UniFluids: Unified Neural Operator Learning with Conditional Flow-matching
arXiv:2603.22309v1 Announce Type: new 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 $x$-predi
arXiv:2603.22309v1 Announce Type: new 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 conduct a large-scale evaluation of UniFluids on several PDE datasets covering spatial dimensions 1D, 2D and 3D. Experimental results show that UniFluids achieves strong prediction accuracy and demonstrates good scalability and cross-scenario generalization capability. The code will be released later.
Executive Summary
This article presents UniFluids, a novel conditional flow-matching framework for unified learning of solution operators across various partial differential equations (PDEs). Building upon the scalability of diffusion transformers, UniFluids achieves parallel sequence generation, making it the first unified operator learning approach. The framework introduces a unified four-dimensional spatiotemporal representation for heterogeneous PDE datasets, enabling joint training and conditional encoding. Experimental results demonstrate strong prediction accuracy, good scalability, and cross-scenario generalization capability on diverse PDE datasets. The authors' introduction of x-prediction in flow-matching operator learning significantly improves prediction accuracy. The UniFluids framework offers significant potential for PDE simulation in scientific research, but its applicability and limitations require further investigation.
Key Points
- ▸ UniFluids is a conditional flow-matching framework for unified learning of solution operators across PDEs.
- ▸ UniFluids achieves parallel sequence generation, making it the first unified operator learning approach.
- ▸ The framework introduces a unified four-dimensional spatiotemporal representation for heterogeneous PDE datasets.
Merits
Strength in Scalability
UniFluids leverages the scalability of diffusion transformers to achieve parallel sequence generation, making it suitable for large-scale PDE simulations.
Demerits
Limited Generalizability
The effectiveness of UniFluids may be limited to specific PDE domains or datasets, requiring further investigation of its generalizability across diverse scenarios.
Expert Commentary
While UniFluids presents a promising approach for unified operator learning, its applicability and limitations require further investigation. The framework's scalability and generalizability across diverse PDE scenarios and datasets are crucial for its widespread adoption. The authors' use of x-prediction in flow-matching operator learning is a significant contribution, but its impact on prediction accuracy needs to be evaluated in more detail. As UniFluids has significant potential for PDE simulation, it is essential to explore its extension to other scientific domains and its integration with existing PDE foundation models.
Recommendations
- ✓ Further investigation is necessary to evaluate the generalizability of UniFluids across diverse PDE scenarios and datasets.
- ✓ The authors should explore the extension of UniFluids to other scientific domains and its integration with existing PDE foundation models.
Sources
Original: arXiv - cs.LG
