Data–physics fusion for complex fluid systems based on Physics‐Constrained Dynamic Mode Decomposition

Abstract The standard Dynamic Mode Decomposition (DMD), when used in complex fluid flow modeling, often suffers from situations like noisy data and translational motion, leading to high errors and non‐physical results. Meanwhile, purely physics‐based numerical methods offer high accuracy but are computationally intensive. To bridge this gap, this paper proposes a Physics‐Constrained Dynamic Mode Decomposition (PCDMD) framework, which integrates governing physical laws into the DMD to constrain predicted results by using Kalman correction. This hybrid approach retains the speed of DMD while improving accuracy by ensuring that predictions obey the underlying physics. We systematically evaluated the PCDMD on flow problems with increasing complexity, including lid‐driven cavity flow, flow around a cylinder with concentration transport, and a rising bubble system. In each case, PCDMD significantly improves both the predictive accuracy and physical consistency. By balancing between the data‐driven modeling and physical correction, the PCDMD remains robust under imperfect data and physical equations.