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Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition,…
The emergent multi-principal element alloys (MPEAs) provide a vast compositional space to search for novel materials for technological advances. However, how to efficiently identify optimal compositions from such a large design space for…
Order versus disorder in the structure of materials plays a key role in the theoretical prediction of their properties. However, this structural description appears to be ineffective for new families of materials such as high entropy alloys…
The design of new High Entropy Alloys that can achieve exceptional mechanical properties is presently of great interest to the materials science community. However, due to the difficulty of designing these alloys using traditional methods,…
High Entropy Alloys (HEAs) contain near equimolar amounts of five or more elements and are a compelling space for materials design. Great emphasis is placed on identifying HEAs that form a homogeneous solid-solution, but the design of such…
Classical methods for model order selection often fail in scenarios with low SNR or few snapshots. Deep learning-based methods are promising alternatives for such challenging situations as they compensate lack of information in the…
We suggest and implement an approach for the bottom-up description of systems undergoing large-scale structural changes and chemical transformations from dynamic atomically resolved imaging data, where only partial or uncertain data on…
The development of high-entropy alloys (HEAs) has marked a paradigm shift in alloy design, moving away from traditional methods that prioritize a dominant base metal enhanced by minor elements. HEAs instead incorporate multiple alloying…
A variational autoencoder (VAE) is a probabilistic machine learning framework for posterior inference that projects an input set of high-dimensional data to a lower-dimensional, latent space. The latent space learned with a VAE offers…
Using the information theory, this study provides insights into how the construction of latent space of autoencoder (AE) using deep neural network (DNN) training finds a smooth low-dimensional manifold in the stiff dynamical system. Our…
In high-entropy alloys (HEAs), the local chemical fluctuations from disordered solute solution state into segregation, precipitation and ordering configurations are complex due to the large number of elements. In this work, the cluster…
A general method is presented for modeling high entropy alloys as ensembles of randomly sampled, ordered configurations on a given lattice. Statistical mechanics is applied post hoc to derive the ensemble properties as a function of…
We present Ordinary Differential Equation Variational Auto-Encoder (ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE$^2$VAE can simultaneously learn…
Variational autoencoder (VAE) has widely been utilized for modeling data distributions because it is theoretically elegant, easy to train, and has nice manifold representations. However, when applied to image reconstruction and synthesis…
We derive an order-parameter field theory for a quantum phase transition between a disordered metal and an exotic (non-s-wave) superconductor. Mode coupling effects between the order parameter and other fermionic soft modes lead to an…
Recently, high-entropy alloys (HEAs) have attracted wide attention due to their extraordinary materials properties. A main challenge in identifying new HEAs is the lack of efficient approaches for exploring their huge compositional space.…
Alloys composed of several elements in roughly equimolar composition, often referred to as high-entropy alloys, have long been of interest for their thermodynamics and peculiar mechanical properties, and more recently for their potential…
This study introduces a language transformer-based machine learning model to predict key mechanical properties of high-entropy alloys (HEAs), addressing the challenges due to their complex, multi-principal element compositions and limited…
We investigate the capability of neural network-based model order reduction, i.e., autoencoder (AE), for fluid flows. As an example model, an AE which comprises of a convolutional neural network and multi-layer perceptrons is considered in…
Traditional metallic alloys are mixtures of elements where the atoms of minority species tend to distribute randomly if they are below their solubility limit, or lead to the formation of secondary phases if they are above it. Recently, the…