利用能量变分方法学习广义扩散
Learning Generalized Diffusions using an Energetic Variational Approach
AI总结：
本文提出利用能量变分方法学习广义扩散，通过连续或离散数据提取物理定律，具备鲁棒性和扩展性，适用于高维系统。
摘要：
从计算或实验数据中提取 governing 物理定律在流体动力学和等离子体物理等领域至关重要。许多这些物理定律由于流体粘性或等离子体碰撞而具有耗散性。对于此类耗散性物理系统，我们提出了一种框架，基于其能量-耗散定律来学习相应系统的定律，假设连续数据（概率密度）或离散数据（粒子）可用。我们的方法提供了几个关键优势，包括对损坏/噪声观测的鲁棒性、易于扩展到更复杂的物理系统，以及解决高维系统的可能性。我们通过代表性数值示例验证了我们的方法，并仔细研究了数据量和数据属性对模型发现的影响。
英文摘要：
Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions. For such a dissipative physical system, we propose a framework to learn the corresponding laws of the systems based on their energy-dissipation laws, assuming either continuous data (probability density) or discrete data (particles) are available. Our methods offer several key advantages, including their robustness to corrupted/noisy observations, their easy extension to more complex physical systems, and the potential to address higher-dimensional systems. We validate our approaches through representative numerical examples and carefully investigate the impacts of data quantity and data property on model discovery.
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