting physical constraints. This strategy requires no additional training data and can be applied to fit out-of-distribution (OOD) inputs faced during inference. We validate our method using the shallow water equation and advection–diffusion equation using a convolutional neural operator (CNO) as the base architecture. Experimental results show a 26.4% improvement in single-step prediction accuracy and a reduction in error accumulation for multi-step predictions.