Characterization of partial wetting by CMAS droplets using multiphase
  many-body dissipative particle dynamics and data-driven discovery based on
  PINNs
Elham Kiyani Mahdi Kooshkbaghi Khemraj Shukla Rahul Babu Koneru Zhen Li Luis Bravo Anindya Ghoshal George Em Karniadakis Mikko Karttunen
The molten sand, 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 (mDPD) 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 coarse parametric ordinary differential equation (ODE)
that captures the spreading radius behavior 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 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 modeling and state-of-the-art machine learning techniques.