We introduce , a Partial Differential Equation (PDE) discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions. uses an adaptive loss function based on weak forms to train a neural network, , to approximate the PDE solution while simultaneously identifying the governing PDE. This approach yields an algorithm that is robust to noise and can discover a range of PDEs directly from noisy, limited measurements of their solutions. We demonstrate the efficacy of by learning several benchmark PDEs.

中文翻译：

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Weak-PDE-LEARN：一种基于弱形式的方法，用于从嘈杂、有限的数据中发现偏微分方程

我们引入了一种偏微分方程 (PDE) 发现算法，可以从噪声、有限的解测量中识别非线性 PDE。使用基于弱形式的自适应损失函数来训练神经网络 ，以逼近 PDE 解，同时识别控制 PDE。这种方法产生了一种对噪声具有鲁棒性的算法，并且可以直接从解决方案的噪声、有限测量中发现一系列偏微分方程。我们通过学习几个基准偏微分方程来证明其有效性。