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

arXiv: https://arxiv.org/abs/2508.08935 · HTML: https://mlsanity.com/paper/2508.08935/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 12 Aug 2025.

## Builds on (most cited first, 9 of 9)

- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Can Physics-Informed Neural Networks beat the Finite Element Method?](https://mlsanity.com/paper/2302.04107/) (2023)
- [A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method](https://mlsanity.com/paper/2206.13103/) (2022)
- [Physics-Informed Neural Networks with Adaptive Localized Artificial Viscosity](https://mlsanity.com/paper/2203.08802/) (2022)
- [Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks](https://mlsanity.com/paper/2407.01613/) (2024)
- [VW-PINNs: A volume weighting method for PDE residuals in physics-informed neural networks](https://mlsanity.com/paper/2401.06196/) (2024)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)

## Built on by (most cited first, 3 of 3)

- [xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning](https://mlsanity.com/paper/2511.12512/) (2025)
- [Residual Attention Physics-Informed Neural Networks for Robust Multiphysics Simulation of Steady-State Electrothermal Energy Systems](https://mlsanity.com/paper/2603.23578/) (2026)
- [From Simple to Complex: Curriculum-Guided Physics-Informed Neural Networks via Gaussian Mixture Models](https://mlsanity.com/paper/2605.19263/) (2026)

## Abstract (arXiv)

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.