Publications

Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications (e.g., the process of CO₂ sequestration). Here, we extend and present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders for the compression and reconstruction and either radial basis function (RBF) interpolation or artificial neural networks (ANNs) for mapping parameters of partial differential equations (PDEs) on the corresponding nonlinear manifolds. To benchmark our approach, we also describe linear compression and reconstruction processes relying on proper orthogonal decomposition (POD) and ANNs. Further, we present comprehensive comparisons among different models through three benchmark problems. The reduced order models, linear and nonlinear approaches, are much faster than the finite element model, obtaining a maximum speed-up of 7 × 10⁶ because our framework is not bound by the Courant–Friedrichs–Lewy condition; hence, it could deliver quantities of interest at any given time contrary to the finite element model. Our model’s accuracy still lies within a relative error of 7% in the worst-case scenario. We illustrate that, in specific settings, the nonlinear approach outperforms its linear counterpart and vice versa. We hypothesize that a visual comparison between principal component analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE) could indicate which method will perform better prior to employing any specific compression strategy.

We propose the use of balanced iterative reducing and clustering using hierarchies (BIRCH) combined with linear regression to predict the reduced Young's modulus and hardness of highly heterogeneous materials from a set of nanoindentation experiments. We first use BIRCH to cluster the dataset according to its mineral compositions, which are derived from the spectral matching of energy-dispersive spectroscopy data through the modular automated processing system (MAPS) platform. We observe that grouping our dataset into five clusters yields the best accuracy as well as a reasonable representation of mineralogy in each cluster. Subsequently, we test four types of regression models, namely linear regression, support vector regression, Gaussian process regression, and extreme gradient boosting regression. The linear regression and Gaussian process regression provide the most accurate prediction, and the proposed framework yields R2 = 0.93 for the test set. Although the study is needed more comprehensively, our results shows that machine learning methods such as linear regression or Gaussian process regression can be used to accurately estimate mechanical properties with a proper number of grouping based on compositional data.

Abstract not provided.