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

TL;DR

UniPINN introduces a unified neural network framework for multi-task learning of diverse Navier-Stokes equations, effectively capturing shared physics, reducing negative transfer, and stabilizing training across different flow regimes.

Contribution

The paper presents a novel multi-flow PINN architecture with shared-specialized design, cross-flow attention, and dynamic loss balancing, addressing key challenges in multi-task fluid dynamics modeling.

Findings

Achieves superior accuracy across multiple flow types

Reduces negative transfer between tasks

Stabilizes training dynamics in heterogeneous regimes

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