相关论文: Multi-objective analysis of the Sand Hypoplasticit…
Stochastic Gradient Descent (SGD) is a cornerstone of large-scale optimization, yet its theoretical behavior under heavy-tailed noise -- common in modern machine learning and reinforcement learning -- remains poorly understood. In this…
We derive a phenomenological continuum saltation model for aeolian sand transport that can serve as an efficient tool for geomorphological applications. The coupled differential equations for the average density and velocity of sand in the…
Heavy-tail phenomena in stochastic gradient descent (SGD) have been reported in several empirical studies. Experimental evidence in previous works suggests a strong interplay between the heaviness of the tails and generalization behavior of…
We investigate the numerical performance of the regularized deconvolution closure introduced recently by the authors. The purpose of the closure is to furnish constitutive equations for Irwing-Kirkwood-Noll procedure, a well known method…
Stochastic Gradient Descent (SGD) has become the method of choice for solving a broad range of machine learning problems. However, some of its learning properties are still not fully understood. We consider least squares learning in…
Identifying relevant factors that influence the multinomial counts in compositional data is difficult in high dimensional settings due to the complex associations and overdispersion. Multivariate count models such as the…
Aggregate load modeling is of fundamental importance for systematic analysis and design of various demand response strategies. Instead of keeping track of the trajectories of individual loads, the aggregate modeling problem focuses on…
The ecophysiological response of plants to environmental heavy metal stress is indicated by the profile of its tissue HM concentrations (Cp) versus the concentration of the HM in the substrate (Cs). We report a systems biology approach to…
The experimental calorimetric two-state criterion requires the van't Hoff enthalpy $\Delta H_{\rm vH}$ around the folding/unfolding transition midpoint to be equal or very close to the calorimetric enthalpy $\Delta H_{\rm cal}$ of the…
We study the surface roughness of prototype models displaying self-organized criticality (SOC) and their noncritical variants in one dimension. For SOC systems, we find that two seemingly equivalent definitions of surface roughness yields…
Order parameter equations, such as the complex Swift-Hohenberg (CSH) equation, offer a simplified and universal description that hold close to an instability threshold. The universality of the description refers to the fact that the same…
Soil Organic Carbon (SOC) constitutes a fundamental component of terrestrial ecosystem functionality, playing a pivotal role in nutrient cycling, hydrological balance, and erosion mitigation. Precise mapping of SOC distribution is…
An in-situ Dynamic Mechanical Analysis (DMA) method for soft matter developed by our group [Wu. et.al. 2022] encounters the problem of irregular samples, which significantly vary in shape and size in practice, therefore a standard sample…
This paper studies sample average approximation (SAA) in solving convex or strongly convex stochastic programming (SP) problems. In estimating SAA's sample efficiency, the state-of-the-art sample complexity bounds entail metric entropy…
In this paper, the mathematical properties and numerical discretizations of multiphase models that simulate the phase separation of an $N$-component mixture are studied. For the general choice of phase variables, the unisolvent property of…
This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical…
Stochastic gradient descent (SGD) is central to simulation optimization, stochastic programming, and online M-estimation, where sampling effort is a decision variable. We study the mini-batch gradient noise as a sampling-design object.…
We present a novel inference approach that we call Sample Out-of-Sample (or SOS) inference. The approach can be used widely, ranging from semi-supervised learning to stress testing, and it is fundamental in the application of data-driven…
Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method for solving the fluid equations that is commonplace in astrophysics, prized for its natural adaptivity and stability. The choice of variable to smooth in SPH has been the topic of…
Charge-density waves are responsible for symmetry-breaking displacements of atoms and concomitant changes in the electronic structure. Linear response theories, in particular density-functional perturbation theory, provide a way to study…