# UniPINN: A Unified PINN Framework for Multi-task Learning of Diverse Navier-Stokes Equations

arXiv: https://arxiv.org/abs/2603.10466 · HTML: https://mlsanity.com/paper/2603.10466/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 49 references that are in the map.
- First posted on arXiv 11 Mar 2026.

## Builds on (most cited first, 18 of 18)

- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Scalable Transformer for PDE Surrogate Modeling](https://mlsanity.com/paper/2305.17560/) (2023)
- [PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks](https://mlsanity.com/paper/2402.00326/) (2024)
- [Multi-Task Learning in Natural Language Processing: An Overview](https://mlsanity.com/paper/2109.09138/) (2021)
- [Sequential Deep Operator Networks (S-DeepONet) for Predicting Full-field Solutions Under Time-dependent Loads](https://mlsanity.com/paper/2306.08218/) (2023)
- [Enhanced Physics-Informed Neural Networks with Augmented Lagrangian Relaxation Method (AL-PINNs)](https://mlsanity.com/paper/2205.01059/) (2022)
- [PID: Physics-Informed Diffusion Model for Infrared Image Generation](https://mlsanity.com/paper/2407.09299/) (2024)
- [Physics-Informed Neural Networks for Time-Domain Simulations: Accuracy, Computational Cost, and Flexibility](https://mlsanity.com/paper/2303.08994/) (2023)
- [Learning Only On Boundaries: a Physics-Informed Neural operator for Solving Parametric Partial Differential Equations in Complex Geometries](https://mlsanity.com/paper/2308.12939/) (2023)
- [Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plants](https://mlsanity.com/paper/2405.06443/) (2024)
- [On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it](https://mlsanity.com/paper/2302.07557/) (2023)
- [Physically Consistent Multiple-Step Data-Driven Predictions Using Physics-based Filters](https://mlsanity.com/paper/2303.09437/) (2023)
- [A Knowledge-Inspired Hierarchical Physics-Informed Neural Network for Pipeline Hydraulic Transient Simulation](https://mlsanity.com/paper/2409.10911/) (2024)
- [AW-EL-PINNs: A Multi-Task Learning Physics-Informed Neural Network for Euler-Lagrange Systems in Optimal Control Problems](https://mlsanity.com/paper/2509.25262/) (2025)

## Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) have shown promise in solving incompressible Navier-Stokes equations, yet existing approaches are predominantly designed for single-flow settings. When extended to multi-flow scenarios, these methods face three key challenges: (1) difficulty in simultaneously capturing both shared physical principles and flow-specific characteristics, (2) susceptibility to inter-task negative transfer that degrades prediction accuracy, and (3) unstable training dynamics caused by disparate loss magnitudes across heterogeneous flow regimes. To address these limitations, we propose UniPINN, a unified multi-flow PINN framework that integrates three complementary components: a shared-specialized architecture that disentangles universal physical laws from flow-specific features, a cross-flow attention mechanism that selectively reinforces relevant patterns while suppressing task-irrelevant interference, and a dynamic weight allocation strategy that adaptively balances loss contributions to stabilize multi-objective optimization. Extensive experiments on three canonical flows demonstrate that UniPINN effectively unifies multi-flow learning, achieving superior prediction accuracy and balanced performance across heterogeneous regimes while successfully mitigating negative transfer. The source code of this paper will be released on https://github.com/Event-AHU/OpenFusion