相关论文: Multi-parameter optimization of attenuation data f…
Lossy data transformations by definition lose information. Yet, in modern machine learning, methods like data pruning and lossy data augmentation can help improve generalization performance. We study this paradox using a solvable model of…
The present paper studies existence and distributional uniqueness of subclasses of stationary hard-core particle systems arising as thinnings of stationary particle processes. These subclasses are defined by natural maximality criteria. We…
Metals and alloys fabricated by fusion-based additive manufacturing (AM), or 3D printing, undergo complex dynamics of melting and solidification, presenting challenges to the effective control of grain structure. Herein, we report on the…
Autoencoders are a prominent model in many empirical branches of machine learning and lossy data compression. However, basic theoretical questions remain unanswered even in a shallow two-layer setting. In particular, to what degree does a…
We address a three-dimensional, coarse-grained description of dislocation networks at grain boundaries between rotated crystals. The so-called amplitude expansion of the phase-field crystal model is exploited with the aid of finite element…
Distributed optimization algorithms are widely used in machine learning. This paper investigates how a small amount of data sharing can improve their performance. Focusing on general linear models, we analyze the effects of data sharing on…
This paper investigates the statistical behavior of two-dimensional grain microstructures during grain growth under anisotropic grain boundary characters. We employ the threshold-dynamics method, which allows for unparalleled computational…
We modify a theory of flow stress introduced in [arXiv:1803.08247[cond-mat.mtrl-sci]], [arXiv:1809.03628[cond-mat.mes-hall]], [arXiv:1908.09338[cond-mat.mtrl-sci]] for a class of polycrystalline materials with equilibrium and…
The method is described and tested for analysis of statistical parameters of reduced neutron widths distributions accounting for possibility of coexistence of superposition of some functions with non-zero mean values of neutron amplitude…
Discovering relationships between materials' microstructures and mechanical properties is a key goal of materials science. Here, we outline a strategy exploiting Bayesian optimization to efficiently search the multidimensional space of…
Atomistic simulations of the molecular dynamics/statics kind are regularly used to study small scale plasticity. Contemporary simulations are performed with tens to hundreds of millions of atoms, with snapshots of these configurations…
The choice of batch-size in a stochastic optimization algorithm plays a substantial role for both optimization and generalization. Increasing the batch-size used typically improves optimization but degrades generalization. To address the…
In this paper, we establish the almost sure convergence of two-timescale stochastic gradient descent algorithms in continuous time under general noise and stability conditions, extending well known results in discrete time. We analyse…
We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…
We solve a coarsening system with small but arbitrary anisotropic surface tension and interface mobility. The resulting size-dependent growth shapes are significantly different from equilibrium microcrystallites, and have a distribution of…
We develop a stochastic-dynamic framework to infer latent grain size distribution from magnetic hysteresis data in M-type hexaferrite materials, offering an alternative to imaging-based characterization. A stochastic nucleation-growth…
We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a…
We study the effect of polydispersity on the macroscopic physical properties of granular packings in two and three dimensions. A mean-field approach is developed to approximate the macroscale quantities as functions of the microscopic ones.…
Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine.…
Extracting the grain size from the microscopic images is a rigorous task involving much human expertise and manual effort. While calculating the grain size, we will be utilizing a finite number of particles which may lead to an uncertainty…