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A method for numerical approximation of a new class of fractional parabolic stochastic evolution equations is introduced and analysed. This class of equations has recently been proposed as a space-time extension of the SPDE-method in…
This paper introduces Generalized Nonnegative Structured Kruskal Tensor Regression (NS-KTR), a novel tensor regression framework that enhances interpretability and performance through mode-specific hybrid regularization and nonnegativity…
Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically…
We consider the Gaussian ensembles of random matrices and describe the normal modes of the eigenvalue spectrum, i.e., the correlated fluctuations of eigenvalues about their most probable values. The associated normal mode spectrum is…
Shapley values have several desirable, theoretically well-supported, properties for explaining black-box model predictions. Traditionally, Shapley values are computed post-hoc, leading to additional computational cost at inference time. To…
Existing numerical methods for modeling magnetization in thin type-II superconducting films have mostly been developed for flat films. This work introduces an efficient spectral method for axisymmetric magnetization problems involving…
In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
We study the implementation of a Chebyshev spectral method with forward Euler integrator to investigate a peridynamic nonlocal formulation of Richards' equation. We prove the convergence of the fully-discretization of the model showing the…
Molecular property regression struggles with cases in chemically relevant target ranges that are underrepresented in datasets. Standard average error minimization approaches underperform in these highly relevant cases, and oversampling…
In this work we study the scalar power spectrum and the spectral index for the Starobinsky inflationary model using the phase integral method up-to third-order of approximation. We show that the semiclassical methods reproduce the scalar…
It has been observed that the performances of many high-dimensional estimation problems are universal with respect to underlying sensing (or design) matrices. Specifically, matrices with markedly different constructions seem to achieve…
We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition…
We present a numerical spectral method to solve systems of differential equations on an infinite interval $y\in (-\infty, \infty)$ in presence of linear differential operators of the form $Q(y) \left(\partial/\partial_y\right)^b$ (where…
Sequential scientific data span many resolutions and domains, and unifying them into a common representation is a key step toward developing foundation models for the sciences. Astronomical spectra exemplify this challenge: massive surveys…
Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum…
The numerical approximation of partial differential equations (PDEs) poses formidable challenges in high dimensions since classical grid-based methods suffer from the so-called curse of dimensionality. Recent attempts rely on a combination…
The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior.…