Related papers: Accelerating Dimensionality Reduction in Wave-Resi…
Neural operators have gained recognition as potent tools for learning solutions of a family of partial differential equations. The state-of-the-art neural operators excel at approximating the functional relationship between input functions…
Industrial design evaluation often relies on high-fidelity simulations of governing partial differential equations (PDEs). While accurate, these simulations are computationally expensive, making dense exploration of design spaces…
Semi-analytical methods, such as rigorous coupled wave analysis, have been pivotal for numerical analysis of photonic structures. In comparison to other methods, they offer much faster computation, especially for structures with constant…
Dimensionality-reduction techniques are a fundamental tool for extracting useful information from high-dimensional data sets. Because secant sets encode manifold geometry, they are a useful tool for designing meaningful data-reduction…
Reliability analysis is a formidable task, particularly in systems with a large number of stochastic parameters. Conventional methods for quantifying reliability often rely on extensive simulations or experimental data, which can be costly…
In this work, we introduce ShipHullGAN, a generic parametric modeller built using deep convolutional generative adversarial networks (GANs) for the versatile representation and generation of ship hulls. At a high level, the new model…
We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…
Gaussian curvature is an important geometric property of surfaces, which has been used broadly in mathematical modeling. Due to the full nonlinearity of the Gaussian curvature, efficient numerical methods for models based on it are uncommon…
The present article is concerned with the s*-compressibility of classical boundary integral operators in anisotropic wavelet coordinates. Having the s*-compressibility at hand, one can design adaptive wavelet algorithms which are…
Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…
The study of high-dimensional differential equations is challenging and difficult due to the analytical and computational intractability. Here, we improve the speed of waveform relaxation (WR), a method to simulate high-dimensional…
We develop a linearly-scaling variant of the Force Coupling Method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205-231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly-periodic geometry with either a…
Resolvent analysis is a powerful tool for studying coherent structures in turbulent flows. However, its application beyond canonical flows with symmetries that can be used to simplify the problem to inherently three-dimensional flows and…
This study explores heated wavy wall shape design in channel flow using machine learning, aiming to minimize temperature variation ($\sigma_T$) while limiting pressure loss ($\Delta p$). A cost function $J$ defined as a product of…
Bayesian inverse design provides a principled framework for inferring aerodynamic geometries from sparse flow observations while quantifying uncertainty. However, its practical use in computational fluid dynamics (CFD) is severely limited…
Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exacerbated by the fact that new simulations…
Direct approaches to the quantum many-body problem suffer from the so-called "curse of dimensionality": the number of parameters needed to fully specify the exact wavefunction grows exponentially with increasing system size. This motivates…
This paper describes the pragmatic design and construction of geometric fabrics for shaping a robot's task-independent nominal behavior, capturing behavioral components such as obstacle avoidance, joint limit avoidance, redundancy…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…