Related papers: GINN: Geometric Illustration of Neural Networks

Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative…

We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and…

Neural network models have shown outstanding performance and successful resolutions to complex problems in various fields. However, the majority of these models are viewed as black-box, requiring a significant amount of data for…

This work addresses the accurate and efficient simulation of physical phenomena governed by parametric Partial Differential Equations (PDEs) characterized by varying boundary conditions, where parametric instances modify not only the…

In this paper, we present a novel approach for detecting the discontinuity interfaces of a discontinuous function. This approach leverages Graph-Instructed Neural Networks (GINNs) and sparse grids to address discontinuity detection also in…

Model-based seismic inversion is a key technique in reservoir characterization, but traditional methods face significant limitations, such as relying on 1D average stationary wavelets and assuming an unrealistic lateral resolution. To…

Physically informed neural networks (PINNs) are a promising emerging method for solving differential equations. As in many other deep learning approaches, the choice of PINN design and training protocol requires careful craftsmanship. Here,…

Physics-Informed Neural Network (PINN) has proven itself a powerful tool to obtain the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the expressivity of deep neural networks and the computing power of…

We introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on…

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of…

Implicit Neural Representations (INRs) are widely used for modeling continuous 2D images, enabling high-fidelity reconstruction, super-resolution, and compression. Architectures such as SIREN, WIRE, and FINER demonstrate their ability to…

Motivated by the growing theoretical understanding of neural networks that employ the Rectified Linear Unit (ReLU) as their activation function, we revisit the use of ReLU activation functions for learning implicit neural representations…

The problem of multi-task regression over graph nodes has been recently approached through Graph-Instructed Neural Network (GINN), which is a promising architecture belonging to the subset of message-passing graph neural networks. In this…

In complex engineering systems such as electro-thermal-fluid coupling, rapid and accurate prediction of multi-physics fields is essential for advanced applications like digital twins and real-time condition monitoring. Traditional numerical…

Deep learning has been widely used in many fields, but the model training process usually consumes massive computational resources and time. Therefore, designing an efficient neural network training method with a provable convergence…

The present work investigates the use of physics-informed neural networks (PINNs) for the 3D reconstruction of unsteady gravity currents from limited data. In the PINN context, the flow fields are reconstructed by training a neural network…

Physics-Informed Neural Networks (PINNs) have emerged as a highly active research topic across multiple disciplines in science and engineering, including computational geomechanics. PINNs offer a promising approach in different applications…

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…

Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints. Their practical effectiveness however can be…

Graph neural network (GNN) is a popular tool to learn the lower-dimensional representation of a graph. It facilitates the applicability of machine learning tasks on graphs by incorporating domain-specific features. There are various options…