Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Variational”

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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

DeepPhenoMem V1.0: deep learning modelling of canopy greenness dynamics accounting for multi-variate meteorological memory effects on vegetation phenology

Abstract. Vegetation phenology plays a key role in controlling the seasonality of ecosystem processes that modulate carbon, water and energy fluxes between the biosphere and atmosphere. Accurate modelling of vegetation phenology in the interplay of Earth's surface and the atmosphere is thus crucial to understand how the coupled system will respond to and shape climatic changes. Phenology is controlled by meteorological conditions at different timescales: on the one hand, changes in key meteorological variables (temperature, water, radiation) can have immediate effects on the vegetation development; on the other hand, phenological changes can be driven by past environmental conditions, known as memory effects. However, the processes governing meteorological memory effects on phenology are not completely understood, resulting in their limited performance of vegetation phenology represented in land surface models. A deep learning model, specifically a long short-term memory network (LSTM), has the potential to capture and model the meteorological memory effects on vegetation phenology. Here, we apply the LSTM to model the vegetation phenology using meteorological drivers and high-temporal-resolution canopy greenness observations through digital repeat photography by the PhenoCam network. We compare a multiple linear regression model, a no-memory-effect LSTM model and a full-memory-effect LSTM model to predict the whole seasonal greenness trajectory and the corresponding phenological transition dates across 50 sites and 317 site years during 2009–2018, covering deciduous broadleaf forests, evergreen needleleaf forests and grasslands. Results show that the deep learning model outperforms the multiple linear regression model, and the full-memory-effect LSTM model performs better than the no-memory-effect model for all three plant function types (median R2 of 0.878, 0.957 and 0.955 for broadleaf forests, evergreen needleleaf forests and grasslands). We also find that the full-memory-effect LSTM model is capable of predicting the seasonal dynamic variations of canopy greenness and reproducing trends in shifting phenological transition dates. We also performed a sensitivity analysis of the full-memory-effect LSTM model to assess its plausibility, revealing its coherence with established knowledge of vegetation phenology sensitivity to meteorological conditions, particularly changes in temperature. Our study highlights that (1) multi-variate meteorological memory effects play a crucial role in vegetation phenology, and (2) deep learning opens up new avenues for improving the representation of vegetation phenological processes in land surface models via a hybrid modelling approach.

Geology↗
DOE OSTI2025

3D Continuous Forcing Dataset from 3D Constrained Variational Analysis at SGP

The continuous 3D large-scale forcing (VARANAL3D) data set derived from 3D constrained variational analysis (3DCVA) extends the conventional constrained variational analysis method by incorporating multiple sub-columns within the analysis domain. This advancement introduces spatial variability into the large-scale forcing fields, thereby enriching the data set’s applicability. The VARANAL3D data set spans from 2004 to 2018 and covers a region of 5˚×4.5˚ domain around the ARM SGP site. The analysis domain is divided into 10×9 sub-columns with 0.5˚ resolution. The 3D large-scale forcing data provides necessary variables to drive and evaluate single-column models (SCM), cloud-resolving models (CRM) ,and large-eddy simulations (LES), as well as information for testing model sensitivity to spatial variability of the large-scale forcing data, facilitating more rigorous testing and refinement of physical processes in SCM/CRM/LES.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Removing Rotational Variations from Shoulder Thermocouples in Friction Stir Welding

Thick plate and lower temperature friction stir welding results in good post-weld properties by welding at very low tool rotational speeds. Low speeds cause large variations in the measured shoulder temperature, making temperature control difficult. This paper describes a computationally light method to correct for oscillating measured temperatures. Data is collected over the previous two revolutions and used to build a compensation table and calculate a derivative. In simulation, measured temperature variations are reduced by a factor of five to ten. Temperature data is preserved and not cornered, nor is any time delay induced by this method, unlike with filtering methods.

Friction Stir Welding, Temperature↗
DOE OSTI2022

Reducing the cost of energy estimation in the variational quantum eigensolver algorithm with robust amplitude estimation

Quantum chemistry and materials is one of the most promising applications of quantum computing. Yet much work is still to be done in matching industry-relevant problems in these areas with quantum algorithms that can solve them. Most previous efforts have carried out resource estimations for quantum algorithms run on large-scale fault-tolerant architectures, which include the quantum phase estimation algorithm. In contrast, few have assessed the performance of near-term quantum algorithms, which include the variational quantum eigensolver (VQE) algorithm. Recently, a large-scale benchmark study [Gonthier et al. 2020] found evidence that the performance of the variational quantum eigensolver for a set of industry-relevant molecules may be too inefficient to be of practical use. This motivates the need for developing and assessing methods that improve the efficiency of VQE. In this work, we predict the runtime of the energy estimation subroutine of VQE when using robust amplitude estimation (RAE) to estimate Pauli expectation values. Under conservative assumptions, our resource estimation predicts that RAE can reduce the runtime over the standard estimation method in VQE by one to two orders of magnitude. Despite this improvement, we find that the runtimes are still too large to be practical. These findings motivate two complementary efforts towards quantum advantage: 1) the investigation of more efficient near-term methods for ground state energy estimation and 2) the development of problem instances that are of industrial value and classically challenging, but better suited to quantum computation.

Johnson, Peter D.↗
DOE OSTI2022

Fermionic approach to variational quantum simulation of Kitaev spin models

We use the variational quantum eigensolver (VQE) to simulate Kitaev spin models with and without integrability breaking perturbations, focusing in particular on the honeycomb and square-octagon lattices. These models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation and is capable of expressing the exact ground state in the solvable limit. We also demonstrate that this ansatz can be extended beyond this limit to provide excellent accuracy when compared to other VQE approaches. In certain cases, this fermionic representation is advantageous because it reduces by a factor of two the number of qubits required to perform the simulation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.

Jahin, Ammar↗
DOE OSTI2023

On Practical Aspects of Variational Consistency in Contact Dynamics

Usage of contact mechanics methodologies is a pervasive modeling requirement in dynamic simulations. While for some trivial problems, solutions taken from analytical geometry are available, use of a finite element framework is common to achieve formulation generality. This work explores two dynamic contact formulations: one based on the traditional node-to-segment (NTS) approach, and a variationally consistent segment-to-segment (STS) mortar formulation. The NTS formulation employed here enforces the constraints kinematically (i.e., the interpenetration is enforced to the solver tolerance), whereas the mortar approach uses Lagrange multipliers to enforce the contact constraints. Both approaches are implemented in the open-source finite element framework Multiphysics Object-Oriented Simulation Environment (MOOSE). The results highlight two relevant contact-interface-related dynamic phenomena in finite element simulations. First, stabilization of contact constraints is discussed, taking into account the evolution of the total energy in a benchmark problem. Second, the influence of finite element discretization on both of the aforementioned contact formulations is analyzed by exercising a large-deformation example with continuous relative sliding. Variationally consistent contact approaches such as the mortar formulation lead to improved energy preservation and avoid spurious excitation of the system's frequencies. This is especially relevant in settings where inertia and vibrations are of importance.

42 ENGINEERING↗
DOE OSTI2024

Noise-induced transition in optimal solutions of variational quantum algorithms

Variational quantum algorithms are promising candidates for delivering practical quantum advantage on noisy intermediate-scale quantum (NISQ) hardware. However, optimizing the noisy cost functions associated with these algorithms is challenging for system sizes relevant to quantum advantage. In this work, we investigate the effect of noise on optimization by studying a variational quantum eigensolver (VQE) algorithm calculating the ground state of a spin chain model, and we observe an abrupt transition induced by noise to the optimal solutions. We will present numerical simulations, a demonstration using an IBM quantum processor unit (QPU), and a theoretical analysis indicating the origin of this transition. Our findings suggest that careful analysis is crucial to avoid misinterpreting the noise-induced features as genuine algorithm results.

Li, Andy C.Y.↗
DOE OSTI2023

Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules

Abstract Materials simulations involving strongly correlated electrons pose fundamental challenges to state‐of‐the‐art electronic structure methods but are hypothesized to be the ideal use case for quantum computing algorithms. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real‐world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near‐term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using the VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies using it have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near‐term feasibility of modeling a molecule with d‐orbitals on real quantum hardware. We demonstrate that the inclusion of d‐orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE + UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Learning and Predicting Photonic Responses of Plasmonic Nanoparticle Assemblies via Dual Variational Autoencoders

In this work, the application of machine learning is demonstrated for rapid and accurate extraction of plasmonic particles cluster geometries from hyperspectral image data via a dual variational autoencoder (dual-VAE). In this approach, the information is shared between the latent spaces of two VAEs acting on the particle shape data and spectral data, respectively, but enforcing a common encoding on the shape-spectra pairs. It is shown that this approach can establish the relationship between the geometric characteristics of nanoparticles and their far-field photonic responses, demonstrating that hyperspectral darkfield microscopy can be used to accurately predict the geometry (number of particles, arrangement) of a multiparticle assemblies below the diffraction limit in an automated fashion with high fidelity (for monomers (0.96), dimers (0.86), and trimers (0.58). This approach of building structure-property relationships via shared encoding is universal and should have applications to a broader range of materials science and physics problems in imaging of both molecular and nanomaterial systems.

variational autoencoder↗
DOE OSTI2024

Variational data augmentation for a learning-based granular predictive model of power outages

As the trend in climate change continues, extreme weather events are expected to occur with increasing frequency and severity and pose a significant threat to the electric power infrastructure. Regardless of the efforts a utility puts towards hardening the grid, storm-induced damage to the utility assets such as cables and distributed energy resources (DERs) that are particularly vulnerable to such events is unavoidable. Access to a highly granular, in space and time, outage forecasting tool with long lead times (i.e., days ahead) will enhance the efficiency of service restoration efforts. Here, in this study, we propose to develop and implement a multi-model framework as an operational tool based on a granular and multi-day outage forecasting model using operational numerical weather prediction model forecasts and detailed component outage information. An innovative two-layered recurrent neural network, i.e., a long-short-term-memory (LSTM)-based variational autoencoder (VAE) framework and a sliding window are used to address the uneven distribution of different types of weather events and make better use of the time-series data. Case studies are performed to demonstrate the performance of the new framework.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Elliptically-Contoured Tensor-variate Distributions with Application to Image Learning

Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate for data arising from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) TV distributions and derive its characterizations, moments, marginal, and conditional distributions. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, for which we extend Tyler’s robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop TV classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and TV analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age, and ethnic origin than the usual TVN-based TANOVA in the celebrated labeled faces of the wild dataset.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Detecting Quantum Critical Points of Correlated Systems by Quantum Convolutional Neural Network Using Data from Variational Quantum Eigensolver

Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable accuracy. The QCNN can be trained to predict the corresponding ‘phase’ of wavefunctions around the putative quantum critical point even though it is trained by wavefunctions far away. The paper provides a basis for exploiting the QCNN to identify the quantum critical point.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Neural Network-Based Variational Methods for Solving Quadratic Porous Medium Equations in High Dimensions

Here, in this paper, we propose and study neural network-based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two weak formulations. For the strong formulation, the solution is directly parameterized with a neural network and optimized by minimizing the PDE residual. It can be proved that the convergence of the optimization problem guarantees the convergence of the approximate solution in the $L^1$ sense. The weak formulations are derived following (Brenier in Examples of hidden convexity in nonlinear PDEs, 2020) which characterizes the very weak solutions of QPME. Specifically speaking, the solutions are represented with intermediate functions who are parameterized with neural networks and are trained to optimize the weak formulations. Extensive numerical tests are further carried out to investigate the pros and cons of each formulation in low and high dimensions. This is an initial exploration made along the line of solving high-dimensional nonlinear PDEs with neural network-based methods, which we hope can provide some useful experience for future investigations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Towards inverse microstructure-centered materials design using generative phase-field modeling and deep variational autoencoders

The field of Integrated Computational Materials Engineering (ICME) combines a broad range of methods to study materials’ responses over a spectrum of length scales. A relatively unexplored aspect of microstructure-sensitive materials design is uncertainty propagation and quantification (UP/UQ) of materials’ microstructure, as well as establishing process-structure–property (PSP) relationships for inverse material design. In this study, an efficient UP technique built on the idea of changing probability measures and a deep generative unsupervised representative machine learning method for microstructure-based design of thermal conductivity of materials is proposed. Probability measures are used to represent microstructure space, and Wasserstein metrics are used to test the efficiency of the UP method. By using deep Variational AutoEncoder (VAE), we identify the correlations between the material/process parameters and the thermal conductivity of heterogeneous dual-phase microstructures. Through high-throughput screening, UP, and the deep-generative VAE method, PSP relationships that are too complex can be revealed by exploiting the materials’ design space with an emphasis on microstructures. As a last point, we demonstrate generative machine learning serves as a useful tool for inverse microstructure-centered materials design, and we demonstrate this by examining the inverse design of thermal conductivity in nano-structured materials. Here, the results reveal the effects of morphology, volume fraction, characteristic length scale, and the individual thermal diffusivity of phases on the thermal conductivity of dual-phase alloys. Our findings emphasize the advantages of high-throughput phase-field modeling and generative deep learning for linking PSP and inverse microstructure-centered materials design.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Predicting critical heat flux with uncertainty quantification and domain generalization using conditional variational autoencoders and deep neural networks

Deep generative models (DGMs) can generate synthetic data samples that closely resemble the original dataset, addressing data scarcity. In this work, we developed a conditional variational autoencoder (CVAE) to augment critical heat flux (CHF) data used for the 2006 Groeneveld lookup table. To compare with traditional methods, a fine-tuned deep neural network (DNN) regression model was evaluated on the same dataset. Both models achieved small mean absolute relative errors, with the CVAE showing more favorable results. Uncertainty quantification (UQ) was performed using repeated CVAE sampling and DNN ensembling. The DNN ensemble improved performance over the baseline, while the CVAE maintained consistent results with less variability and higher confidence. Both models achieved small errors inside and outside the training domain, with slightly larger errors outside. Altogether, the CVAE performed better than the DNN in predicting CHF and exhibited better uncertainty behavior.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Large-eddy simulation study on cycle-to-cycle variation of knocking combustion in a spark-ignition engine

The cycle-to-cycle variation in the knock intensity is commonly encountered under abnormal combustion conditions. The severity of these abnormal combustion events can vary significantly, and the efficiency of engines at high loads is limited in practice by heavy knocking phenomena. Since, a thorough analysis of such recurrent but non-cyclic phenomena via experiments alone becomes highly cumbersome, in the present work, a multi-cycle large-eddy simulation study was performed to quantitatively predict cyclic variability in the combustion process and cyclic knock intensity variability in a direct injection spark-ignition engine. To account for the turbulence-chemistry interaction effects on flame propagation, the G-equation combustion model was used. Detailed chemistry was solved outside the flame front with a toluene primary reference fuel skeletal kinetic mechanism. For both the mild knock and heavy knock conditions, the numerical results were validated against experimental measurements. Based on the simulation results, a correlation analysis was performed considering combustion phasing, peak cylinder pressure and maximum amplitude of pressure oscillation. Furthermore, a detailed three-dimensional spatial analysis illustrated the evolution of auto-ignition kernel development and propagation of pressure waves during knocking combustion for three typical cycles with different knock intensities. In this process, it was found that an early occurrence of auto-ignition in the end gas was prone to high knock intensity. Although multiple auto-ignition kernels were observed in different cycles, the degree of coupling between chemical heat release and pressure waves varied, thereby leading to different maximum amplitude of pressure oscillation values.

42 ENGINEERING↗
DOE OSTI2020

Data-driven variational multiscale reduced order models

We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost. The VMS methodology is a natural fit for the hierarchical structure of the ROM basis: In the first step, we use the ROM projection to separate the scales into three categories: (i) resolved large scales, (ii) resolved small scales, and (iii) unresolved scales. In the second step, we explicitly identify the VMS–ROM closure terms, i.e., the terms representing the interactions among the three types of scales. In the third step, we use available data to model the VMS–ROM closure terms. Thus, instead of phenomenological models used in VMS for standard numerical discretizations (e.g., eddy viscosity models), we utilize available data to construct new structural VMS–ROM closure models. Specifically, we build ROM operators (vectors, matrices, and tensors) that are closest to the true ROM closure terms evaluated with the available data. We test the new data-driven VMS–ROM in the numerical simulation of four test cases: (i) the 1D Burgers equation with viscosity coefficient v = 10 -3 ; (ii) a 2D flow past a circular cylinder at Reynolds numbers, Re = 100, Re = 500, and Re= 1000; (iii) the quasi-geostrophic equations at Reynolds number Re = 450 and Rossby number Ro = 0.0036; and (iv) a 2D flow over a backward facing step at Reynolds number Re = 1000. The numerical results show that the data-driven VMS–ROM is significantly more accurate than standard ROMs.

42 ENGINEERING↗
DOE OSTI2020

hp -VPINNs: Variational physics-informed neural networks with domain decomposition

We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto the space of high-order polynomials. The trial space is the space of neural network, which is defined globally over the entire computational domain, while the test space contains piecewise polynomials. Specifically in this study, the hp-refinement corresponds to a global approximation with a local learning algorithm that can efficiently localize the network parameter optimization. Here, we demonstrate the advantages of hp-VPINNs in both accuracy and training cost for several numerical examples of function approximation and in solving differential equations.

42 ENGINEERING↗