naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurement

Researchers introduce naPINN (Noise-Adaptive Physics-Informed Neural Networks), a novel machine learning approach that recovers accurate physical equations from corrupted or noisy measurement data without requiring prior knowledge of noise characteristics. The method uses energy-based models to identify and filter outliers while maintaining data integrity, substantially outperforming existing robust PINN methods across benchmark tests with non-Gaussian noise and varying outlier rates.

Physics-Informed Neural Networks represent a critical intersection of machine learning and scientific computing, enabling researchers to discover governing equations directly from observational data. The naPINN advancement addresses a fundamental limitation that has constrained PINN applications in real-world scenarios: their vulnerability to measurement noise and outliers that degrade solution quality. Traditional approaches either require explicit noise distribution knowledge or perform poorly under complex corruption patterns, limiting their utility for practical experimental data where noise characteristics remain unknown.

This research emerges from growing demand in scientific machine learning to handle messy real-world datasets. Traditional numerical methods struggle with noisy inputs, while standard neural networks lack physical constraints. naPINN bridges this gap by embedding an energy-based model that learns residual distributions adaptively during training. The reliability gate mechanism intelligently weights data points based on learned energy patterns, while rejection cost regularization prevents the network from simply discarding valid measurements—a common failure mode in noise-robust systems.

The implications extend across computational physics, climate modeling, materials science, and engineering applications where measurement corruption is endemic. By enabling accurate equation discovery from imperfect data, naPINN reduces preprocessing costs and expands PINN applicability to real laboratory and observational contexts. The demonstrated superiority over existing baselines suggests this approach could accelerate scientific discovery timelines.

Future developments should explore computational efficiency at scale, application to high-dimensional PDEs, and integration with experimental feedback loops. The framework's generalizability to different noise types and outlier distributions will determine its adoption across scientific domains.

• →naPINN robustly recovers physics from corrupted measurements without requiring prior noise distribution knowledge.
• →Energy-based models with adaptive reliability gates enable intelligent data filtering while preserving valid measurements.
• →Benchmarks show significant performance gains over existing robust PINN methods under non-Gaussian noise and outliers.
• →The approach addresses a major limitation preventing PINN adoption for real-world noisy experimental data.
• →Applications span computational physics, climate modeling, and materials science where measurement corruption is common.