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For many complex systems the interaction of different scales is among the most interesting and challenging features. It seems not very successful to extract the physical properties in different scale regimes by the existing approaches, such…
The accurate electromagnetic modeling of both low- and high-frequency physics is crucial in the signal and power integrity analysis of electrical interconnects. The boundary element method (BEM) is appealing for lossy conductor modeling…
Density matrix embedding theory (DMET) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In…
Unveiling numerical trends among either atomic or equivalent weights that somehow preserved resemblances among elements was frequent in the 1860s. Standing out from the crowd, Meyer and Mendeleev went beyond numerical relationships,…
We develop a family of expanded mixed Multiscale Finite Element Methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed Multiscale Finite Element formulation in the sense…
The exponential growth of volume, variety and velocity of data is raising the need for investigations of automated or semi-automated ways to extract useful patterns from the data. It requires deep expert knowledge and extensive…
Transmission Electron Microscopy (TEM) is a powerful tool for imaging material structure and characterizing material chemistry. Recent advances in data collection technology for TEM have enabled high-volume and high-resolution data…
We systematically study various network Expectation-Maximization (EM) algorithms for the Gaussian mixture model within the framework of decentralized federated learning. Our theoretical investigation reveals that directly extending the…
The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule's…
In recent decades, the study of quantum magnets, which feature unconventional behaviour such as exotic quantum phase transitions and quantum spin liquids, and unconventional magnetic states of matter, has made remarkable progress. However,…
The next generation of particle physics experiments will face a new era of challenges in data acquisition, due to unprecedented data rates and volumes along with extreme environments and operational constraints. Harnessing this data for…
One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for…
We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation. ExpMsFEM…
Scanning Electron Microscopy (SEM) is indispensable in modern materials science, enabling high-resolution imaging across a wide range of structural, chemical, and functional investigations. However, SEM imaging remains constrained by…
Matrix factorization is a fundamental method in statistics and machine learning for inferring and summarizing structure in multivariate data. Modern data sets often come with "side information" of various forms (images, text, graphs) that…
Despite the long history of electrochemistry, there is a lack of quantitative algorithms that rigorously correlate experiment with theory. Electrochemical modeling has had advanced across empirical, analytical, numerical, and data-driven…
The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains, since it reduces the discretization to the domain boundaries, thereby condensing the…
Magnetostatic field calculations in micromagnetic simulations can be numerically expensive, particularly in the case of large-scale finite element simulations. The established finite element / boundary element method (FEM/BEM) by Fredkin &…
The EM algorithm is a powerful tool for maximum likelihood estimation with missing data. In practice, the calculations required for the EM algorithm are often intractable. We review numerous methods to circumvent this intractability, all of…
The relationship between magnetoelectricity and electromagnetism is a subject of a strong interest and numerous discussions in microwave and optical wave physics and material sciences. The definition of the energy and momentum of the…