论文标题
通过物理编码的学习从稀缺数据中发现非线性PDE
Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning
论文作者
论文摘要
利用实验测量来发现控制复杂物理现象的基本偏微分方程（PDE），人们对利益的兴趣越来越大。尽管过去的研究尝试在数据驱动的PDE发现方面取得了巨大成功，但是在处理低质量测量数据时，无法保证现有方法的鲁棒性。为了克服这一挑战，我们提出了一个新型物理编码的离散学习框架，以从稀缺和嘈杂的数据中发现时空PDE。一般的想法是（1）首先引入一个新型的深卷卷积转向网络，该网络可以编码先前的物理知识（例如已知的PDE术语，假定的PDE结构，初始/边界条件等），同时保持在表示能力上的灵活性，以准确地重新构建高效数据，并（2）识别posents process process expose poss expose poss expons exposity expose poss expons expons expose posents poss expons exposity expons exposity exponsed exposity。我们在三个非线性PDE系统上验证方法。证明了所提出的方法比基线模型的有效性和优越性。
There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success in data-driven PDE discovery, the robustness of the existing methods cannot be guaranteed when dealing with low-quality measurement data. To overcome this challenge, we propose a novel physics-encoded discrete learning framework for discovering spatiotemporal PDEs from scarce and noisy data. The general idea is to (1) firstly introduce a novel deep convolutional-recurrent network, which can encode prior physics knowledge (e.g., known PDE terms, assumed PDE structure, initial/boundary conditions, etc.) while remaining flexible on representation capability, to accurately reconstruct high-fidelity data, and (2) perform sparse regression with the reconstructed data to identify the explicit form of the governing PDEs. We validate our method on three nonlinear PDE systems. The effectiveness and superiority of the proposed method over baseline models are demonstrated.
