Related papers: Domain-Decomposed Graph Neural Network Surrogate M…
An efficient strategy to construct physics-based local surrogate models for parametric linear elliptic problems is presented. The method relies on proper generalized decomposition (PGD) to reduce the dimensionality of the problem and on an…
During the COVID-19 crisis, mechanistic models have guided evidence-based decision making. However, time-critical decisions in a dynamical environment limit the time available to gather supporting evidence. We address this bottleneck by…
Discrete dislocation dynamics (DDD) is a widely employed computational method to study plasticity at the mesoscale that connects the motion of dislocation lines to the macroscopic response of crystalline materials. However, the…
Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…
Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…
Graph transformation that predicts graph transition from one mode to another is an important and common problem. Despite much progress in developing advanced graph transformation techniques in recent years, the fundamental assumption…
In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…
Surrogate models for the rapid inference of nonlinear boundary value problems in mechanics are helpful in a broad range of engineering applications. However, effective surrogate modeling of applications involving the contact of deformable…
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…
The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…
Graph neural networks (GNNs) learn representations from network data with naturally distributed architectures, rendering them well-suited candidates for decentralized learning. Oftentimes, this decentralized graph support changes with time…
Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…
We describe a computationally efficient, stochastic graph-regularization technique that can be utilized for the semi-supervised training of deep neural networks in a parallel or distributed setting. We utilize a technique, first described…
The optimization of structural parameters, such as mass(m), stiffness(k), and damping coefficient(c), is critical for designing efficient, resilient, and stable structures. Conventional numerical approaches, including Finite Element Method…
For computational efficiency, surrogate models have been used to emulate mathematical simulators for physical or biological processes. High-speed simulation is crucial for conducting uncertainty quantification (UQ) when the simulation is…
Nonlinear finite element crash simulations are accurate but computationally expensive, limiting their use in iterative design optimisation. Machine-learning surrogate models based on graph neural networks (GNNs) offer a faster alternative.…
Despite the recent success of Graph Neural Networks, it remains challenging to train a GNN on large graphs with millions of nodes and billions of edges, which are prevalent in many graph-based applications. Traditional sampling-based…
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…
Numerical simulation of multi-phase fluid dynamics in porous media is critical to a variety of geoscience applications. Data-driven surrogate models using Convolutional Neural Networks (CNNs) have shown promise but are constrained to…
Graph Neural Networks (GNNs) are powerful deep learning models to generate node embeddings on graphs. When applying deep GNNs on large graphs, it is still challenging to perform training in an efficient and scalable way. We propose a novel…