The molten sand that is a mixture of calcia, magnesia, alumina and silicate, known as CMAS, is characterized by its high viscosity, density and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a parametric ordinary differential equation (ODE) that captures the spreading radius behaviour of the CMAS droplets. The ODE parameters are then identified based on the physics-informed neural network (PINN) framework. Subsequently, the closed-form dependency of parameter values found by the PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modelling and state-of-the-art machine-learning techniques.

中文翻译：

---

使用多相多体耗散粒子动力学和基于 PINN 的数据驱动发现来表征 CMAS 液滴的部分润湿

熔砂是氧化钙、氧化镁、氧化铝和硅酸盐的混合物，称为 CMAS，具有高粘度、高密度和表面张力的特点。 CMAS 的独特性能使其成为高温应用中具有挑战性的材料，需要创新的解决方案和材料来防止其积聚和损坏关键设备。在这里，我们使用多相多体耗散粒子动力学模拟来研究高粘度熔融 CMAS 液滴的润湿动力学。模拟在三个维度上进行，具有不同的初始液滴尺寸和平衡接触角。我们提出了一个参数常微分方程（ODE）来捕获 CMAS 液滴的扩散半径行为。然后根据物理信息神经网络 (PINN) 框架识别 ODE 参数。随后，使用符号回归给出 PINN 发现的参数值对初始半径和接触角的封闭形式依赖性。最后，我们采用贝叶斯 PINN (B-PINN) 来评估和量化与发现的参数相关的不确定性。简而言之，这项研究通过融合简单的参数 ODE 建模和最先进的机器学习技术，深入了解 CMAS 液滴的扩散动力学。