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Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale, in the context of multi-scale simulation given a periodic micro-structure mesh and mean, macro-scale, stress…

Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…

The paper presents an efficient and robust data-driven deep learning (DL) computational framework developed for linear continuum elasticity problems. The methodology is based on the fundamentals of the Physics Informed Neural Networks…

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

Nuclear physics experiments are aimed at uncovering the fundamental building blocks of matter. The experiments involve high-energy collisions that produce complex events with many particle trajectories. Tracking charged particles resulting…

Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and…

Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution while a PDE-induced NN is coupled to the solution NN,…

Image segmentation is a fundamental task in computer vision. Data annotation for training supervised methods can be labor-intensive, motivating unsupervised methods. Current approaches often rely on extracting deep features from pre-trained…

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

Graph Neural Networks (GNNs) have emerged as the predominant approach for learning over graph-structured data. However, most GNNs operate as black-box models and require post-hoc explanations, which may not suffice in high-stakes scenarios…

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…

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,…

Graph Neural Networks (GNNs) are key tools for graph representation learning, demonstrating strong results across diverse prediction tasks. In this paper, we present Convexified Message-Passing Graph Neural Networks (CGNNs), a novel and…

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a…

Information on natural phenomena and engineering systems is typically contained in data. Data can be corrupted by systematic errors in models and experiments. In this paper, we propose a tool to uncover the spatiotemporal solution of the…

Recent work has demonstrated that geometric deep learning methods such as graph neural networks (GNNs) are well suited to address a variety of reconstruction problems in high energy particle physics. In particular, particle tracking data is…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into…

Data-driven discovery of governing equations in computational science has emerged as a new paradigm for obtaining accurate physical models and as a possible alternative to theoretical derivations. The recently developed physics-informed…