Search NASA⌕ Search

SEARCH · Search NASA

Results for “Manifold model”

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 OSTI2023

Using Co-Optimized Machine Learned Manifolds for Modeling Chemically Reacting Flows

Chemically reacting flows play a key role in a wide range of engineered systems, from chemical and polymer processing to combustion-based energy conversion technologies. Simulations of these flows involve solving a coupled set of partial differential equations for mass, momentum, energy, and all relevant chemical species in the system. Chemical reaction pathways may be extremely complex and involve hundreds or more intermediate species, with reactions that occur over timescales varying by several orders of magnitude - presenting a significant numerical stiffness challenge. The combination of these factors makes simulation of chemically reacting flows vastly more expensive than nonreactive simulations, and often makes direct solution of the governing equations intractable. It is necessary to apply lower-fidelity models in place of the detailed governing equations in order to reduce computational cost to enable reacting flow simulation tools to be used in the engineering design process. Many of the models employed for this purpose are based on reducing the dimension of the thermochemical state, motivated by the observation that the observed thermochemical states in a system lie on a low-dimensional manifold in thermochemical state space. This behavior occurs due to the fast equilibration of certain reactive and transport processes, and physics-based manifold models rely on idealized assumptions about the balance of timescales and the way in which chemistry and transport are coupled. In this work, we apply a novel method for data-driven manifold-based modeling that can leverage data from high-fidelity reacting flow simulations to improve model accuracy in cases where the physics-based modeling assumptions break down. The approach is designed to be broadly applicable across chemically reacting flow systems but is applied here to turbulent combustion modeling.

machine learning↗
DOE OSTI2024

Domain-decomposition nonlinear manifold reduced order model

This software combines nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD) techniques. NM-ROMs, which utilize a shallow, sparse autoencoder trained with full order model (FOM) snapshot data, approximate the FOM state on a nonlinear manifold. These models offer advantages over linear-subspace ROMs (LS-ROMs) particularly in scenarios with slowly decaying Kolmogorov n-width. However, the training of NM-ROMs involves a number of parameters that scale with the size of the FOM, and storing high-dimensional FOM snapshots can significantly increase the cost of ROM training for extreme-scale problems. To mitigate these costs, the software employs DD to partition the FOM into smaller subdomains, computes NM-ROMs for each, and then integrates these to form a global NM-ROM. This strategy offers multiple benefits: it enables parallel training of subdomain NM-ROMs, reduces the number of parameters needed, decreases the dimensional requirements of subdomain FOM training data, and allows for customization to the unique characteristics of each FOM subdomain. The use of a shallow, sparse autoencoder architecture in each subdomain NM-ROM facilitates the application of hyper-reduction (HR), simplifying the nonlinear complexities and enhancing computational speed. This software marks the inaugural application of NM-ROM combined with HR to a DD problem. It features an algebraic DD reformulation of the FOM, training of NM-ROMs with HR for each subdomain, and employs a sequential quadratic programming (SQP) solver for the evaluation of the coupled global NMROM. The effectiveness of the DD NM-ROM with HR is numerically demonstrated on the 2D steady-state Burgers' equation, showing an order of magnitude improvement in accuracy over the DD LS-ROM with HR.

Diaz, AlejandroN↗
DOE OSTI2024

A fast and accurate domain decomposition nonlinear manifold reduced order model

Here, this paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each sub domain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

CMLM (Co-Optimized Machine-Learned Manifolds) [SWR-23-41]

Co-optimized Machine-Learned Manifolds (CMLM) is a data-driven approach for developing reduced-order manifold models for high-dimensional chemically reacting systems. It involves a specially designed neural network, the training of which simultaneously optimizes linear combinations of species that define the manifold, nonlinear mapping to outputs of interest such as reaction rates, and (optionally) subfilter closure for large eddy simulation. This software package provides an implementation of the CMLM approach in Python using the PyTorch machine learning library. A few example cases are included, showing how the tool can be applied to different types of data from 0D and 1D reacting simulations performed using Cantera. The neural networks can be saved in a format that is readable by the Pele suite of combustion solvers for use in reacting computational fluid dynamics simulations. This software repository contains several python scripts to perform various tasks associated with the Co-optimized Machine Learned Manifolds (CMLM) model, which is described in Perry, Henry de Frahan, and Yellapantula, CNF, 2022 (https://doi.org/10.1016/j.combustflame.2022.112286). This includes not only the code that defines the CMLM model, but also scripts to generate suitable training data, scripts to pre-process the data, scripts to train the CMLM model, and scripts to plot the output, as well as various other helper files. The scripts depend on several commonly used python libraries for data analysis and chemical reaction computations. The trained models that result from this tool are designed to work with the an interface being implemented in the Pele suite of reacting flow solvers (https://github.com/AMReX-Combustion).

Perry, Bruce↗
DOE OSTI2026

Data-based filtered dissipation rate modelling for multi-modal turbulent combustion: evaluating a priori model generalizability

Manifold-based models offer a computationally efficient alternative to directly transporting the thermochemical state in computational simulations of turbulent reacting flows, projecting the high-dimensional thermochemical state-space onto a low-dimensional manifold. Recent efforts have yielded a manifold-based model applicable to multi-modal combustion, enabling reconstruction of the thermochemical state from solutions to two-dimensional manifold equations in mixture fraction and generalized progress variable that are parameterised by three scalar dissipation rates. In coarse-grained simulations such as Large Eddy Simulation (LES), closure of the multi-modal manifold equations and subfilter variances/covariance requires closure of three filtered scalar dissipation rates. Here, the present work adopts a data-based approach, providing closure for the three filtered scalar dissipation rates via deep neural networks (DNNs). High-fidelity datasets corresponding to an autoigniting n-dodecane jet flame and a bluff body swirl-stabilized confined lifted spray flame of two aviation fuels (Jet-A and C1) with different ignition propensities are leveraged to generate training data that spans a diverse range of thermodynamic conditions and combustion modes, including low- and high-temperature ignition regimes in addition to premixed and nonpremixed behaviour. A final DNN model is trained to enforce inherent physical constraints by learning nonlinear functional transformations of the three filtered scalar dissipation rates. The generalizability of this constrained DNN model is demonstrated a priori via conditional statistics evaluated on the lifted spray flame with C1–a configuration that had not been included in the training data. Excellent DNN agreement with conditional DNS statistics is observed, and integrated gradients are computed to identify the most sensitive input variables. The similarity of the marginal PDFs of the most informative input variables and outputs across configurations are quantified via the Wasserstein metric, demonstrating that data-based models may successfully generalize to unseen parametric conditions so long as the most informative input variables share similar distributions across training and testing datasets.

Data-based modelling↗
DOE OSTI2025

Generative learning of densities on manifolds

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an Itô stochastic differential equation in the latent space. Additional realizations of the data are generated by lifting the samples back to the ambient space using Double Diffusion Maps , a recently introduced technique typically employed in studying dynamical system reduction; here the focus lies in sampling densities rather than system dynamics. The proposed approaches enable sampling high dimensional data densities restricted to low-dimensional, a priori unknown manifolds. The efficacy of the proposed framework is demonstrated through a benchmark problem and a material with multiscale structure.

Double diffusion maps↗
DOE OSTI2024

Nonlinear manifold reduced order model

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a lowdimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our software takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique.

Choi, Youngsoo↗
DOE OSTI2024

Learning physics-based reduced-order models from data using nonlinear manifolds

Here we present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Signature analysis of high-throughput transcriptomics screening data for mechanistic inference and chemical grouping

Abstract High-throughput transcriptomics (HTTr) uses gene expression profiling to characterize the biological activity of chemicals in in vitro cell-based test systems. As an extension of a previous study testing 44 chemicals, HTTr was used to screen an additional 1,751 unique chemicals from the EPA’s ToxCast collection in MCF7 cells using 8 concentrations and an exposure duration of 6 h. We hypothesized that concentration-response modeling of signature scores could be used to identify putative molecular targets and cluster chemicals with similar bioactivity. Clustering and enrichment analyses were conducted based on signature catalog annotations and ToxPrint chemotypes to facilitate molecular target prediction and grouping of chemicals with similar bioactivity profiles. Enrichment analysis based on signature catalog annotation identified known mechanisms of action (MeOAs) associated with well-studied chemicals and generated putative MeOAs for other active chemicals. Chemicals with predicted MeOAs included those targeting estrogen receptor (ER), glucocorticoid receptor (GR), retinoic acid receptor (RAR), the NRF2/KEAP/ARE pathway, AP-1 activation, and others. Using reference chemicals for ER modulation, the study demonstrated that HTTr in MCF7 cells was able to stratify chemicals in terms of agonist potency, distinguish ER agonists from antagonists, and cluster chemicals with similar activities as predicted by the ToxCast ER Pathway model. Uniform manifold approximation and projection (UMAP) embedding of signature-level results identified novel ER modulators with no ToxCast ER Pathway model predictions. Finally, UMAP combined with ToxPrint chemotype enrichment was used to explore the biological activity of structurally related chemicals. The study demonstrates that HTTr can be used to inform chemical risk assessment by determining in vitro points of departure, predicting chemicals’ MeOA and grouping chemicals with similar bioactivity profiles.

Toxicology↗
DOE OSTI2023

Data-driven prediction of α IIb β 3 integrin activation paths using manifold learning and deep generative modeling

The integrin heterodimer is a transmembrane protein critical for driving cellular process and is a therapeutic target in the treatment of multiple diseases linked to its malfunction. Activation of integrin involves conformational transitions between bent and extended states. Some of the conformations that are intermediate between bent and extended states of the heterodimer have been experimentally characterized, but the full activation pathways remain unresolved both experimentally due to their transient nature and computationally due to the challenges in simulating rare barrier crossing events in these large molecular systems. An understanding of the activation pathways can provide new fundamental understanding of the biophysical processes associated with the dynamic interconversions between bent and extended states and unveil new putative therapeutic targets. In this work, we apply nonlinear manifold learning to coarse-grained molecular dynamics simulations of bent, extended, and two intermediate states of αI I b β3 integrin to learn a low-dimensional embedding of the configurational phase space. We then train deep generative models to learn an inverse mapping between the low-dimensional embedding and high-dimensional molecular space and use these models to interpolate the molecular configurations constituting the activation pathways between the experimentally characterized states. Furthermore, this work furnishes plausible predictions of integrin activation pathways and reports a generic and transferable multi-scale technique to predict transition pathways for biomolecular systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

G2Aero: A Python package for separable shape tensors

G2Aero is a Python package for the design and deformation of discrete planar curves and tubular surfaces using a geometric data-driven approach. G2Aero utilizes a topology of product manifolds: the Grassmannian, $\mathcal{G}$($\mathcal{n}$, 2) - the set of 2-dimensional subspaces in $\mathbb{R}$ $\mathcal{n}$ - and the symmetric positive-definite (SPD) manifold, $\mathcal{S}^{2}_{++}$ - the set of 2x2 SPD matrices. The package provides a novel framework for representing separable deformations to shapes, which consist of stretching, scaling, rotating, and translating - also known as affine deformations - and a set of complementary deformations - which we refer to as undulation-type deformations. We focus on airfoil and blade design applications to emphasize the utility of the methods in an environment where the separation of affine and undulation-type deformations is critical. Notable functionalities of the framework for blade design include: 1) generating novel 2D (airfoil) shapes informed by a database of physically relevant airfoils, 2) building 3D blades by interpolating sequences of 2D airfoil cross-sections, and 3) generating blades with consistent perturbations along the blade span. We discuss the framework and provide examples in the context of wind energy applications, specifically wind turbine blade design. Figure 1 shows the wire frame obtained by interpolating airfoils defining the IEA 15-MW wind turbine blade and applying affine transformations corresponding to twist, chordal scaling, and bending. This, and all other figures in the paper, can be reproduced following examples and referencing supporting documentation provided in the G2Aero package.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Deep nonparametric estimation of intrinsic data structures by chart autoencoders: Generalization error and robustness

Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled near a low-dimensional manifold, we employ chart autoencoders, which encode data into low-dimensional latent features on a collection of charts, preserving the topology and geometry of the data manifold. Our paper establishes statistical guarantees on the generalization error of chart autoencoders, and we demonstrate their denoising capabilities by considering n noisy training samples, along with their noise-free counterparts, on a d-dimensional manifold. By training autoencoders, we show that chart autoencoders can effectively denoise the input data with normal noise. We prove that, under proper network architectures, chart autoencoders achieve a squared generalization error in the order of n–$\frac{2}{d+2}$log 4 n, which depends on the intrinsic dimension of the manifold and only weakly depends on the ambient dimension and noise level. We further extend our theory on data with noise containing both normal and tangential components, where chart autoencoders still exhibit a denoising effect for the normal component. As a special case, our theory also applies to classical autoencoders, as long as the data manifold has a global parametrization. Furthermore, our results provide a solid theoretical foundation for the effectiveness of autoencoders, which is further validated through several numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A manifold learning perspective on surrogate modeling of nitrate concentration in the Kansas River

Abstract A non-linear surrogate model of nitrate concentration in the Kansas River (USA) is described. The model is an (almost) Piece-wise Linear response surface that provides a mean field approximation to the dynamics of the measured data for nitrate plus nitrite (target product) correlations to turbidity and chlorophyll-a concentrations (input variables). The method extends the United States Geological Survey’s linear procedures for surrogate data modeling allowing for better approximations for river systems exhibiting algal blooms due to nutrient-rich source waters. The model and visualization procedures illustrated in the Kansas River example should be generally applicable to many medium-size rivers in agricultural regions.

Tufillaro, Nicholas (ORCID:0009000628968832)↗
DOE OSTI2023

Multifidelity uncertainty quantification with models based on dissimilar parameters

Multifidelity uncertainty quantification (MF UQ) sampling approaches have been shown to significantly reduce the variance of statistical estimators while preserving the bias of the highest-fidelity model, provided that the low-fidelity models are well correlated. However, maintaining a high level of correlation can be challenging, especially when models depend on different input uncertain parameters, which drastically reduces the correlation. Existing MF UQ approaches do not adequately address this issue. In this work, we propose a new sampling strategy that exploits a shared space to improve the correlation among models with dissimilar parameterization. We achieve this by transforming the original coordinates onto an auxiliary manifold using the adaptive basis (AB) method (Tipireddy and Ghanem, 2014). The AB method has two main benefits: (1) it provides an effective tool to identify the low-dimensional manifold on which each model can be represented, and (2) it enables easy transformation of polynomial chaos representations from high- to low-dimensional spaces. This latter feature is used to identify a shared manifold among models without requiring additional evaluations. Here we present two algorithmic flavors of the new estimator to cover different analysis scenarios, including those with legacy and non-legacy high-fidelity (HF) data. We provide numerical results for analytical examples, a direct field acoustic test, and a finite element model of a nuclear fuel assembly. For all examples, we compare the proposed strategy against both single-fidelity and MF estimators based on the original model parameterization.

42 ENGINEERING↗
DOE OSTI2024

NS5-brane backgrounds and coset CFT partition functions

Worldsheet string theory is solvable for a variety of backgrounds involving Neveu-Schwarz fivebranes, in terms of gauged nonlinear sigma models on group manifolds. We compute the worldsheet torus partition function of these models, and propose gauging of null isometries as a unifying principle and conceptual framework for this large family of string backgrounds. In the process, we explain how partition functions of asymmetrically gauged Wess-Zumino-Witten models can be computed from the path integral, and organize and systematize various results scattered throughout the literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

Here, this work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.

97 MATHEMATICS AND COMPUTING↗