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We consider the problem of approximating a subset $M$ of a Hilbert space $X$ by a low-dimensional manifold $M_n$, using samples from $M$. We propose a nonlinear approximation method where $M_n $ is defined as the range of a smooth nonlinear…

Raman spectroscopy is a label-free, chemically specific optical technique which provides detailed information about the chemical composition and structure of the excited analyte. Because of this, there is growing research interest in…

Machine learning promises to deliver powerful new approaches to neutron scattering from magnetic materials. Large scale simulations provide the means to realise this with approaches including spin-wave, Landau Lifshitz, and Monte Carlo…

Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One…

Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates…

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Microplastics (MPs) are ubiquitous pollutants with demonstrated potential to impact ecosystems and human health. Their microscopic size complicates detection, classification, and removal, especially in biological and environmental samples.…

Femtosecond laser fabrication enables the creation of a wide range of devices, but its scalability and yield can be limited by the lack of real-time, in-situ monitoring tools. In particular, there is a strong need for metrics that directly…

We introduce a scheme based on machine learning and deep neural networks to model the environmental dependence of the electronic polarizability in insulating materials. Application to liquid water shows that training the network with a…

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…

A data-driven framework was used to predict the macroscopic mechanical behavior of dense packings of polydisperse granular materials. The Discrete Element Method, DEM, was used to generate 92,378 sphere packings that covered many different…

Wide-angle light scattering (WALS) offers the possibility of a highly temporally and spatially resolved measurement of droplets in spray-based methods for nanoparticle synthesis. The size of these droplets is a critical variable affecting…

High-throughput computational screening of polymers offers a powerful way to address the imbalance between the vast number of polymers synthesised for diverse applications and the relatively small subset that can be studied using atomistic…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

Nonlinear manifold learning (ML) based reduced-order models (ROMs) can substantially improve the quality of nonlinear flow-field modeling. However, noise and the lack of physical information often distort the dimensionality-reduction…

Deep learning classifiers for Raman spectroscopy are increasingly reported to outperform classical chemometric approaches. However their evaluations are often conducted in isolation or compared against traditional machine learning methods…

Laser machining is a highly flexible non-contact manufacturing technique that has been employed widely across academia and industry. Due to nonlinear interactions between light and matter, simulation methods are extremely crucial, as they…

A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In this paper, we design a…

Reliable estimation of the raindrop size distribution (RSD) is important for applications including quantitative precipitation estimation, soil erosion modelling, and wind turbine blade erosion. While in situ instruments such as…