Related papers: Deep Micro Solvers for Rough-Wall Stokes Flow in a…

Factorial Hidden Markov Models (FHMMs) are powerful models for sequential data but they do not scale well with long sequences. We propose a scalable inference and learning algorithm for FHMMs that draws on ideas from the stochastic…

In this work, a modified neural architecture search method (NAS) based physics-informed deep learning model is presented for stochastic analysis in heterogeneous porous material. Monte Carlo method based on a randomized spectral…

Learning computational fluid dynamics (CFD) traditionally relies on computationally intensive simulations of the Navier-Stokes equations. Recently, large language models (LLMs) have shown remarkable pattern recognition and reasoning…

Scour around bridge piers is a critical challenge for infrastructures around the world. In the absence of analytical models and due to the complexity of the scour process, it is difficult for current empirical methods to achieve accurate…

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…

The NURBS-enhanced finite element method (NEFEM) combined with a hybridisable discontinuous Galerkin (HDG) approach is presented for the first time. The proposed technique completely eliminates the uncertainty induced by a polynomial…

Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of…

A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and…

This work presents a robust and efficient sharp interface immersed boundary (IBM) framework, which is applicable for all-speed flow regimes and is capable of handling arbitrarily complex bodies (stationary or moving). The work deploys an…

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…

This paper introduces Helix, a distributed system for high-throughput, low-latency large language model (LLM) serving in heterogeneous GPU clusters. The key idea behind Helix is to formulate inference computation of LLMs over heterogeneous…

In this paper, we suggest a new heterogeneous multiscale method (HMM) for the time-harmonic Maxwell equations in locally periodic media. The method is constructed by using a divergence-regularization in one of the cell problems. This allows…

A upscaled lattice Boltzmann method (LBM) for flow simulations in heterogeneous porous media, at both pore and Darcy scales, is proposed in this paper. In the micro-scale simulations, we model flows using LBM with the modified Guo et al.…

Computational studies that use block-structured adaptive mesh refinement (AMR) approaches suffer from unnecessarily high mesh resolution in regions adjacent to important solution features. This deficiency limits the performance of AMR…

This paper proposes a deep neural network approach for predicting multiphase flow in heterogeneous domains with high computational efficiency. The deep neural network model is able to handle permeability heterogeneity in high dimensional…

We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier--Stokes equations. Traditional numerical solvers incur significant computational costs to respect…

Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that…

Physics-Informed Neural Networks (PINNs) have demonstrated considerable success in solving complex fluid dynamics problems. However, their performance often deteriorates in regimes characterized by steep gradients, intricate boundary…

Current GPU-accelerated supercomputers promise to enable large-scale simulations of turbulent flows. Lattice Boltzmann Methods (LBM) are particularly well-suited to fulfilling this promise due to their intrinsic compatibility with highly…

The objective for this work is to develop a data-driven proxy to high-fidelity numerical flow simulations using digital images. The proposed model can capture the flow field and permeability in a large verity of digital porous media based…