Related papers: Scalar Field Prediction on Meshes Using Interpolat…

Detecting a specific horizon in seismic images is a valuable tool for geological interpretation. Because hand-picking the locations of the horizon is a time-consuming process, automated computational methods were developed starting three…

Partial differential equations (PDEs) have become an essential tool for modeling complex physical systems. Such equations are typically solved numerically via mesh-based methods, such as finite element methods, with solutions over the…

This work presents a machine learning approach to predict peak-stress clusters in heterogeneous polycrystalline materials. Prior work on using machine learning in the context of mechanics has largely focused on predicting the effective…

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical…

In this paper we design a neural interpolation operator to improve the boundary data for regional weather models, which is a challenging problem as we are required to map multi-scale dynamics between grid resolutions. In particular, we…

Temporal interpolation often plays a crucial role to learn meaningful representations in dynamic scenes. In this paper, we propose a novel method to train spatiotemporal neural radiance fields of dynamic scenes based on temporal…

Thermal errors in machine tools significantly impact machining precision and productivity. Traditional thermal error correction/compensation methods rely on measured temperature-deformation fields or on transfer functions. Most existing…

This paper presents a neural scheme for the topology-aware interpolation of time-varying scalar fields. Given a time-varying sequence of persistence diagrams, along with a sparse temporal sampling of the corresponding scalar fields, denoted…

This study presents a data-driven spatial interpolation algorithm based on physics-informed graph neural networks used to develop national temperature-at-depth maps for the conterminous United States. The model was trained to approximately…

A data-driven framework for spatial-temporal prediction is proposed for reducing the computational cost of industrial thermal striping applications. The framework aims to efficiently identify the flow features and utilize them in…

As the role played by statistical and computational sciences in climate and environmental modelling and prediction becomes more important, Machine Learning researchers are becoming more aware of the relevance of their work to help tackle…

Understanding the nonlinear dynamics of coupled scalar fields often necessitates simulations on a 3D mesh. These simulations can be computationally expensive if a large scale separation is involved. A common solution is adaptive mesh…

The mechanical problem discussed in this paper focuses on the stress state estimation in a composite laminate in the vicinity of a free edge or microcracks. To calculate these stresses, we use two models called Multiparticle Models of…

Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them…

We explore the application of a Convolutional Neural Network (CNN) to image the shear modulus field of an almost incompressible, isotropic, linear elastic medium in plane strain using displacement or strain field data. This problem is…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

Robust and scalable function evaluation at any arbitrary point in the finite/spectral element mesh is required for querying the partial differential equation solution at points of interest, comparison of solution between different meshes,…

The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

In this paper, based on neural networks, we develop a data-driven model for extremely fast prediction of steady-state heat convection of a hot object with arbitrary complex geometry in a two-dimensional space. According to the governing…

Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural…