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Tag: operator

  • An operator splitting analysis of Wasserstein–Fisher–Rao gradient flows

    An operator splitting analysis of Wasserstein–Fisher–Rao gradient flows arXiv:2511.18060v1 Announce Type: new Abstract: Wasserstein-Fisher-Rao (WFR) gradient flows have been recently proposed as a powerful sampling tool that combines the advantages of pure Wasserstein (W) and pure Fisher-Rao (FR) gradient flows. Existing algorithmic developments implicitly make use of operator splitting techniques to numerically approximate the WFR…

  • Operator Models for Continuous-Time Offline Reinforcement Learning

    Operator Models for Continuous-Time Offline Reinforcement Learning arXiv:2511.10383v1 Announce Type: new Abstract: Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline reinforcement learning from historical data. However, there is limited statistical understanding of the approximation errors…

  • Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning

    Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning arXiv:2509.11070v1 Announce Type: new Abstract: 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 admit discrete spectral decompositions, and (ii) diagonal kernels of the form $K(x,x’)=k(x,x’)T$, where $k$…

  • Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations

    Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equations arXiv:2509.05186v1 Announce Type: new Abstract: In-context operator networks (ICON) are a class of operator learning methods based on the novel architectures of foundation models. Trained on a diverse set of datasets of initial and boundary conditions paired with corresponding solutions to…

  • Polynomial Chaos Expansion for Operator Learning

    Polynomial Chaos Expansion for Operator Learning arXiv:2508.20886v1 Announce Type: new Abstract: Operator learning (OL) has emerged as a powerful tool in scientific machine learning (SciML) for approximating mappings between infinite-dimensional functional spaces. One of its main applications is learning the solution operator of partial differential equations (PDEs). While much of the progress in this area…

  • Thompson Sampling in Function Spaces via Neural Operators

    Thompson Sampling in Function Spaces via Neural Operators arXiv:2506.21894v1 Announce Type: new Abstract: We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator’s output. We assume that functional evaluations are inexpensive, while queries to the operator (such as running a high-fidelity…

  • From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems

    From Local Interactions to Global Operators: Scalable Gaussian Process Operator for Physical Systems arXiv:2506.15906v1 Announce Type: new Abstract: Operator learning offers a powerful paradigm for solving parametric partial differential equations (PDEs), but scaling probabilistic neural operators such as the recently proposed Gaussian Processes Operators (GPOs) to high-dimensional, data-intensive regimes remains a significant challenge. In this…

  • Operator Learning for Schr”{o}dinger Equation: Unitarity, Error Bounds, and Time Generalization

    Operator Learning for Schr”{o}dinger Equation: Unitarity, Error Bounds, and Time Generalization arXiv:2505.18288v1 Announce Type: new Abstract: We consider the problem of learning the evolution operator for the time-dependent Schr”{o}dinger equation, where the Hamiltonian may vary with time. Existing neural network-based surrogates often ignore fundamental properties of the Schr”{o}dinger equation, such as linearity and unitarity, and…

  • Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels

    Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels arXiv:2504.18184v1 Announce Type: new Abstract: This paper investigates regularized stochastic gradient descent (SGD) algorithms for estimating nonlinear operators from a Polish space to a separable Hilbert space. We assume that the regression operator lies in a vector-valued reproducing kernel Hilbert space induced by an operator-valued…

  • Nonparametric Sparse Online Learning of the Koopman Operator

    Nonparametric Sparse Online Learning of the Koopman Operator arXiv:2501.16489v1 Announce Type: new Abstract: The Koopman operator provides a powerful framework for representing the dynamics of general nonlinear dynamical systems. Data-driven techniques to learn the Koopman operator typically assume that the chosen function space is closed under system dynamics. In this paper, we study the Koopman…