Related papers: Improving Long-Range Interactions in Graph Neural …

Reasoning system dynamics is one of the most important analytical approaches for many scientific studies. With the initial state of a system as input, the recent graph neural networks (GNNs)-based methods are capable of predicting the…

Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems. In many application domains across science and engineering,…

Simulation of the dynamics of physical systems is essential to the development of both science and engineering. Recently there is an increasing interest in learning to simulate the dynamics of physical systems using neural networks.…

In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit…

Quantum simulators have the potential to solve quantum many-body problems that are beyond the reach of classical computers, especially when they feature long-range entanglement. To fulfill their prospects, quantum simulators must be fully…

We explore the use of Physics Informed Neural Networks to analyse nonlinear Hamiltonian Dynamical Systems with a first integral of motion. In this work, we propose an architecture which combines existing Hamiltonian Neural Network…

Recurrent neural networks (RNNs) have gained a great deal of attention in solving sequential learning problems. The learning of long-term dependencies, however, remains challenging due to the problem of a vanishing or exploding hidden…

Graph neural networks (GNNs) are widely used for modelling graph-structured data in numerous applications. However, with their inherently finite aggregation layers, existing GNN models may not be able to effectively capture long-range…

The great learning ability of deep learning models facilitates us to comprehend the real physical world, making learning to simulate complicated particle systems a promising endeavour. However, the complex laws of the physical world pose…

Simulating object deformations is a critical challenge across many scientific domains, including robotics, manufacturing, and structural mechanics. Learned Graph Network Simulators (GNSs) offer a promising alternative to traditional…

Simulating complex dynamics like fluids with traditional simulators is computationally challenging. Deep learning models have been proposed as an efficient alternative, extending or replacing parts of traditional simulators. We investigate…

Neural networks with physics based inductive biases such as Lagrangian neural networks (LNN), and Hamiltonian neural networks (HNN) learn the dynamics of physical systems by encoding strong inductive biases. Alternatively, Neural ODEs with…

Graph Neural Networks (GNNs) have become the standard for graph representation learning but remain vulnerable to structural perturbations. We propose a novel framework that integrates persistent homology features with stability…

Simulating rigid collisions among arbitrary shapes is notoriously difficult due to complex geometry and the strong non-linearity of the interactions. While graph neural network (GNN)-based models are effective at learning to simulate…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

The Ice-sheet and Sea-level System Model (ISSM) provides numerical solutions for ice sheet dynamics using finite element and fine mesh adaption. However, considering ISSM is compatible only with central processing units (CPUs), it has…

Graph Neural Networks (GNNs) have emerged as powerful tools for various graph mining tasks, yet existing scalable solutions often struggle to balance execution efficiency with prediction accuracy. These difficulties stem from iterative…

Data-centric methods have shown great potential in understanding and predicting spatiotemporal dynamics, enabling better design and control of the object system. However, deep learning models often lack interpretability, fail to obey…

Graph neural networks (GNNs) have emerged as a powerful tool for effectively mining and learning from graph-structured data, with applications spanning numerous domains. However, most research focuses on static graphs, neglecting the…

Graphs are a highly expressive abstraction for modeling entities and their relations, such as molecular structures, social networks, and traffic networks. Deep Graph Networks (DGNs) have emerged as a family of deep learning models that can…