LFR-PINO: A Layered Fourier Reduced Physics-Informed Neural Operator for Parametric PDEs

TL;DR

LFR-PINO introduces a layered hypernetwork and frequency-domain reduction to improve the efficiency and accuracy of physics-informed neural operators for solving parametric PDEs, enabling better generalization and computational savings.

Contribution

It proposes a novel layered hypernetwork architecture combined with frequency-domain reduction for efficient, accurate PDE solutions with improved generalization capabilities.

Findings

Achieves 22.8%-68.7% error reduction over baselines.

Reduces memory usage by 28.6%-69.3% compared to Hyper-PINNs.

Demonstrates effectiveness on four PDE problems.

Abstract

Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across parameter spaces. However, existing methods either suffer from limited expressiveness due to fixed basis/coefficient designs, or face computational challenges due to the high dimensionality of the parameter-to-weight mapping space. We present LFR-PINO, a novel physics-informed neural operator that introduces two key innovations: (1) a layered hypernetwork architecture that enables specialized parameter generation for each network layer, and (2) a frequency-domain reduction strategy that significantly reduces parameter count while preserving essential spectral features. This design enables efficient learning of a universal PDE solver through pre-training, capable of directly handling new equations while allowing optional fine-tuning for enhanced precision. The effectiveness of this approach is demonstrated through comprehensive experiments on four representative PDE problems, where LFR-PINO achieves 22.8%-68.7% error reduction compared to state-of-the-art baselines. Notably, frequency-domain reduction strategy reduces memory usage by 28.6%-69.3% compared to Hyper-PINNs while maintaining solution accuracy, striking an optimal balance between computational efficiency and solution fidelity.