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

• URL: http://arxiv.org/abs/2603.10466v1
• Date: Wed, 11 Mar 2026 06:37:55 GMT
• Title: UniPINN: A Unified PINN Framework for Multi-task Learning of Diverse Navier-Stokes Equations
• Abstract summary: Physics-Informed Neural Networks (PINNs) have shown promise in solving incompressible Navier-Stokes equations.<n>We propose UniPINN, a unified multi-flow PINN framework that integrates three complementary components.<n>We show that UniPINN effectively unifies multi-flow learning, achieving superior prediction accuracy and balanced performance across heterogeneous regimes.
• Score: 19.601674679509184
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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

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