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Metasurfaces -- ultrathin structures composed of subwavelength optical elements -- have revolutionized light manipulation by enabling precise control over electromagnetic waves' amplitude, phase, polarization, and spectral properties.…
Registration of optical and synthetic aperture radar (SAR) remote sensing images serves as a critical foundation for image fusion and visual navigation tasks. This task is particularly challenging because of their modal discrepancy,…
The exploration of novel architectures requires physics-based simulation due to a lack of prior experience to start from, which introduces two specific challenges for optimization algorithms: evaluations become more expensive (in time) and…
Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…
Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial…
An accurate algorithm is proposed to improve the prediction of a particle in collision with a moving wall within the direct simulation Monte Carlo (DSMC) framework for the simulation of unsteady rarefied flows. This algorithm is able to…
We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a…
Representing underwater 3D scenes is a valuable yet complex task, as attenuation and scattering effects during underwater imaging significantly couple the information of the objects and the water. This coupling presents a significant…
The key task of physical simulation is to solve partial differential equations (PDEs) on discretized domains, which is known to be costly. In particular, high-fidelity solutions are much more expensive than low-fidelity ones. To reduce the…
Efficient hybrid DFT simulations of solid state materials would be extremely beneficial for computational chemistry and materials science, but is presently bottlenecked by difficulties in computing Hartree-Fock (HF) exchange with plane wave…
Recently, 3D Gaussian Splatting (3DGS) has demonstrated impressive novel view synthesis results, while allowing the rendering of high-resolution images in real-time. However, leveraging 3D Gaussians for surface reconstruction poses…
We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…
4D millimeter-wave radar is a promising sensing modality for autonomous driving, yet effective 3D object detection from 4D radar and monocular images remains challenging. Existing fusion approaches either rely on instance proposals lacking…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group $O(d)$ and naturally reductive homogeneous manifolds obtained from the action of the rotation group $SO(d)$. We theoretically and…
We introduce an efficient method to construct optimal and system adaptive basis sets for use in electronic structure and quantum Monte Carlo calculations. The method is based on an embedding scheme in which a reference atom is singled out…
Diffeomorphic matching (only one of several names for this technique) is a technique for non-rigid registration of curves and surfaces in which the curve or surface is embedded in the flow of a time-series of vector fields. One seeks the…
In this paper, we develop a Monte Carlo algorithm named the Frozen Gaussian Sampling (FGS) to solve the semiclassical Schr\"odinger equation based on the frozen Gaussian approximation. Due to the highly oscillatory structure of the wave…
Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of…
We investigate the unconstrained global optimization of functions with low effective dimensionality, that are constant along certain (unknown) linear subspaces. Extending the technique of random subspace embeddings in [Wang et al., Bayesian…