Related papers: Dynamic Gaussian Graph Operator: Learning parametr…

Deep Gaussian Process (DGP) models offer a powerful nonparametric approach for Bayesian inference, but exact inference is typically intractable, motivating the use of various approximations. However, existing approaches, such as mean-field…

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to…

A common theoretical approach to understanding neural networks is to take an infinite-width limit, at which point the outputs become Gaussian process (GP) distributed. This is known as a neural network Gaussian process (NNGP). However, the…

We present an operator learning framework for solving non-perturbative functional renormalization group equations, which are integro-differential equations defined on functionals. Our proposed approach uses Gaussian process operator…

Predicting time-dependent dynamics of complex systems governed by non-linear partial differential equations (PDEs) with varying parameters and domains is a challenging task motivated by applications across various fields. We introduce a…

Graph Neural Networks (GNNs) are important across different domains, such as social network analysis and recommendation systems, due to their ability to model complex relational data. This paper introduces subgraph queries as a new task for…

Modelling robot dynamics accurately is essential for control, motion optimisation and safe human-robot collaboration. Given the complexity of modern robotic systems, dynamics modelling remains non-trivial, mostly in the presence of…

Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint…

Dynamic graph neural networks (DGNNs) have emerged as a leading paradigm for learning from dynamic graphs, which are commonly used to model real-world systems and applications. However, due to the evolving nature of dynamic graph data…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…

The prosperity of computer vision (CV) and natural language procession (NLP) in recent years has spurred the development of deep learning in many other domains. The advancement in machine learning provides us with an alternative option…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…

Graph representation learning aims to encode all nodes of a graph into low-dimensional vectors that will serve as input of many compute vision tasks. However, most existing algorithms ignore the existence of inherent data distribution and…

Learning the mapping between two function spaces has garnered considerable research attention. However, learning the solution operator of partial differential equations (PDEs) remains a challenge in scientific computing. Fourier neural…

Graph learning (GL) can dynamically capture the distribution structure (graph structure) of data based on graph convolutional networks (GCN), and the learning quality of the graph structure directly influences GCN for semi-supervised…

In this work, we use Deep Gaussian Processes (DGPs) as statistical surrogates for stochastic processes with complex distributions. Conventional inferential methods for DGP models can suffer from high computational complexity as they require…

Recent advances in Deep Gaussian Processes (DGPs) show the potential to have more expressive representation than that of traditional Gaussian Processes (GPs). However, there exists a pathology of deep Gaussian processes that their learning…

Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution…