Related papers: A stochastic method to compute the $L^2$ localisat…
The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential…
In this paper, we propose a method to perform empirical analysis of the loss landscape of machine learning (ML) models. The method is applied to two ML models for scientific sensing, which necessitates quantization to be deployed and are…
We present here a model of carrier distribution and transport in semiconductor alloys accounting for quantum localization effects in disordered materials. This model is based on the recent development of a mathematical theory of quantum…
Eldan's stochastic localization is a probabilistic construction that has proved instrumental to modern breakthroughs in high-dimensional geometry and the design of sampling algorithms. Motivated by sampling under non-Euclidean geometries…
We report an attempt to calculate energy eigenvalues of large quantum systems by the diagonalization of an effectively truncated Hamiltonian matrix. For this purpose we employ a specific way to systematically make a set of orthogonal states…
The current burst in research activities on disordered semiconductors calls for the development of appropriate theoretical tools that reveal the features of electron states in random potentials while avoiding the time-consuming numerical…
In order to efficiently explore the chemical space of all possible small molecules, a common approach is to compress the dimension of the system to facilitate downstream machine learning tasks. Towards this end, we present a data driven…
In the context of Monte Carlo sampling for lattice models, the complexity of the energy landscape often leads to Markov chains being trapped in local optima, thereby increasing the correlation between samples and reducing sampling…
The stationary points of the potential energy function of the \phi^4 model on a two-dimensional square lattice with nearest-neighbor interactions are studied by means of two numerical methods: a numerical homotopy continuation method and a…
Motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes (PELs) for several statistical mechanics models, we perform a numerical study of the finite size $2$-spin spherical model using both…
We have performed a detailed exploration of the energy landscape for configurations of points on the sphere, interacting via the logarithmic potential, and corresponding to local minima of the total energy, up to $N = 160$. The growth of…
The application of geostatistical and machine learning methods based on Gaussian processes to big space-time data is beset by the requirement for storing and numerically inverting large and dense covariance matrices. Computationally…
Based on the concept of a nonequilibrium steady state, we present a novel method to experimentally determine energy landscapes acting on colloidal systems. By measuring the stationary probability distribution and the current in the system,…
Anticipating the low energy arrangements of atoms in space is an indispensable scientific task. Modern stochastic approaches to searching for these configurations depend on the optimisation of structures to nearby local minima in the energy…
We propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A classical approach for generating these samples is the…
We study rough high-dimensional landscapes in which an increasingly stronger preference for a given configuration emerges. Such energy landscapes arise in glass physics and inference. In particular we focus on random Gaussian functions, and…
Energy landscapes provide a conceptual framework for structure prediction, and a detailed understanding of their topological features is necessary to develop efficient methods for their exploration. The ability to visualise these surfaces…
Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive…
We develop a Bayesian Land Surface Phenology (LSP) model and examine its performance using Enhanced Vegetation Index (EVI) observations derived from the Harmonized Landsat Sentinel-2 (HLS) dataset. Building on previous work, we propose a…
High-dimensional networks producing oscillatory dynamics are ubiquitous in biological systems. Unravelling the mechanism of oscillatory dynamics in biological networks with stochastic perturbations becomes paramountly significant. Although…