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.

翻译：我们展示了一种能够在严重噪声条件下从非线性薛定谔方程中恢复物理参数的深度学习框架。通过将物理信息神经网络与自动微分技术相结合，我们仅使用500个稀疏、随机采样且被20%加性高斯噪声污染的数据点，便实现了对非线性系数beta的重建，其相对误差低于0.2%。这一噪声水平通常会导致传统有限差分方法因数值导数中的噪声放大而失效。我们验证了该方法在不同物理参数区间（beta介于0.5至2.0之间）和不同数据量（训练点数量介于100至1000之间）下的泛化能力，均展现出低于1%的稳定精度。在多次独立运行上的统计分析证实了其稳健性（当beta等于1.0时，标准差小于0.15%）。完整流程在中等云GPU资源上执行时间约为80分钟，使得该方法易于广泛采用。我们的结果表明，基于物理的正则化能有效过滤高测量不确定性，这使PINN成为解决时空动力学反问题的一种可行替代方案，尤其适用于实验数据稀缺且噪声大的场景。所有代码均已公开，以促进可复现性。