Search NASA⌕ Search

SEARCH · Search NASA

Results for “Latent variable”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Latent variable Gaussian process models: A rank‐based analysis and an alternative approach

Abstract Gaussian process (GP) models have been extended to emulate expensive computer simulations with both qualitative/categorical and quantitative/continuous variables. Latent variable (LV) GP models, which have been recently developed to map each qualitative variable to some underlying numerical LVs, have strong physics‐based justification and have achieved promising performance. Two versions use LVs in Cartesian (LV‐Car) space and hyperspherical (LV‐sph) space, respectively. Despite their success, the effects of these different LV structures are still poorly understood. This article illuminates this issue with two contributions. First, we develop a theorem on the effect of the ranks of the qualitative factor correlation matrices of mixed‐variable GP models, from which we conclude that the LV‐sph model restricts the interactions between the input variables and thus restricts the types of response surface data with which the model can be consistent. Second, following a rank‐based perspective like in the theorem, we propose a new alternative model named LV‐mix that combines the LV‐based correlation structures from both LV‐Car and LV‐sph models to achieve better model flexibility than them. Through extensive case studies, we show that LV‐mix achieves higher average accuracy compared with the existing two.

Tao, Siyu↗
DOE OSTI2025

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗
DOE OSTI2021

Toward Decoding the Relationship between Domain Structure and Functionality in Ferroelectrics via Hidden Latent Variables

Polarization switching mechanisms in ferroelectric materials are fundamentally linked to local domain structure and the presence of the structural defects, which both can act as nucleation and pinning centers and create local electrostatic and mechanical depolarization fields affecting wall dynamics. However, the general correlative mechanisms between domain structure and polarization dynamics are only weakly explored, precluding insight into the associated physical mechanisms. In this work, the correlation between local domain structures and switching behavior in ferroelectric materials is explored using convolutional encoder–decoder networks, enabling image to spectral (im2spec) and spectral to image (spec2im) translations via encoding of latent variables. The latter reflect the assumption that the relationship between domain structure and polarization switching is parsimonious, i.e., is based upon a small number of local mechanisms. The analysis of latent variables distributions and their real-space representations provides insight into the predictability of the local switching behavior and hence associated physical mechanisms. We further pose that the regions where these correlative relationships are violated, i.e., predictability of the polarization dynamics from domain structure is reduced, represent the obvious target for detailed studies, e.g., in the context of automated experiments. This approach provides a workflow to establish the presence of correlation between local spectral responses and local structure and can be universally applied to spectral imaging techniques such as piezoresponse force microscopy (PFM), scanning tunneling microscopy (STM) and spectroscopy, and electron energy loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM).

36 MATERIALS SCIENCE↗
DOE OSTI2025

A Latent-Variable Formulation of the Poisson Canonical Polyadic Tensor Model: Maximum Likelihood Estimation and Fisher Information

We establish parameter inference for the Poisson canonical polyadic (PCP) tensor model through a latent-variable formulation. Our approach exploits the observation that any random PCP tensor can be derived by marginalizing an unobservable random tensor of one dimension larger. The loglikelihood of this larger dimensional tensor, referred to as the “complete” loglikelihood, is comprised of multiple rank one PCP loglikelihoods. Using this methodology, we first derive maximum likelihood estimators for the PCP model and demonstrate that several existing algorithms for fitting non-negative matrix and tensor factorizations are Expectation-Maximization algorithms. Next, we derive the observed and expected Fisher information matrices for the PCP model. The Fisher information provides us crucial insights into the well-posedness of the tensor model, such as the role that tensor rank plays in identifiability and indeterminacy. For the special case of rank one PCP models, we demonstrate that these results are greatly simplified.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Mapping Post-Climate Change Biogeographical Regions with Deep Latent Variable Models

Forecasting future changes to biodiversity due to shifts in climate is challenging due to nonlinear interactions between species as recorded in their presence/absence data. This work proposes using variational autoencoders with environmental covariates to identify low-dimensional structure in species’ joint co-occurrence patterns and leveraging this simplified representation to provide multivariate predictions of their habitat extent under future climate scenarios. We pursue a latent space clustering approach to map biogeographical regions of frequently co-occurring species and apply this methodology to a dataset from northern Belgium, generating predictive maps illustrating how these regions may expand or contract with changing temperature under a future climate scenario.

Krapu, Chris↗
DOE OSTI2021

Deep-freeze graph training for latent learning

Scientific and engineering advances are primarily driven by multi-tier conceptual constructs and conditional theoretical frameworks. The theories allow predictions of hypothetical system responses, given a set of approximate conditions (ranges of applicability) imposed on latent parameters that cannot be measured directly. Learning to estimate the latent variables (Latent Learning) helps to pinpoint the anticipated range-edge anomalies and improves the confidence in interpretation, interpolation and extrapolation of limited experimental data. Due to high dimensionality and extreme non-linearity of the materials science problems, very large datasets are typically required for conventional data-driven model development. The vital experimental data collection, particularly on microstructural phases, is very challenging, which makes it difficult to compile a high-quality database. Incorporation of the domain knowledge into the computational graph structure, initialization and optimization processes presents a viable mechanism for developing accurate models, with limited datasets. Furthermore, this study successfully utilized the approach to build the Deep Freeze Graph (DeepFreG) by mapping known causality relationships and by digitizing empirical domain knowledge for Latent Learning (LL), with specific applications in materials science.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Towards sharp error analysis of extended Lagrangian molecular dynamics

The extended Lagrangian molecular dynamics (XLMD) method provides a useful framework for reducing the computational cost of a class of molecular dynamics simulations with constrained latent variables. The XLMD method relaxes the constraints by introducing a fictitious mass ε for the latent variables and solving a set of singularly perturbed ordinary differential equations. While favorable numerical performance of XLMD has been demonstrated in several different contexts in the past decade, mathematical analysis of the method remains scarce. Here, we propose the first error analysis of the XLMD method in the context of a classical polarizable force field model. While the dynamics with respect to the atomic degrees of freedom are general and nonlinear, the key mathematical simplification of the polarizable force field model is that the constraints on the latent variables are given by a linear system of equations. We prove that when the initial value of the latent variables is compatible in a sense that we define, XLMD converges as the fictitious mass ε is made small with $\mathscr{O}$(ε) error for the atomic degrees of freedom and with $\mathscr{O}$($\sqrt{ε}$) error for the latent variables, when the dimension of the latent variable d' is 1. Furthermore, when the initial value of the latent variables is improved to be optimally compatible in a certain sense, we prove that the convergence rate can be improved to $\mathscr{O}$(ε) for the latent variables as well. Numerical results verify that both estimates are sharp not only for d'=1, but also for arbitrary d'. In the setting of general d', we do obtain convergence, but with the non-sharp rate of $\mathscr{O}$($\sqrt{ε}$) for both the atomic and latent variables.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

How do perceptions of safety and car ownership importance affect autonomous vehicle adoption?

In this study, we explicitly modeled how individuals' perceptions of automated vehicle (AV) safety and the importance they place on car ownership affect mode choices involving conventional and automated vehicles in the context of privately owned cars and ridehailing services. We adopted psychometric questions to capture these two latent variables and designed a stated preference survey based on the participants' actual travel patterns. Then, we quantified the impact of these latent variables on mode choices using an integrated choice and latent variable (ICLV) model. We found that both latent variables have a statistically significant effect on mode choices. The results show that car ownership importance has the most potent effect on privately owned cars (conventional car and self-driving car), followed by driverless ridehailing and conventional ridehailing. We also found that changes in safety perception are equivalent to sizable changes in price. In addition, we further investigated the impact of improvements in safety perception through four scenarios. The scenario testing results show that as the distribution of perceived safety is compressed toward positive safety perception, the market share of AVs spikes and dominates regular cars. Our results demonstrate that based on our respondents' current understanding of AVs, even if AV prices were comparable to regular cars, we cannot expect widespread use of AVs. However, improvements in AVs' safety and, consequently, consumer safety perception can considerably expand AVs' market share, and may offset the high cost of using the technology.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Multi-objective, robust constraints enforced global topology optimizer for optical devices

A method for optimization of photonic devices is disclosed. The method includes receiving a set of unconstrained latent variables; mapping the set of unconstrained latent variables to a constrained space to generate a constrained device; calculating the permittivity across each element of the constrained device; determining a permittivity-constrained width gradient based at least partially on the permittivity across each element; and optimizing the set of unconstrained latent variables by at least partially using the permittivity-constrained width gradient.

Fan, Jonathan↗
DOE OSTI2023

A Graphical Model for Fusing Diverse Microbiome Data

This paper develops a Bayesian graphical model for fusing disparate types of count data. The motivating application is the study of bacterial communities from diverse high-dimensional features, in this case, transcripts, collected from different treatments. In such datasets, there are no explicit correspondences between the communities and each corresponds to different factors, making data fusion challenging. We introduce a flexible multinomial-Gaussian generative model for jointly modeling such count data. This latent variable model jointly characterizes the observed data through a common multivariate Gaussian latent space that parameterizes the set of multinomial probabilities of the transcriptome counts. The covariance matrix of the latent variables induces a covariance matrix of co-dependencies between all the transcripts, effectively fusing multiple data sources. We present a computationally scalable variational Expectation-Maximization (EM) algorithm for inferring the latent variables and the parameters of the model. Here, the inferred latent variables provide a common dimensionality reduction for visualizing the data and the inferred parameters provide a predictive posterior distribution. In addition to simulation studies that demonstrate the variational EM procedure, we apply our model to a bacterial microbiome dataset.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Do-calculus enables estimation of causal effects in partially observed biomolecular pathways

Abstract Motivation Estimating causal queries, such as changes in protein abundance in response to a perturbation, is a fundamental task in the analysis of biomolecular pathways. The estimation requires experimental measurements on the pathway components. However, in practice many pathway components are left unobserved (latent) because they are either unknown, or difficult to measure. Latent variable models (LVMs) are well-suited for such estimation. Unfortunately, LVM-based estimation of causal queries can be inaccurate when parameters of the latent variables are not uniquely identified, or when the number of latent variables is misspecified. This has limited the use of LVMs for causal inference in biomolecular pathways. Results In this article, we propose a general and practical approach for LVM-based estimation of causal queries. We prove that, despite the challenges above, LVM-based estimators of causal queries are accurate if the queries are identifiable according to Pearl’s do-calculus and describe an algorithm for its estimation. We illustrate the breadth and the practical utility of this approach for estimating causal queries in four synthetic and two experimental case studies, where structures of biomolecular pathways challenge the existing methods for causal query estimation. Availability and implementation The code and the data documenting all the case studies are available at https://github.com/srtaheri/LVMwithDoCalculus. Supplementary information Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

A simple introduction to the SiMPL method for density-based topology optimization

We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounced as “the simple method”) optimizes a design using only first-order derivative information of the objective function. The bound constraints on the density field are enforced with the help of the (negative) Fermi–Dirac entropy, which is also used to define a non-symmetric distance function called a Bregman divergence on the set of admissible designs. This Bregman divergence leads to a simple update rule that is further simplified with the help of a so-called latent variable. Because the SiMPL method involves discretizing the latent variable, it produces a sequence of pointwise-feasible iterates, even when high-order finite elements are used in the discretization. Numerical experiments demonstrate that the method outperforms other popular first-order optimization algorithms. In conclusion, to outline the general applicability of the technique, we include examples with (self-load) compliance minimization and compliant mechanism optimization problems.

Calculus of Variations and Optimization↗
DOE OSTI2021

Disentangling ferroelectric domain wall geometries and pathways in dynamic piezoresponse force microscopy via unsupervised machine learning

In this work, domain switching pathways in ferroelectric materials visualized by dynamic piezoresponse force microscopy (PFM) are explored via variational autoencoder, which simplifies the elements of the observed domain structure, crucially allowing for rotational invariance, thereby reducing the variability of local polarization distributions to a small number of latent variables. For small sampling window sizes the latent space is degenerate, and variability is observed only in the direction of a single latent variable that can be identified with the presence of domain wall. For larger window sizes, the latent space is 2D, and the disentangled latent variables can be generally interpreted as the degree of switching and complexity of domain structure. Applied to multiple consecutive PFM images acquired while monitoring domain switching, the polarization switching mechanism can thus be visualized in the latent space, providing insight into domain evolution mechanisms and their correlation with the microstructure.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Towards interpretable Cryo-EM: disentangling latent spaces of molecular conformations

Molecules are essential building blocks of life and their different conformations (i.e., shapes) crucially determine the functional role that they play in living organisms. Cryogenic Electron Microscopy (cryo-EM) allows for acquisition of large image datasets of individual molecules. Recent advances in computational cryo-EM have made it possible to learn latent variable models of conformation landscapes. However, interpreting these latent spaces remains a challenge as their individual dimensions are often arbitrary. The key message of our work is that this interpretation challenge can be viewed as an Independent Component Analysis (ICA) problem where we seek models that have the property of identifiability. That means, they have an essentially unique solution, representing a conformational latent space that separates the different degrees of freedom a molecule is equipped with in nature. Thus, we aim to advance the computational field of cryo-EM beyond visualizations as we connect it with the theoretical framework of (nonlinear) ICA and discuss the need for identifiable models, improved metrics, and benchmarks. Moving forward, we propose future directions for enhancing the disentanglement of latent spaces in cryo-EM, refining evaluation metrics and exploring techniques that leverage physics-based decoders of biomolecular systems. Moreover, we discuss how future technological developments in time-resolved single particle imaging may enable the application of nonlinear ICA models that can discover the true conformation changes of molecules in nature. The pursuit of interpretable conformational latent spaces will empower researchers to unravel complex biological processes and facilitate targeted interventions. This has significant implications for drug discovery and structural biology more broadly. More generally, latent variable models are deployed widely across many scientific disciplines. Thus, the argument we present in this work has much broader applications in AI for science if we want to move from impressive nonlinear neural network models to mathematically grounded methods that can help us learn something new about nature.

59 BASIC BIOLOGICAL SCIENCES↗