Density estimation in RKHS with application to Korobov spaces in high dimensions

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The electron density is an important object in quantum chemistry that is crucial for many downstream tasks in drug design. Recent deep learning approaches predict the electron density around a molecule from atom types and atom positions. Most of these meth ...

We study the glass transition by exploring a broad class of kinetic rules that can significantly modify the normal dynamics of supercooled liquids while maintaining thermal equilibrium. Beyond the usual dynamics of liquids, this class includes dynamics in ...

We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a d -dimensional simple hypercubic lattice, in the limit of infinite dimensionality d -> infinity . In the analysis we ...

The Super-X Divertor (SXD) is an alternative divertor configuration leveraging total flux expansion at the Outer Strike Point (OSP). While the extended 2-Point Model (2PM) predicts facilitated detachment access and control in the SXD configuration, these a ...

We consider fluid flows, governed by the Navier-Stokes equations, subject to a steady symmetry-breaking bifurcation and forced by a weak noise acting on a slow timescale. By generalizing the multiple-scale weakly nonlinear expansion technique employed in t ...

Pyroelectricity in a recently developed all-organic composite electret with a polar polynorbornene-based filler and polydimethylsiloxane (PDMS) matrix has been studied with the help of thermal and dielectric techniques. Measurement of the pyroelectric p co ...

This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposi ...

We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of Double-struck capital R. An order-1 autoregressive model in this context is to be understood as a Markov chain, where ...

As large, data-driven artificial intelligence models become ubiquitous, guaranteeing high data quality is imperative for constructing models. Crowdsourcing, community sensing, and data filtering have long been the standard approaches to guaranteeing or imp ...

We propose a novel approach to evaluating the ionic Seebeck coefficient in electrolytes from relatively short equilibrium molecular dynamics simulations, based on the Green-Kubo theory of linear response and Bayesian regression analysis. By exploiting the ...

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

In the context of discrete choice modeling, the extraction of potential behavioral insights from large datasets is often limited by the poor scalability of maximum likelihood estimation. This paper proposes a simple and fast dataset-reduction method that i ...

In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and the network width ...

Random Fourier features (RFFs) provide a promising way for kernel learning in a spectral case. Current RFFs-based kernel learning methods usually work in a two-stage way. In the first-stage process, learn-ing an optimal feature map is often formulated as a ...

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for time-dependent n ...

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...

Given a hyperelliptic hyperbolic surface S of genus g >= 2, we find bounds on the lengths of homologically independent loops on S. As a consequence, we show that for any lambda is an element of (0, 1) there exists a constant N(lambda) such that every such ...

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, ...

Density estimation in RKHS with application to Korobov spaces in high dimensions

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Lagnet: Better Electron Density Prediction for Lcao-based Data and Drug-like Substances

Testing Theories of the Glass Transition with the Same Liquid but Many Kinetic Rules

Frustrated magnets in the limit of infinite dimensions: Dynamics and disorder-free glass transition

Parallel flows as a key component to interpret Super-X divertor experiments

Noise-induced transitions past the onset of a steady symmetry-breaking bifurcation: The case of the sudden expansion

Pyroelectricity in poled all-organic polar polynorbornene/polydimethylsiloxane-based stretchable electrets

High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization

On distributional autoregression and iterated transportation

Extensions of Peer Prediction Incentive Mechanisms

Seebeck Coefficient of Ionic Conductors from Bayesian Regression Analysis

Towards Trustworthy Deep Learning for Image Reconstruction

Resampling estimation of discrete choice models

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Bayes-optimal Learning of Deep Random Networks of Extensive-width

End-to-end kernel learning via generative random Fourier features

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Detecting whether a stochastic process is finitely expressed in a basis

Short homology bases for hyperelliptic hyperbolic surfaces

Stochastic particle transport by deep-water irregular breaking waves