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In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…

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…

Traditional computational fluid dynamics calculates the physical information of the flow field by solving partial differential equations, which takes a long time to calculate and consumes a lot of computational resources. We build a fluid…

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…

Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically…

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…

This work presents a novel resolution-invariant model order reduction strategy for multifidelity applications. We base our architecture on a novel neural network layer developed in this work, the graph feedforward network, which extends the…

Computational fluid dynamics (CFD) simulations are crucial in automotive, aerospace, maritime and medical applications, but are limited by the complexity, cost and computational requirements of directly calculating the flow, often taking…

In modern computer vision, images are typically represented as a fixed uniform grid with some stride and processed via a deep convolutional neural network. We argue that deforming the grid to better align with the high-frequency image…

Solving flow through porous media is a crucial step in the topology optimisation of cold plates, a key component in modern thermal management. Traditional computational fluid dynamics (CFD) methods, while accurate, are often prohibitively…

In this paper, we explore the graph partitioning problem, a pivotal combina-torial optimization challenge with extensive applications in various fields such as science, technology, and business. Recognized as an NP-hard prob-lem, graph…

Graph neural networks (GNNs) have shown their superiority in modeling graph data. Owing to the advantages of federated learning, federated graph learning (FGL) enables clients to train strong GNN models in a distributed manner without…

The accelerated method in solving optimization problems has always been an absorbing topic. Based on the fixed-time (FxT) stability of nonlinear dynamical systems, we provide a unified approach for designing FxT gradient flows (FxTGFs).…

To solve the problem that convolutional neural networks (CNNs) are difficult to process non-grid type relational data like graphs, Kipf et al. proposed a graph convolutional neural network (GCN). The core idea of the GCN is to perform…

Recent advances in graph machine learning have shifted to data-centric paradigms, driven by two emerging fields: (1) Federated graph learning (FGL) enables multi-client collaboration but faces challenges from data and task heterogeneity,…

Finite difference methods (FDMs) are widely used for solving partial differential equations (PDEs) due to their relatively simple implementation. However, they face significant challenges when applied to non-rectangular domains and in…

In this work, we propose to employ information-geometric tools to optimize a graph neural network architecture such as the graph convolutional networks. More specifically, we develop optimization algorithms for the graph-based…

Graph convolutional networks (GCNs) suffer from the irregularity of graphs, while more widely-used convolutional neural networks (CNNs) benefit from regular grids. To bridge the gap between GCN and CNN, in contrast to previous works on…

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…

Graph Convolutional Networks (GCNs) have emerged as the state-of-the-art method for graph-based learning tasks. However, training GCNs at scale is still challenging, hindering both the exploration of more sophisticated GCN architectures and…