naPINN可自动识别并过滤噪声数据，从损坏测量中恢复物理规律。
naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurement
- 引入能量模型学习预测残差分布，动态判断数据可靠性。
- 在非高斯噪声和高比例异常值下，重构精度显著优于现有方法。
- 适合处理真实世界含噪数据的物理方程发现任务。
物理信息神经网络（PINNs）在求解逆问题和从观测数据中发现控制方程方面表现良好，但在复杂测量噪声和严重异常值下性能明显下降。为解决此问题，我们提出噪声自适应物理信息神经网络（naPINN），可在未知噪声分布的情况下，稳健地从被污染的数据中恢复物理解。naPINN将基于能量的模型嵌入训练过程，学习预测残差的潜在分布；利用学习到的能量景观，通过可训练的可靠性门动态过滤高能量数据点，并采用拒绝成本正则化防止有效数据被误删。我们在多种带非高斯噪声及不同异常值率的偏微分方程基准测试中验证了naPINN的有效性，结果表明其显著优于现有鲁棒PINN基线，能成功分离异常值并准确重建严重数据污染下的系统动力学。
原文摘要 · Abstract (English)
Physics-Informed Neural Networks (PINNs) are effective methods for solving inverse problems and discovering governing equations from observational data. However, their performance degrades significantly under complex measurement noise and gross outliers. To address this issue, we propose the Noise-Adaptive Physics-Informed Neural Network (naPINN), which robustly recovers physical solutions from corrupted measurements without prior knowledge of the noise distribution. naPINN embeds an energy-based model into the training loop to learn the latent distribution of prediction residuals. Leveraging the learned energy landscape, a trainable reliability gate adaptively filters data points exhibiting high energy, while a rejection cost regularization prevents trivial solutions where valid data are discarded. We demonstrate the efficacy of naPINN on various benchmark partial differential equations corrupted by non-Gaussian noise and varying rates of outliers. The results show that naPINN significantly outperforms existing robust PINN baselines, successfully isolating outliers and accurately reconstructing the dynamics under severe data corruption.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。