相场DeepONet：基于物理信息的深度算子神经网络，用于自由能泛函梯度流控制的图案形成的快速模拟
Phase-Field DeepONet: Physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionals
摘要：
科学机器学习的最新进展已经揭示了模式形成系统的建模。然而，真实模式的模拟仍然会产生显著的计算成本，这可以通过利用大型图像数据集来缓解。基于物理信息的机器学习和算子学习是这一应用的两个新兴且有前途的概念。在这里，我们提出了“相场DeepONet”，这是一个物理信息算子神经网络框架，可以预测由自由能泛函梯度流控制的系统的动态响应。用于验证该方法的可行性和准确性的例子包括Allen-Cahn和Cahn-Hilliard方程，作为化学混合物非平衡热力学反应相场模型的特殊情况。这是通过将最小化运动方案纳入框架来实现的，该框架优化和控制系统的总自由能如何演变，而不是直接求解控制方程。经过训练的算子神经网络可以作为显式时间步进器工作，将当前状态作为输入并输出下一个状态。这可能有助于快速实时预测模式形成动力系统，例如相分离锂离子电池，乳液，胶体显示器或生物模式。
英文摘要：
Recent advances in scientific machine learning have shed light on the modeling of pattern-forming systems. However, simulations of real patterns still incur significant computational costs, which could be alleviated by leveraging large image datasets. Physics-informed machine learning and operator learning are two new emerging and promising concepts for this application. Here, we propose "Phase-Field DeepONet", a physics-informed operator neural network framework that predicts the dynamic responses of systems governed by gradient flows of free-energy functionals. Examples used to validate the feasibility and accuracy of the method include the Allen-Cahn and Cahn-Hilliard equations, as special cases of reactive phase-field models for nonequilibrium thermodynamics of chemical mixtures. This is achieved by incorporating the minimizing movement scheme into the framework, which optimizes and controls how the total free energy of a system evolves, instead of solving the governing equations directly. The trained operator neural networks can work as explicit time-steppers that take the current state as the input and output the next state. This could potentially facilitate fast real-time predictions of pattern-forming dynamical systems, such as phase-separating Li-ion batteries, emulsions, colloidal displays, or biological patterns.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
