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Microfluidic devices offer numerous advantages in medical applications, including the capture of single cells in microwell-based platforms for genomic analysis. As the cost of sequencing decreases, the demand for high-throughput single-cell…

Inspired by Pople diagrams popular in quantum chemistry, we introduce a hierarchical scheme, based on the multi-level combination (C) technique, to combine various levels of approximations made when calculating molecular energies within…

This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…

Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal…

Multi-task learning (MTL) improves generalization and data efficiency by jointly learning related tasks through shared representations. In the widely used hard-parameter-sharing setting, a shared backbone is combined with task-specific…

Quantum computing offers a promising avenue for advancing computational methods in science and engineering. In this work, we introduce the quantum asymptotic numerical method (qANM), a framework for solving nonlinear problems using quantum…

We present sharp convergence results for the Cauchy--Born approximation of general classical atomistic interactions, for both static and dynamic problems, for small data.

Low-discrepancy point sets and digital sequences underpin quasi-Monte Carlo (QMC) methods for high-dimensional integration. We cast two long-standing QMC design problems as program synthesis and solve them with an LLM-guided evolutionary…

We present a posteriori error estimates for a recently developed atomistic/continuum coupling method, the Consistent Energy-Based QC Coupling method. The error estimate of the deformation gradient combines a residual estimate and an a…

Molecular dynamics simulations have been performed to investigate in detail collective modes spectra of two-dimensional Coulomb fluids in a wide range of coupling. The obtained dispersion relations are compared with theoretical approaches…

We extend the recently introduced phaseless auxiliary-field quantum Monte Carlo (QMC) approach to any single-particle basis, and apply it to molecular systems with Gaussian basis sets. QMC methods in general scale favorably with system…

We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…

Non-local operations play a crucial role in computer vision enabling the capture of long-range dependencies through weighted sums of features across the input, surpassing the constraints of traditional convolution operations that focus…

Hybrid quantum-classical machine learning offers a promising direction for advancing automated quality control in industrial settings. In this study, we investigate two hybrid quantum-classical approaches for classifying defects in…

Atomistic/continuum coupling method is a class of multiscale computational method for the efficient simulation of crystalline defects. The recently developed blended ghost force correction (BGFC) method combines the efficiency of blending…

This paper proposed a new explicit nonlinear dimensionality reduction using neural networks for image retrieval tasks. We first proposed a Quasi-curvature Locally Linear Embedding (QLLE) for training set. QLLE guarantees the linear…

Atomistic/continuum coupling methods aim to achieve optimal balance between accuracy and efficiency. Adaptivity is the key for the efficient implementation of such methods. In this paper, we carry out a rigorous a posteriori analysis of the…

Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in constructing such a coupling consists in defining a coupled…

We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable…

While deep learning offers tremendous promise for scientific and medical imaging, any failures and hallucinations (predictions that do not coincide with reality) are hard to pinpoint and can have serious downstream consequences. Uncertainty…