Related papers: Combining Differentiable PDE Solvers and Graph Neu…

This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

Computational fluid dynamics (CFD) simulation is an irreplaceable modelling step in many engineering designs, but it is often computationally expensive. Some graph neural network (GNN)-based CFD methods have been proposed. However, the…

Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural…

Computational Fluid Dynamics (CFD) is used in the design and optimization of gas turbines and many other industrial/ scientific applications. However, the practical use is often limited by the high computational cost, and the accurate…

One of the main challenges in solving time-dependent partial differential equations is to develop computationally efficient solvers that are accurate and stable. Here, we introduce a graph neural network approach to finding efficient PDE…

Computational cardiovascular flow modeling plays a crucial role in understanding blood flow dynamics. While 3D models provide acute details, they are computationally expensive, especially with fluid-structure interaction (FSI) simulations.…

The design of microfluidic devices is a cumbersome and tedious process that can be significantly improved by simulation. Methods based on Computational Fluid Dynamics (CFD) are considered state-of-the-art, but require extensive compute time…

Differentiable physical simulators are proving to be valuable tools for developing data-driven models for computational fluid dynamics (CFD). In particular, these simulators enable end-to-end training of machine learning (ML) models…

Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…

Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…

This study aims to overcome the limitations of conventional deep-learning approaches based on convolutional neural networks in complex geometries and unstructured meshes by exploring the potential of Graph U-Nets for unsteady flow-field…

Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while…

Accurate simulation of granular flow dynamics is crucial for assessing various geotechnical risks, including landslides and debris flows. Granular flows involve a dynamic rearrangement of particles exhibiting complex transitions from…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

One of the current challenges in physically-based simulations, and, more specifically, fluid simulations, is to produce visually appealing results at interactive rates, capable of being used in multiple forms of media. In recent times, a…

Water distribution systems (WDSs) are an important part of critical infrastructure becoming increasingly significant in the face of climate change and urban population growth. We propose a robust and scalable surrogate deep learning (DL)…

Dynamic graphs exhibit complex temporal dynamics due to the interplay between evolving node features and changing network structures. Recently, Graph Neural Controlled Differential Equations (Graph Neural CDEs) successfully adapted Neural…

This work aims to improve fuel chamber injectors' performance in turbofan engines, thus implying improved performance and reduction of pollutants. This requires the development of models that allow real-time prediction and improvement of…