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Chemical abundances of stellar streams can be used to determine the nature of a stream's progenitor. Here we study the progenitor of the recently discovered Leiptr stellar stream, which was previously suggested to be a tidally disrupted halo globular cluster. We obtain high-resolution spectra of five red giant branch stars selected from the Gaia DR2 STREAMFINDER catalog with Magellan/MIKE. One star is a clear non-member. The remaining four stars display chemical abundances consistent with those of a low-mass dwarf galaxy: they have a low mean metallicity, $\langle{\rm[Fe/H]}\rangle = -2.2$; they do not all have identical metallicities; and they display low [$\alpha$/Fe] $\sim 0$ and [Sr/Fe] and [Ba/Fe] $\sim -1$. This pattern of low $\alpha$ and neutron-capture element abundances is only found in intact dwarf galaxies with stellar mass $\lesssim 10^5 M_\odot$. Although more data are needed to be certain, Leiptr's chemistry is consistent with being the lowest-mass dwarf galaxy stream without a known intact progenitor, possibly in the mass range of ultra-faint dwarf galaxies. Leiptr thus preserves a record of one of the lowest-mass early accretion events into the Milky Way., Comment: 18 pages, 12 figures, 8 tables, to be submitted to The Open Journal of Astrophysics

We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches capture phenomena taking into account thermal and dissipative energy exchanges, hydrodynamic coupling, and correlated spontaneous fluctuations. Our methods allow for modeling non-uniform time-varying temperature fields, fluid momentum fields, and their impacts on particle drift-diffusion dynamics. We show how practical stochastic numerical methods can be developed for these systems by performing analysis to factor operators analytically to obtain efficient algorithms for generating the fluctuating fields. We demonstrate our methods in a few simulation studies showing how they can be used to capture particle heating of the interface and the roles of thermal gradients on hydrodynamic fluctuations. The methods developed provide modeling and simulation approaches that can be used for further investigations of non-equilibrium phenomena in active soft materials, complex fluids, and biophysical systems., Comment: 21 pages, 5 figures

The semantic similarity between documents of a text corpus can be visualized using map-like metaphors based on two-dimensional scatterplot layouts. These layouts result from a dimensionality reduction on the document-term matrix or a representation within a latent embedding, including topic models. Thereby, the resulting layout depends on the input data and hyperparameters of the dimensionality reduction and is therefore affected by changes in them. Furthermore, the resulting layout is affected by changes in the input data and hyperparameters of the dimensionality reduction. However, such changes to the layout require additional cognitive efforts from the user. In this work, we present a sensitivity study that analyzes the stability of these layouts concerning (1) changes in the text corpora, (2) changes in the hyperparameter, and (3) randomness in the initialization. Our approach has two stages: data measurement and data analysis. First, we derived layouts for the combination of three text corpora and six text embeddings and a grid-search-inspired hyperparameter selection of the dimensionality reductions. Afterward, we quantified the similarity of the layouts through ten metrics, concerning local and global structures and class separation. Second, we analyzed the resulting 42817 tabular data points in a descriptive statistical analysis. From this, we derived guidelines for informed decisions on the layout algorithm and highlight specific hyperparameter settings. We provide our implementation as a Git repository at https://github.com/hpicgs/Topic-Models-and-Dimensionality-Reduction-Sensitivity-Study and results as Zenodo archive at https://doi.org/10.5281/zenodo.12772898., Comment: To be published at IEEE VIS 2024 conference

Standard datasets are frequently used to train and evaluate Machine Learning models. However, the assumed standardness of these datasets leads to a lack of in-depth discussion on how their labels match the derived categories for the respective use case. In other words, the standardness of the datasets seems to fog coherency and applicability, thus impeding the trust in Machine Learning models. We propose to adopt Grounded Theory and Hypotheses Testing through Visualization as methods to evaluate the match between use case, derived categories, and labels of standard datasets. To showcase the approach, we apply it to the 20 Newsgroups dataset and the MNIST dataset. For the 20 Newsgroups dataset, we demonstrate that the labels are imprecise. Therefore, we argue that neither a Machine Learning model can learn a meaningful abstraction of derived categories nor one can draw conclusions from achieving high accuracy. For the MNIST dataset, we demonstrate how the labels can be confirmed to be defined well. We conclude that a concept of standardness of a dataset implies that there is a match between use case, derived categories, and class labels, as in the case of the MNIST dataset. We argue that this is necessary to learn a meaningful abstraction and, thus, improve trust in the Machine Learning model.

Scientists often model physical processes to understand the natural world and uncover the causation behind observations. Due to unavoidable simplification, discrepancies often arise between model predictions and actual observations, in the form of systematic biases, whose impact varies with model completeness. Classical model inversion methods such as Bayesian inference or regressive neural networks tend either to overlook biases or make assumptions about their nature during data preprocessing, potentially leading to implausible results. Inspired by recent work in inverse graphics, we replace the decoder stage of a standard autoencoder with a physical model followed by a bias-correction layer. This generalisable approach simultaneously inverts the model and corrects its biases in an end-to-end manner without making strong assumptions about the nature of the biases. We demonstrate the effectiveness of our approach using two physical models from disparate domains: a complex radiative transfer model from remote sensing; and a volcanic deformation model from geodesy. Our method matches or surpasses results from classical approaches without requiring biases to be explicitly filtered out, suggesting an effective pathway for understanding the causation of various physical processes., Comment: arXiv admin note: text overlap with arXiv:2403.02922

Scientific datasets present unique challenges for machine learning-driven compression methods, including more stringent requirements on accuracy and mitigation of potential invalidating artifacts. Drawing on results from compressed sensing and rate-distortion theory, we introduce effective data compression methods by developing autoencoders using high dimensional latent spaces that are $L^1$-regularized to obtain sparse low dimensional representations. We show how these information-rich latent spaces can be used to mitigate blurring and other artifacts to obtain highly effective data compression methods for scientific data. We demonstrate our methods for short angle scattering (SAS) datasets showing they can achieve compression ratios around two orders of magnitude and in some cases better. Our compression methods show promise for use in addressing current bottlenecks in transmission, storage, and analysis in high-performance distributed computing environments. This is central to processing the large volume of SAS data being generated at shared experimental facilities around the world to support scientific investigations. Our approaches provide general ways for obtaining specialized compression methods for targeted scientific datasets., Comment: 11 pages, 6 figures

We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii) to approximate Partial Differential Equations (PDEs) on manifolds, (iii) learn solution maps for Laplace-Beltrami (LB) operators, and (iv) to solve Bayesian inverse problems for identifying manifold shapes. The methods allow for handling geometries of general shape including point-cloud representations. The developed GNPs provide approaches for incorporating the roles of geometry in data-driven learning of operators.

Advances in machine learning have boosted the use of Earth observation data for climate change research. Yet, the interpretability of machine-learned representations remains a challenge, particularly in understanding forests' biophysical reactions to climate change. Traditional methods in remote sensing that invert radiative transfer models (RTMs) to retrieve biophysical variables from spectral data often fail to account for biases inherent in the RTM, especially for complex forests. We propose to integrate RTMs into an auto-encoder architecture, creating an end-to-end learning approach. Our method not only corrects biases in RTMs but also outperforms traditional techniques for variable retrieval like neural network regression. Furthermore, our framework has potential generally for inverting biased physical models. The code is available on https://github.com/yihshe/ai-refined-rtm.git.

Topic models are a class of unsupervised learning algorithms for detecting the semantic structure within a text corpus. Together with a subsequent dimensionality reduction algorithm, topic models can be used for deriving spatializations for text corpora as two-dimensional scatter plots, reflecting semantic similarity between the documents and supporting corpus analysis. Although the choice of the topic model, the dimensionality reduction, and their underlying hyperparameters significantly impact the resulting layout, it is unknown which particular combinations result in high-quality layouts with respect to accuracy and perception metrics. To investigate the effectiveness of topic models and dimensionality reduction methods for the spatialization of corpora as two-dimensional scatter plots (or basis for landscape-type visualizations), we present a large-scale, benchmark-based computational evaluation. Our evaluation consists of (1) a set of corpora, (2) a set of layout algorithms that are combinations of topic models and dimensionality reductions, and (3) quality metrics for quantifying the resulting layout. The corpora are given as document-term matrices, and each document is assigned to a thematic class. The chosen metrics quantify the preservation of local and global properties and the perceptual effectiveness of the two-dimensional scatter plots. By evaluating the benchmark on a computing cluster, we derived a multivariate dataset with over 45 000 individual layouts and corresponding quality metrics. Based on the results, we propose guidelines for the effective design of text spatializations that are based on topic models and dimensionality reductions. As a main result, we show that interpretable topic models are beneficial for capturing the structure of text corpora. We furthermore recommend the use of t-SNE as a subsequent dimensionality reduction., Comment: To be published at IEEE VIS 2023 conference

We introduce adversarial learning methods for data-driven generative modeling of the dynamics of $n^{th}$-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable $m$-step stochastic numerical integrators. We introduce different formulations and training methods for learning models of stochastic dynamics based on observation of trajectory samples. We develop approaches using discriminators based on Maximum Mean Discrepancy (MMD), training protocols using conditional and marginal distributions, and methods for learning dynamic responses over different time-scales. We show how our approaches can be used for modeling physical systems to learn force-laws, damping coefficients, and noise-related parameters. The adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems., Comment: 7 figures

We develop computational methods that incorporate shear into fluctuating hydrodynamics methods. We are motivated by the rheological responses of complex fluids and soft materials. Our approach is based on continuum stochastic hydrodynamic equations that are subject to shear boundary conditions on the unit periodic cell in a manner similar to the Lees-Edwards conditions of molecular dynamics. Our methods take into account consistently the microstructure elastic mechanics, fluid-structure hydrodynamic coupling, and thermal fluctuations. For practical simulations, we develop numerical methods for efficient stochastic field generation that handle the sheared generalized periodic boundary conditions. We show that our numerical methods are consistent with fluctuation dissipation balance and near-equilibrium statistical mechanics. As a demonstration in practice, we present several prototype rheological response studies. These include (i) shear thinning of a polymeric fluid, (ii) complex moduli for the oscillatory responses of a polymerized lipid vesicle, and (iii) aging under shear of a gel-like material., Comment: software: http://atzberger.org, https://github.com/atzberg/mango-selm. arXiv admin note: text overlap with arXiv:0910.5739

We introduce exponential numerical integration methods for stiff stochastic dynamical systems of the form $d\mathbf{z}_t = L(t)\mathbf{z}_tdt + \mathbf{f}(t)dt + Q(t)d\mathbf{W}_t$. We consider the setting of time-varying operators $L(t), Q(t)$ where they may not commute $L(t_1)L(t_2) \neq L(t_2)L(t_1)$, raising challenges for exponentiation. We develop stochastic numerical integration methods using Mangus expansions for preserving statistical structures and for maintaining fluctuation-dissipation balance for physical systems. For computing the contributions of the fluctuation terms, our methods provide alternative approaches without needing directly to evaluate stochastic integrals. We present results for our methods for a class of SDEs arising in particle simulations and for SPDEs for fluctuations of concentration fields in spatially-extended systems. For time-varying stochastic dynamical systems, our introduced discretization approaches provide general exponential numerical integrators for preserving statistical structures while handling stiffness., Comment: 7 figures

We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. We develop approaches for learning nonlinear state space models of the dynamics for general manifold latent spaces using training strategies related to Variational Autoencoders (VAEs). Our methods are referred to as Geometric Dynamic (GD) Variational Autoencoders (GD-VAEs). We learn encoders and decoders for the system states and evolution based on deep neural network architectures that include general Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and Transpose CNNs (T-CNNs). Motivated by problems arising in parameterized PDEs and physics, we investigate the performance of our methods on tasks for learning low dimensional representations of the nonlinear Burgers equations, constrained mechanical systems, and spatial fields of reaction-diffusion systems. GD-VAEs provide methods for obtaining representations for use in diverse learning tasks involving dynamics., Comment: 15 figures. arXiv admin note: text overlap with arXiv:2012.03448

We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic strength, protein kinetics, and self-assembly of clusters. We perform simulation studies for model spine geometries varying the neck size to investigate how phase-separation and protein organization is influenced by different shapes. We also show how our methods can be used to study the roles of geometry in reaction-diffusion systems including Turing instabilities. Our methods provide general approaches for investigating protein kinetics and drift-diffusion dynamics within curved membrane structures.

MLMOD is a software package for incorporating machine learning approaches and models into simulations of microscale mechanics and molecular dynamics in LAMMPS. Recent machine learning approaches provide promising data-driven approaches for learning representations for system behaviors from experimental data and high fidelity simulations. The package faciliates learning and using data-driven models for (i) dynamics of the system at larger spatial-temporal scales (ii) interactions between system components, (iii) features yielding coarser degrees of freedom, and (iv) features for new quantities of interest characterizing system behaviors. MLMOD provides hooks in LAMMPS for (i) modeling dynamics and time-step integration, (ii) modeling interactions, and (iii) computing quantities of interest characterizing system states. The package allows for use of machine learning methods with general model classes including Neural Networks, Gaussian Process Regression, Kernel Models, and other approaches. Here we discuss our prototype C++/Python package, aims, and example usage. The package is integrated currently with the mesocale and molecular dynamics simulation package LAMMPS and PyTorch. For related papers, examples, updates, and additional information see https://github.com/atzberg/mlmod and http://atzberger.org/.

We develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics $d\mathbf{X}_t = a(\mathbf{X}_t)dt + \mathbf{b}(\mathbf{X}_t)d\mathbf{W}_t$. We formulate descriptions of Brownian motion and general drift-diffusion processes on surfaces. We consider statistics of the form $u(\mathbf{x}) = \mathbb{E}^{\mathbf{x}}\left[\int_0^\tau g(\mathbf{X}_t)dt \right] + \mathbb{E}^{\mathbf{x}}\left[f(\mathbf{X}_\tau)\right]$ for a domain $\Omega$ and the exit stopping time $\tau = \inf_t \{t > 0 \; |\; \mathbf{X}_t \not\in \Omega\}$, where $f,g$ are general smooth functions. For computing these statistics, we develop high-order Generalized Moving Least Squares (GMLS) solvers for associated surface PDE boundary-value problems based on Backward-Kolmogorov equations. We focus particularly on the mean First Passage Times (FPTs) given by the case $f = 0,\, g = 1$ where $u(\mathbf{x}) = \mathbb{E}^{\mathbf{x}}\left[\tau\right]$. We perform studies for a variety of shapes showing our methods converge with high-order accuracy both in capturing the geometry and the surface PDE solutions. We then perform studies showing how statistics are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities.

We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning from observations nonlinear state space models. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems.