KaleidoFlow: an autonomous data engine for learning flows on diverse geometries

Neural operators are emerging as surrogates that predict a flow much faster than a numerical solver. However, a neural operator generalizes only within the geometry families it was trained on. This limitation comes from the data. Every existing flow dataset depends heavily on human experts to design every geometry and to verify its mesh, so it is expensive to scale. Thus, each dataset can cover only a single geometry or similar geometries from the same family. We present KaleidoFlow, an autonomous data engine that scales a flow dataset to diverse geometries in three stages, all without human intervention. First, a language model agent continuously proposes new geometry families, together with the geometric parameters and the Reynolds numbers that vary them. Second, the agent designs the mesh of every family and repairs it iteratively until a convergence test verifies its discretization error. Third, OpenFOAM solves every combination of the geometric parameters and the Reynolds number, and each solution is one trajectory. The engine has produced 3,948 distinct geometries from 459 families, with 16,512 trajectories. Our results show that (1) the engine proposes diverse geometries automatically, covering 10 application categories from cyclones to biomedical vessels, and (2) it successfully repairs the mesh strategies that fail, which most of the families require. With this dataset, we build the first benchmark that measures how far a neural operator generalizes across geometry families. On the benchmark, we find that (1) current neural operators generalize poorly to a new geometry family, where the error of all nine architectures we evaluate increases by 3× to 6× from G2 to G3, and (2) the error on new families decreases with the number of training families approximately as a power law, for a convolutional, a transformer, and a spectral architecture. We will release the engine and the benchmark for future development of foundation neural operators that generalize across diverse geometries.