Title: Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data Show Chinese title

Title: 深度学习从微观模拟数据中发现粘性重力流的宏观控制方程

Abstract: Although deep-learning has been successfully applied in a variety of science and engineering problems owing to its strong high-dimensional nonlinear mapping capability, it is of limited use in scientific knowledge discovery. In this work, we propose a deep-learning based framework to discover the macroscopic governing equation of viscous gravity current based on high-resolution microscopic simulation data without the need for prior knowledge of underlying terms. For two typical scenarios with different viscosity ratios, the deep-learning based equations exactly capture the same dominated terms as the theoretically derived equations for describing long-term asymptotic behaviors, which validates the proposed framework. Unknown macroscopic equations are then obtained for describing short-term behaviors, and additional deep-learned compensation terms are eventually discovered. Comparison of posterior tests shows that the deep-learning based PDEs actually perform better than the theoretically derived PDEs in predicting evolving viscous gravity currents for both long-term and short-term regimes. Moreover, the proposed framework is proven to be very robust against non-biased data noise for training, which is up to 20%. Consequently, the presented deep-learning framework shows considerable potential for discovering unrevealed intrinsic laws in scientific semantic space from raw experimental or simulation results in data space. Show Chinese abstract

Abstract: 尽管深度学习由于其强大的高维非线性映射能力已被成功应用于多种科学和工程问题，但在科学知识发现方面用途有限。 在本工作中，我们提出了一种基于深度学习的框架，仅需高分辨率微观模拟数据即可发现粘性重力流的宏观控制方程，而无需事先了解底层项。 对于两种具有不同粘度比的典型场景，基于深度学习的方程准确捕捉到了与理论推导方程相同的主要项，用于描述长期渐近行为，这验证了所提出的框架。 随后获得了未知的宏观方程来描述短期行为，并最终发现了额外的深度学习补偿项。 后验测试的比较表明，基于深度学习的偏微分方程在预测长期和短期范围内的演化粘性重力流方面实际上优于理论推导的偏微分方程。 此外，所提出的框架被证明对训练中的非偏向数据噪声非常鲁棒，噪声高达20%。 因此，所提出的深度学习框架显示出从数据空间中的原始实验或模拟结果中发现科学语义空间中未揭示的基本规律的巨大潜力。