Related papers: IKNO: Infinite-order Kernel Neural Operators

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…

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. While these operators perform effectively in either the time or frequency domain, their performance may be limited when applied to…

Koopman operator theory is a popular candidate for data-driven modeling because it provides a global linearization representation for nonlinear dynamical systems. However, existing Koopman operator-based methods suffer from shortcomings in…

We consider solving a probably infinite dimensional operator equation, where the operator is not modeled by physical laws but is specified indirectly via training pairs of the input-output relation of the operator. Neural operators have…

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…

Neural Operators (NOs) have emerged as powerful tools for learning mappings between function spaces. Among them, the kernel integral operator has been widely used in universally approximating architectures. Following the original…

We propose Super-resolution Neural Operator (SRNO), a deep operator learning framework that can resolve high-resolution (HR) images at arbitrary scales from the low-resolution (LR) counterparts. Treating the LR-HR image pairs as continuous…

Inverse Optimization (IO) is a framework for learning the unknown objective function of an expert decision-maker from a past dataset. In this paper, we extend the hypothesis class of IO objective functions to a reproducing kernel Hilbert…

Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…

In computational physics, a longstanding challenge lies in finding numerical solutions to partial differential equations (PDEs). Recently, research attention has increasingly focused on Neural Operator methods, which are notable for their…

Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator…

The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture allows for the evaluation of the solution field at any…

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…

The Monte Carlo-type Neural Operator (MCNO) introduces a framework for learning solution operators of one-dimensional partial differential equations (PDEs) by directly learning the kernel function and approximating the associated integral…

Topology optimization is a critical task in engineering design, where the goal is to optimally distribute material in a given space for maximum performance. We introduce Neural Implicit Topology Optimization (NITO), a novel approach to…

Operator learning is reshaping scientific computing by amortizing inference across infinite families of problems. While neural operators (NOs) are increasingly well understood for regression, far less is known for classification and its…

Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring…

As artificial intelligence emerges as a transformative enabler for fusion energy commercialization, fast and accurate solvers become increasingly critical. In magnetic confinement nuclear fusion, rapid and accurate solution of the…