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Found 5 papers, 0 papers with code
Generative modeling of Sparse Approximate Inverse Preconditioners
We present a new deep learning paradigm for the generation of sparse approximate inverse (SPAI) preconditioners for matrix systems arising from the mesh-based discretization of elliptic differential operators.
Investigating Guiding Information for Adaptive Collocation Point Sampling in PINNs
Physics-informed neural networks (PINNs) provide a means of obtaining approximate solutions of partial differential equations and systems through the minimisation of an objective function which includes the evaluation of a residual function at a set of collocation points within the domain.
Understanding the Efficacy of U-Net & Vision Transformer for Groundwater Numerical Modelling
This paper presents a comprehensive comparison of various machine learning models, namely U-Net, U-Net integrated with Vision Transformers (ViT), and Fourier Neural Operator (FNO), for time-dependent forward modelling in groundwater systems.
Attention U-Net as a surrogate model for groundwater prediction
This manuscript presents an Attention U-Net model that attempts to capture the fundamental input-output relations of the groundwater system and generates solutions of hydraulic head in the whole domain given a set of physical parameters and boundary conditions.
MeshingNet: A New Mesh Generation Method based on Deep Learning
The framework that we have developed is based around training an artificial neural network (ANN) to guide standard mesh generation software, based upon a prediction of the required local mesh density throughout the domain.
