Related papers: An FEA surrogate model with Boundary Oriented Grap…

Finite Element Analysis (FEA) is a powerful but computationally intensive method for simulating physical phenomena. Recent advancements in machine learning have led to surrogate models capable of accelerating FEA. Yet there are still…

We address the solution of large-scale Bayesian optimal experimental design (OED) problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields. The OED problem seeks to find sensor locations that…

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural…

Graph neural networks (GNNs) provide powerful insights for brain neuroimaging technology from the view of graphical networks. However, most existing GNN-based models assume that the neuroimaging-produced brain connectome network is a…

Accurate and scalable surrogate models for AC power flow are essential for real-time grid monitoring, contingency analysis, and decision support in increasingly dynamic and inverter-dominated power systems. However, most existing surrogates…

Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often…

Driven by the need to accelerate numerical simulations, the use of machine learning techniques is rapidly growing in the field of computational solid mechanics. Their application is especially advantageous in concurrent multiscale finite…

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…

We present a method whereby the finite element method is used to train physics-informed neural networks that are suitable for surrogate modeling. The method is based on a custom convolutional operation called stencil convolution which…

Graph Neural Networks (GNNs) are important across different domains, such as social network analysis and recommendation systems, due to their ability to model complex relational data. This paper introduces subgraph queries as a new task for…

Graph embedding (GE) methods embed nodes (and/or edges) in graph into a low-dimensional semantic space, and have shown its effectiveness in modeling multi-relational data. However, existing GE models are not practical in real-world…

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…

Correctly capturing intraoperative brain shift in image-guided neurosurgical procedures is a critical task for aligning preoperative data with intraoperative geometry for ensuring accurate surgical navigation. While the finite element…

Generative models (GMs) such as Generative Adversary Network (GAN) and Variational Auto-Encoder (VAE) have thrived these years and achieved high quality results in generating new samples. Especially in Computer Vision, GMs have been used in…

As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…

This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical homogenization, which compresses fine-scale coefficients into…

Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…

For Bayesian optimization (BO) on high-dimensional data with complex structure, neural network-based kernels for Gaussian processes (GPs) have been used to learn flexible surrogate functions by the high representation power of deep…

A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs,…

Accurate calibration of finite element (FE) models is essential across various biomechanical applications, including human intervertebral discs (IVDs), to ensure their reliability and use in diagnosing and planning treatments. However,…