One-Shot Transfer Learning for Nonlinear PDEs with Perturbative PINNs

arXiv — cs.LG•Monday, November 17, 2025 at 5:00:00 AM

- A novel framework has been introduced for addressing nonlinear PDEs by merging perturbation theory with one-shot transfer learning in PINNs, enabling efficient solutions to complex equations. This method's ability to adapt quickly to new instances while maintaining accuracy is significant for fields relying on PDEs, such as physics and engineering, where rapid computation is essential. The absence of related articles highlights the innovative nature of this research, emphasizing its potential impact on advancing computational methods in nonlinear dynamics.

— via World Pulse Now AI Editorial System

Read Original

Was this article worth reading? Share it

Recommended Readings

arXiv — cs.LG20 hours ago

Physics-Informed Neural Networks for Real-Time Gas Crossover Prediction in PEM Electrolyzers: First Application with Multi-Membrane Validation

PositiveArtificial Intelligence

The study presents the first application of physics-informed neural networks (PINNs) for predicting hydrogen crossover in polymer electrolyte membrane (PEM) electrolyzers. This innovation addresses safety and efficiency concerns in green hydrogen production, as hydrogen crossover can lead to explosive limits and reduce Faradaic efficiency. The PINN model integrates mass conservation, Fick's diffusion law, and Henry's solubility law, achieving validation across six membranes under various industrial conditions.

Read full article

via arXiv — cs.LG

arXiv — cs.LG3 days ago

Neuro-Spectral Architectures for Causal Physics-Informed Networks

PositiveArtificial Intelligence

Neuro-Spectral Architectures (NeuSA) have been introduced as a new class of Physics-Informed Neural Networks (PINNs) aimed at solving complex partial differential equations (PDEs). Traditional MLP-based PINNs often struggle with convergence in intricate initial value problems, leading to solutions that can violate causality. NeuSA addresses these challenges by learning a projection of the underlying PDE onto a spectral basis, thus improving convergence and enforcing causality through its integration with Neural ODEs.

Read full article

via arXiv — cs.LG

arXiv — cs.LG3 days ago

Augmented data and neural networks for robust epidemic forecasting: application to COVID-19 in Italy

PositiveArtificial Intelligence

This study introduces a data augmentation strategy designed to enhance the training of neural networks, thereby improving prediction accuracy. By generating synthetic data using a compartmental model and incorporating uncertainty, the model is calibrated with available data and integrated with deep learning techniques. The findings indicate that neural networks trained on these augmented datasets demonstrate significantly better predictive performance, particularly with Physics-Informed Neural Networks (PINNs) and Nonlinear Autoregressive (NAR) models.

Read full article

via arXiv — cs.LG