[2603.22309] UniFluids: Unified Neural Operator Learning with Conditional Flow-matching

Computer Science > Machine Learning arXiv:2603.22309 (cs) [Submitted on 19 Mar 2026] Title:UniFluids: Unified Neural Operator Learning with Conditional Flow-matching Authors:Haosen Li, Qi Meng, Jiahao Li, Rui Zhang, Ruihua Song, Liang Ma, Zhi-Ming Ma View a PDF of the paper titled UniFluids: Unified Neural Operator Learning with Conditional Flow-matching, by Haosen Li and 6 other authors View PDF HTML (experimental) Abstract:Partial differential equation (PDE) simulation holds extensive significance in scientific research. Currently, the integration of deep neural networks to learn solution operators of PDEs has introduced great potential. In this paper, we present UniFluids, a conditional flow-matching framework that harnesses the scalability of diffusion Transformer to unify learning of solution operators across diverse PDEs with varying dimensionality and physical variables. Unlike the autoregressive PDE foundation models, UniFluids adopts flow-matching to achieve parallel sequence generation, making it the first such approach for unified operator learning. Specifically, the introduction of a unified four-dimensional spatiotemporal representation for the heterogeneous PDE datasets enables joint training and conditional encoding. Furthermore, we find the effective dimension of the PDE dataset is much lower than its patch dimension. We thus employ $x$-prediction in the flow-matching operator learning, which is verified to significantly improve prediction accuracy. We cond...