用深度学习从严重噪声数据中精准恢复物理参数,效果远超传统方法。
Robust Physics Discovery from Highly Corrupted Data: A PINN Framework Applied to the Nonlinear Schrödinger Equation
- 结合物理约束与自动微分,构建抗噪强的反演框架。
- 仅用500个带20%噪声的数据点,参数误差低于0.2%。
- 适合实验数据稀疏且含噪的物理系统逆问题研究。
我们展示了一种深度学习框架,可在严重噪声条件下从非线性薛定谔方程(NLSE)中恢复物理参数。通过将物理信息神经网络(PINNs)与自动微分结合,仅使用500个随机采样的稀疏数据点、含20%加性高斯噪声的情况下,即可实现非线性系数β的重建,相对误差小于0.2%,而传统有限差分法在此类场景下因数值导数放大噪声通常失效。我们在β值在0.5至2.0之间及训练点数100至1000的多种物理情形和数据量下验证了方法的泛化能力,均保持亚1%精度。多次独立运行的统计分析表明其鲁棒性良好(β=1.0时标准差低于0.15%)。整个流程在中等云GPU资源(NVIDIA Tesla T4)上约需80分钟,具备广泛可复用性。结果表明,基于物理的正则化可有效过滤高测量不确定性,使PINNs成为时空动力学逆问题中实验数据稀缺且含噪场景下的可行替代方案。所有代码已公开,便于复现。
原文摘要 · Abstract (English)
We demonstrate a deep learning framework capable of recovering physical parameters from the Nonlinear Schrodinger Equation (NLSE) under severe noise conditions. By integrating Physics-Informed Neural Networks (PINNs) with automatic differentiation, we achieve reconstruction of the nonlinear coefficient beta with less than 0.2 percent relative error using only 500 sparse, randomly sampled data points corrupted by 20 percent additive Gaussian noise, a regime where traditional finite difference methods typically fail due to noise amplification in numerical derivatives. We validate the method's generalization capabilities across different physical regimes (beta between 0.5 and 2.0) and varying data availability (between 100 and 1000 training points), demonstrating consistent sub-1 percent accuracy. Statistical analysis over multiple independent runs confirms robustness (standard deviation less than 0.15 percent for beta equals 1.0). The complete pipeline executes in approximately 80 minutes on modest cloud GPU resources (NVIDIA Tesla T4), making the approach accessible for widespread adoption. Our results indicate that physics-based regularization acts as an effective filter against high measurement uncertainty, positioning PINNs as a viable alternative to traditional optimization methods for inverse problems in spatiotemporal dynamics where experimental data is scarce and noisy. All code is made publicly available to facilitate reproducibility.
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