PINP: Physics-Informed Neural Predictor with latent estimation of fluid flows

TL;DR

PINP tackles long-horizon fluid-p dynamics forecasting by jointly estimating latent physical fields (e.g., velocity and pressure) and predicting observable quantities through a discretized NS-based framework. It integrates discretized PDEs into a neural predictor, using a 3D U-Net for complex mapping and a correction network to counteract discretization errors, while enforcing data, physical, and temporal constraints. The approach achieves state-of-the-art or competitive performance across simulated 2D/3D flows, smoke diffusion, and real-world nowcasting benchmarks, with the added benefit of interpretable latent fields as evidence of the underlying dynamics. This physics-informed, multi-quantity representation enhances temporal extrapolation and spatial generalization, offering a robust tool for forecasting complex fluid systems with noisy observations and limited access to full state information.

Abstract

Accurately predicting fluid dynamics and evolution has been a long-standing challenge in physical sciences. Conventional deep learning methods often rely on the nonlinear modeling capabilities of neural networks to establish mappings between past and future states, overlooking the fluid dynamics, or only modeling the velocity field, neglecting the coupling of multiple physical quantities. In this paper, we propose a new physics-informed learning approach that incorporates coupled physical quantities into the prediction process to assist with forecasting. Central to our method lies in the discretization of physical equations, which are directly integrated into the model architecture and loss function. This integration enables the model to provide robust, long-term future predictions. By incorporating physical equations, our model demonstrates temporal extrapolation and spatial generalization capabilities. Experimental results show that our approach achieves the state-of-the-art performance in spatiotemporal prediction across both numerical simulations and real-world extreme-precipitation nowcasting benchmarks.

Figures (28)

• Figure 1: Model has the following capabilities: (a) Temporal extrapolation, (b) Spatial generalization, (c) Latent physical quantities Estimation.
• Figure 2: Schematic architecture of the proposed Physics-Informed Neural Predictor (PINP).
• Figure 3: Overview of the data with spatial resolution.
• Figure 4: Comparison of MSE for different models on each prediction frame.
• Figure 5: (a) A comparison of the 40th frame prediction results between our method and U-NO, U-FNO. (b) The inferred and predicted velocity and pressure fields at the 40th frame.