Related papers: Learning time-dependent PDE via graph neural netwo…

Graph Neural Networks (GNNs) have made significant advances on several fundamental inference tasks. As a result, there is a surge of interest in using these models for making potentially important decisions in high-regret applications.…

Graph Neural Networks (GNNs) are gaining extensive attention for their application in graph data. However, the black-box nature of GNNs prevents users from understanding and trusting the models, thus hampering their applicability. Whereas…

The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…

Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical…

Graph neural networks (GNNs) learn the representation of graph-structured data, and their expressiveness can be further enhanced by inferring node relations for propagation. Attention-based GNNs infer neighbor importance to manipulate the…

In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two…

The Deep Operator Network (DeepONet) structure has shown great potential in approximating complex solution operators with low generalization errors. Recently, a sequential DeepONet (S-DeepONet) was proposed to use sequential learning models…

Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional…

The study of partial differential equations (PDE) through the framework of deep learning emerged a few years ago leading to the impressive approximations of simple dynamics. Graph neural networks (GNN) turned out to be very useful in those…

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a…

We present a data-driven control framework for partial differential equations (PDEs). Our approach integrates Time-Integrated Deep Operator Networks (TI-DeepONets) as differentiable PDE surrogate models within the Differentiable Predictive…

Operator learning has emerged as a promising tool for accelerating the solution of partial differential equations (PDEs). The Deep Operator Networks (DeepONets) represent a pioneering framework in this area: the "vanilla" DeepONet is valued…

Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state configurations, which complicates the task of encompassing all…

We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented…

Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space…

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…