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Problems of interest in hydrogeology and hydrocarbon resources involve complex heterogeneous geological formations. Such domains are most accurately represented in reservoir simulations by unstructured computational grids. Finite element…
We develop a diffuse solid method that is versatile and accurate for modeling wetting and multiphase flows in highly complex geometries. In this scheme, we harness N + 1-component phase field models to investigate interface shapes and flow…
Learning-based models for fluid dynamics often operate in unconstrained function spaces, leading to physically inadmissible, unstable simulations. While penalty-based methods offer soft regularization, they provide no structural guarantees,…
We present a microfluidic platform for two-dimensional manipulation of water droplets immersed in bulk oil-based ferrofluid. Although non-magnetic, the droplets are exclusively controlled by magnetic fields, without any pressure-driven…
A computational method based on the non-linear Gaussian process (GP), known as deep Gaussian processes (deep GPs) for uncertainty quantification & propagation in modelling of flow through heterogeneous porous media is presented. The method…
This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of…
We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media. The method is based on divergence-conforming discontinuous…
In this study, three-dimensional simulations of a reacting hydrogen jet in supersonic crossflow using a structure-preserving discontinuous Galerkin (DG) formulation are examined. The hydrogen jet, with a momentum flux ratio of five, is…
We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for $N$ dimensional data by embedding paths…
We use a novel non-equilibrium algorithm to simulate steady-state fluid transport through a two-dimensional (2D) membrane due to a concentration gradient by molecular dynamics (MD) for the first time. We confirm that, as required by the…
Granular dynamics driven by fluid flow is ubiquitous in many industrial and natural processes, such as fluvial and coastal sediment transport. Yet, their complex multiphysics nature challenges the accuracy and efficiency of numerical…
A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo and Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic…
Significant progress has been made to increase access to droplet microfluidics for labs with limited microfluidics expertise or fabrication equipment. In particular, using off-the-shelf systems has been a valuable approach. However, the…
In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an attractive approach for numerical simulations of compressible flows. This paper presents an overview of the recent development of DG methods for compressible…
Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit…
We introduce a framework for joint grounded scene graph - image generation, a challenging task involving high-dimensional, multi-modal structured data. To effectively model this complex joint distribution, we adopt a factorized approach:…
Effective mixing is essential for biochemical reactions. In droplet-based microfluidics, immediate mixing of substances upon contact in the droplet formation stage can greatly enhance the uniformity of chemical reactions. Furthermore, it…
We consider the maximum mean discrepancy ($\mathrm{MMD}$) GAN problem and propose a parametric kernelized gradient flow that mimics the min-max game in gradient regularized $\mathrm{MMD}$ GAN. We show that this flow provides a descent…
As a counterpoint to recent numerical methods for crystal surface evolution, which agree well with microscopic dynamics but suffer from significant stiffness that prevents simulation on fine spatial grids, we develop a new numerical method…
The interaction of multiple fluids through a heterogeneous pore space leads to complex pore-scale flow dynamics, such as intermittent pathway flow. The non-local nature of these dynamics, and the size of the 4D datasets acquired to capture…