We propose the geometry-informed neural operator (GINO), a highly efficient approach to
learning the solution operator of large-scale partial differential equations with varying …

We estimate the expressive power of certain deep neural networks (DNNs for short) on a
class of countably-parametric, holomorphic maps u: U→ ℝ on the parameter domain U=[− 1 …

Learning approximations to smooth target functions of many variables from finite sets of
pointwise samples is an important task in scientific computing and its many applications in …

We propose an efficient, deterministic algorithm for constructing exponentially convergent
deep neural network (DNN) approximations of multivariate, analytic maps f:[-1, 1] K→ R. We …

We establish universality and expression rate bounds for a class of neural Deep Operator
Networks (DON) emulating Lipschitz (or H\" older) continuous maps $\mathcal G:\mathcal …

Approximation rates are analyzed for deep surrogates of maps between infinite-dimensional
function spaces, arising, eg, as data-to-solution maps of linear and nonlinear partial …

Approximation rates are analyzed for deep surrogates of maps between infinite-dimensional
function spaces, arising eg as data-to-solution maps of linear and nonlinear partial …

For time-harmonic electromagnetic waves scattered by either perfectly conducting or
dielectric bounded obstacles, we show that the fields depend holomorphically on the shape …

We analyse convergence rates of Smolyak integration for parametric maps u: U→ X taking
values in a Banach space X, defined on the parameter domain U=[− 1, 1] N. For parametric …

We analyze the complexity of the sparse-grid interpolation and sparse-grid quadrature of
countably-parametric functions which take values in separable Banach spaces with …