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

2026-03-11

AI Summary

This work addresses the challenge faced by existing physics-informed neural networks (PINNs) in solving multi-flow Navier–Stokes equations, where balancing shared physical laws with flow-specific characteristics is difficult, often leading to training instability due to negative transfer across tasks and disparities in loss magnitudes. To overcome this, the authors propose UniPINN, a unified framework that decouples universal physical features from flow-specific ones through a shared–specific network architecture. UniPINN integrates a cross-flow attention mechanism and a dynamic loss weighting strategy to mitigate negative transfer and enhance training stability. Experimental results demonstrate that UniPINN significantly improves prediction accuracy across three representative flow fields and achieves balanced performance among heterogeneous flows.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Multiagent Systems: Adversarial Agents
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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

Problem

• multi-task learning
• Navier-Stokes equations
• negative transfer
• training instability
• heterogeneous flow regimes

Innovation

• Physics-Informed Neural Networks
• Multi-task Learning
• Navier-Stokes Equations
• Negative Transfer Mitigation
• Dynamic Loss Weighting