Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

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.

On the Parameter Combinations That Matter and on Those That do Not

We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the dynamic output behavior: a set of effective parameters for the model. Furthermore, we use Conformal Autoencoder Neural Networks, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters, nonlinear combinations of the physical ones, has previously been established analytically.

Coarse-scale PDEs from fine-scale observations via machine learning

Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through e.g. atomistic, agent-based or lattice models) based on first principles. Some of these processes can also be successfully modeled at the macroscopic level using e.g. partial differential equations (PDEs) describing the evolution of the right few macroscopic observables (e.g. concentration and momentum fields). Deriving good macroscopic descriptions (the so-called "closure problem") is often a time-consuming process requiring deep understanding/intuition about the system of interest. Recent developments in data science provide alternative ways to effectively extract/learn accurate macroscopic descriptions approximating the underlying microscopic observations. In this paper, we introduce a data-driven framework for the identification of unavailable coarse-scale PDEs from microscopic observations via machine learning algorithms. Specifically, using Gaussian Processes, Artificial Neural Networks, and/or Diffusion Maps, the proposed framework uncovers the relation between the relevant macroscopic space fields and their time evolution (the right-hand-side of the explicitly unavailable macroscopic PDE). Interestingly, several choices equally representative of the data can be discovered. The framework will be illustrated through the data-driven discovery of macroscopic, concentration-level PDEs resulting from a fine-scale, Lattice Boltzmann level model of a reaction/transport process. Once the coarse evolution law is identified, it can be simulated to produce long-term macroscopic predictions. Different features (pros as well as cons) of alternative machine learning algorithms for performing this task (Gaussian Processes and Artificial Neural Networks), are presented and discussed.