Related papers: MIONet: Learning multiple-input operators via tens…

Neural Operator Networks (ONets) represent a novel advancement in machine learning algorithms, offering a robust and generalizable alternative for approximating partial differential equations (PDEs) solutions. Unlike traditional Neural…

Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…

Multimodal learning has shown great potentials in numerous scenes and attracts increasing interest recently. However, it often encounters the problem of missing modality data and thus suffers severe performance degradation in practice. To…

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of…

Ground settlement prediction during the process of mechanized tunneling is of paramount importance and remains a challenging research topic. Typically, two paradigms are existing: a physics-driven approach utilizing process-oriented…

We give a self-contained and introductory account of some basic functional analytic tools needed to understand maximal monotone operators in Hilbert spaces. We review domains of (possibly unbounded) operators, closed sets and closed…

Neural network based approximate computing is a universal architecture promising to gain tremendous energy-efficiency for many error resilient applications. To guarantee the approximation quality, existing works deploy two neural networks…

The study of operator learning involves the utilization of neural networks to approximate operators. Traditionally, the focus has been on single-operator learning (SOL). However, recent advances have rapidly expanded this to include the…

Future intelligent robots are expected to process multiple inputs simultaneously (such as image and audio data) and generate multiple outputs accordingly (such as gender and emotion), similar to humans. Recent research has shown that…

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…

Operator learning is a recent development in the simulation of Partial Differential Equations (PDEs) by means of neural networks. The idea behind this approach is to learn the behavior of an operator, such that the resulting neural network…

This paper introduces a novel theoretical framework for the analysis of vector-valued neural networks through the development of vector-valued variation spaces, a new class of reproducing kernel Banach spaces. These spaces emerge from…

This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…

Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…

Generative models in function spaces, situated at the intersection of generative modeling and operator learning, are attracting increasing attention due to their immense potential in diverse scientific and engineering applications. While…

Neural processes have recently emerged as a class of powerful neural latent variable models that combine the strengths of neural networks and stochastic processes. As they can encode contextual data in the network's function space, they…

Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning…

Neural networks and particularly Deep learning have been comparatively little studied from the theoretical point of view. Conversely, Mathematical Morphology is a discipline with solid theoretical foundations. We combine these domains to…

Neural operators are capable of capturing nonlinear mappings between infinite-dimensional functional spaces, offering a data-driven approach to modeling complex functional relationships in classical density functional theory (cDFT). In this…