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We formulate well-posed continuous-time generative flows for learning distributions that are supported on low-dimensional manifolds through Wasserstein proximal regularizations of $f$-divergences. Wasserstein-1 proximal operators regularize…
This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…
We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the SAV approach combined with the Lagrangian multiplier approach. They are as efficient…
High-order discontinuous Galerkin (DG) methods equipped with subcell finite-volume (FV) limiters provide an efficient framework for the simulation of nonlinear hyperbolic balance laws featuring shocks and complex flow structures. However,…
Grad-div stabilization is a classical remedy in conforming mixed finite element methods for incompressible flow problems, for mitigating velocity errors that are sometimes called poor mass conservation. Such errors arise due to the…
The paper considers distributed gradient flow (DGF) for multi-agent nonconvex optimization. DGF is a continuous-time approximation of distributed gradient descent that is often easier to study than its discrete-time counterpart. The paper…
In this paper, we study FPGA based pipelined and superscalar design of two variants of conjugate gradient methods for solving Laplacian equation on a discrete grid; the first version corresponds to the original conjugate gradient algorithm,…
In conventional transmon qubits, decoherence is dominated by a large number of parasitic two-level systems (TLS) residing at the edges of its large area coplanar shunt capacitor and junction leads. Avoiding these defects by improvements in…
The interfacial diffusion associated with finite volume method (FVM) discretizations of multiphase flows creates the need for an interface sharpening mechanism. Such solutions for structured quadrilateral grids are well documented, but…
Detailed measurements of intrinsic axial flow generation parallel to the magnetic field in the controlled shear decorrelation experiment linear plasma device with no axial momentum input are presented and compared to theory. The results…
This study presents a three-dimensional transient computational fluid dynamics simulation of droplet generation in a flow-focusing microfluidic device using the Coupled Level Set and Volume of Fluid method for interface capturing. We…
We develop a hydrodynamic description of self-generated electrolyte flow in capillaries whose bounding walls feature both non-uniform distributions of charge and non-uniform active ionic fluxes. The hydrodynamic velocity arising in such a…
Dissipative Particle Dynamics (DPD) is becoming a popular particle based method to study flow through microchannels due to the ease with which the presence of biological cells or DNA chains can be modeled. Many Lab-On-Chip (LOC) devices…
Recent advances in generative models have shown promise in generating behavior plans for long-horizon, sparse reward tasks. While these approaches have achieved promising results, they often lack a principled framework for hierarchical…
Diffusion models (DMs) have emerged as the new state-of-the-art family of deep generative models. To gain deeper insights into the limitations of diffusion models in recommender systems, we investigate the fundamental structural disparities…
The design of materials with tailored properties is crucial for technological progress. However, most deep generative models focus exclusively on perfectly ordered crystals, neglecting the important class of disordered materials. To address…
In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy…
High-dimensional generative modeling is fundamentally a manifold-learning problem: real data concentrate near a low-dimensional structure embedded in the ambient space. Effective generators must therefore balance support fidelity -- placing…
The precise encapsulation of deformable particles in multiphase flows involves complex transient Fluid-Structure Interactions (FSI) and topological interfacial changes. In the context of single-cell analysis, a numerical framework that…
Numerical simulation of multi-phase fluid dynamics in porous media is critical to a variety of geoscience applications. Data-driven surrogate models using Convolutional Neural Networks (CNNs) have shown promise but are constrained to…