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

Researchers propose LNN-PINN, an enhanced physics-informed neural network framework that integrates liquid residual gating architecture to improve predictive accuracy for complex scientific problems. The method maintains existing physics modeling pipelines while refining the hidden-layer architecture, demonstrating consistent error reductions across benchmark tests without requiring hyperparameter adjustments.

Physics-informed neural networks represent a critical intersection between machine learning and scientific computing, enabling neural networks to respect domain-specific constraints encoded in partial differential equations. LNN-PINN addresses a fundamental limitation in this field: while PINNs excel at incorporating physical laws, their predictive accuracy often deteriorates on complex, high-dimensional problems. This research contributes a targeted architectural solution that preserves the entire existing optimization framework while introducing lightweight gating mechanisms exclusively within hidden layers.

The significance of this approach lies in its backward compatibility. Rather than proposing a complete redesign that would require retraining infrastructure and hyperparameter optimization, LNN-PINN functions as a drop-in enhancement. The consistent reduction in both RMSE and MAE metrics across four benchmark problems suggests the gating mechanism effectively captures nonlinear relationships without destabilizing the physics constraints. The demonstrated stability across varying dimensionality and boundary conditions indicates robustness rather than problem-specific tuning.

For the scientific computing and engineering domains, this advancement accelerates practical adoption of physics-informed learning. Organizations already invested in PINN implementations can incrementally upgrade architectures with minimal operational disruption. The framework's demonstrated adaptability across operator characteristics suggests applicability across diverse problem domains—from fluid dynamics to materials science. This modularity principle aligns with broader industry trends favoring composable AI systems that enhance rather than replace existing workflows, positioning physics-informed approaches as increasingly viable for mission-critical engineering applications.

• →LNN-PINN introduces liquid residual gating exclusively in hidden layers, preserving all existing physics modeling and optimization protocols.
• →Framework demonstrates consistent RMSE and MAE improvements across multiple benchmark problems under identical training conditions.
• →Architecture maintains stability across varying dimensions, boundary conditions, and operator characteristics without requiring hyperparameter adjustments.
• →Backward-compatible design enables existing PINN implementations to adopt improvements as modular architectural enhancements.
• →Approach validates that targeted neural network refinements can enhance physics-informed learning without compromising constraint enforcement.