Related papers: Geometry-Informed Neural Networks

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving partial differential equations~(PDEs) in various scientific and engineering domains. However, traditional PINN architectures typically rely on large, fully…

Convolutional Neural Networks (CNNs) achieve impressive performance in a wide variety of fields. Their success benefited from a massive boost when very deep CNN models were able to be reliably trained. Despite their merits, CNNs fail to…

In this paper, we review the new method Physics-Informed Neural Networks (PINNs) that has become the main pillar in scientific machine learning, we present recent practical extensions, and provide a specific example in data-driven discovery…

Training deep graph neural networks (GNNs) is notoriously hard. Besides the standard plights in training deep architectures such as vanishing gradients and overfitting, it also uniquely suffers from over-smoothing, information squashing,…

Physics-informed neural networks (PINNs) have demonstrated promise in solving forward and inverse problems involving partial differential equations. Despite recent progress on expanding the class of problems that can be tackled by PINNs,…

Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the…

In this paper, we develop a deep learning approach for the accurate solution of challenging problems of near-field microscopy that leverages the powerful framework of physics-informed neural networks (PINNs) for the inversion of the complex…

Graph Neural Networks (GNNs) have become the state-of-the-art method for many applications on graph structured data. GNNs are a model for graph representation learning, which aims at learning to generate low dimensional node embeddings that…

Graph neural networks (GNNs) are the predominant approach for graph-based machine learning. While neural networks have shown great performance at learning useful representations, they are often criticized for their limited high-level…

Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…

Unsupervised learning for geometric perception (depth, optical flow, etc.) is of great interest to autonomous systems. Recent works on unsupervised learning have made considerable progress on perceiving geometry; however, they usually…

In this paper, we introduce a new deep learning framework for discovering the phase field models from existing image data. The new framework embraces the approximation power of physics informed neural networks (PINN), and the computational…

Physics-Informed Neural Networks (PINNs) are fast becoming an important tool to solve differential equations rapidly and accurately, and to identify the systems parameters that best agree with a given set of measurements. PINNs have been…

This article introduces Perception-Informed Neural Networks (PrINNs), a framework designed to incorporate perception-based information into neural networks, addressing both systems with known and unknown physics laws or differential…

Graph Neural Networks (GNNs) are the first choice for learning algorithms on graph data. GNNs promise to integrate (i) node features as well as (ii) edge information in an end-to-end learning algorithm. How does this promise work out…

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…

Recently, graph neural networks (GNNs) have proved to be suitable in tasks on unstructured data. Particularly in tasks as community detection, node classification, and link prediction. However, most GNN models still operate with static…

We present GERN, a novel scalable framework for training GNNs in node classification tasks, based on effective resistance, a standard tool in spectral graph theory. Our method progressively refines the GNN weights on a sequence of random…