LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks

TL;DR

LNN-PINN introduces a liquid residual gating architecture to physics-informed neural networks, significantly enhancing predictive accuracy while maintaining the original training pipeline.

Contribution

It proposes a novel liquid residual gating mechanism within PINNs that improves accuracy without altering the existing training process.

Findings

Consistently reduces RMSE and MAE across four benchmark problems.

Demonstrates robustness across different dimensions, boundary conditions, and operators.

Maintains stability and adaptability in complex scenarios.

Abstract

Physics-informed neural networks (PINNs) have attracted considerable attention for their ability to integrate partial differential equation priors into deep learning frameworks; however, they often exhibit limited predictive accuracy when applied to complex problems. To address this issue, we propose LNN-PINN, a physics-informed neural network framework that incorporates a liquid residual gating architecture while preserving the original physics modeling and optimization pipeline to improve predictive accuracy. The method introduces a lightweight gating mechanism solely within the hidden-layer mapping, keeping the sampling strategy, loss composition, and hyperparameter settings unchanged to ensure that improvements arise purely from architectural refinement. Across four benchmark problems, LNN-PINN consistently reduced RMSE and MAE under identical training conditions, with absolute error plots further confirming its accuracy gains. Moreover, the framework demonstrates strong adaptability and stability across varying dimensions, boundary conditions, and operator characteristics. In summary, LNN-PINN offers a concise and effective architectural enhancement for improving the predictive accuracy of physics-informed neural networks in complex scientific and engineering problems.