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Continuous data assimilation (CDA) methods, such as the nudging algorithm introduced by Azouani, Olson, and Titi (AOT), have proven to be highly effective in deterministic settings for asymptotically synchronizing approximate solutions with…
The discontinuous Galerkin (DG) method is widely being used to solve hyperbolic partial differential equations (PDEs) due to its ability to provide high-order accurate solutions in complex geometries, capture discontinuities, and exhibit…
Cognitive diagnosis model (CDM) is a fundamental and upstream component in intelligent education. It aims to infer students' mastery levels based on historical response logs. However, existing CDMs usually follow the ID-based embedding…
Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the…
Recent hybrid video generation models combine autoregressive temporal dynamics with diffusion-based spatial denoising, but their sequential, iterative nature leads to error accumulation and long inference times. In this work, we propose a…
We introduce a full-Lagrangian heterogeneous multiscale method (LHMM) to model complex fluids with microscopic features that can extend over large spatio-temporal scales, such as polymeric solutions and multiphasic systems. The proposed…
In this article we present a parallel algorithm for simulation of the heat conduction process inside the so-called pulse cryogenic cell. This simulation is important for designing the device for portion injection of working gases into…
We present a dual-resolution molecular dynamics (MD) simulation of liquid water employing a recently introduced Adaptive Resolution Scheme (AdResS). The spatially adaptive molecular resolution procedure allows for changing from a…
The scalability of time-dependent partial differential equation (PDE) solvers based on the discontinuous Galerkin (DG) method is increasingly limited by data communication and synchronization requirements across processing elements (PEs) at…
Non-adiabatic molecular dynamics (NAMD) simulations have become an indispensable tool for investigating excited-state dynamics in solids. In this work, we propose a general framework, N$^2$AMD which employs an E(3)-equivariant deep neural…
We develop an efficient parallel multiscale method that bridges the atomistic and mesoscale regimes, from nanometer to micron and beyond, via concurrent coupling of atomistic simulation and mesoscopic dynamics. In particular, we combine an…
Computational fluid dynamics (CFD) has become a cornerstone of modern water engineering, providing quantitative tools for the analysis, prediction, and management of complex hydraulic systems across a wide range of spatial and temporal…
Classical Computational Fluid Dynamics (CFD) of long-time processes with strongly separated time scales is computationally extremely demanding if not impossible. Consequently, the state-of-the-art description of such systems is not capable…
In this paper we would like to share our experience for transforming a parallel code for a Computational Fluid Dynamics (CFD) problem into a parallel version for the RedisDG workflow engine. This system is able to capture heterogeneous and…
An adpative integration technique for time advancement of particle motion in the context of coupled computational fluid dynamics (CFD) - discrete element method (DEM) simulations is presented in this work. CFD-DEM models provide an accurate…
The application of deep neural networks (DNNs) holds considerable promise as a substitute for the direct integration of chemical source terms in combustion simulations. However, challenges persist in ensuring high precision and…
Machine learning has been successfully applied to grid-based PDE modeling in various scientific applications. However, learned PDE solvers based on Lagrangian particle discretizations, which are the preferred approach to problems with free…
This paper presents a 2D/3D Free Surface Lattice Boltzmann Method simulation package called LBfoam for the simulation of foaming processes. The model incorporates the essential physics of foaming phenomena: gas diffusion into nucleated…
Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…
This study presents a novel approach to applying data assimilation techniques for particle-based simulations using the Ensemble Kalman Filter. While data assimilation methods have been effectively applied to Eulerian simulations, their…