Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “inverse problems”

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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Inverse Calculation of Burden Distribution Matrix Using B-spline Model Based PDF control in Blast Furnace Burden Charging Process

The inverse calculation of burden distribution matrix (BDM) is one of the most important challenges in the blast furnace operation in iron-making processes. In general, blast furnace consumes 65% of the total energy for the whole steel-making. Focusing on this practical challenge, this article proposes a new burden distribution spatial model in calculating burden charging process, and develops a B-spline approximation-based probability density function (PDF) control algorithm to assign the expected thickness distribution of burden layer and, thus, develops a new method for the required inverse calculation of BDM. First, a novel method for the thickness distribution of burden layer is given using B-spline model to produce an expected distribution shape subjected to a desired tracking within a specific spatial constraint. Then, according to the coexistence of continuous and bounded discrete variables in BDM, a novel hybrid optimization control method by combining integer programming and PDF tracking is further established for the effective inverse calculation of BDM. Finally, the proposed PDF-based iterative inverse calculation of BDM using B-spline models are tested using various data from industrial examples. Furthermore, the simulation results show that the proposed method is well suited to solve the BDM inverse calculation problem in practice.

42 ENGINEERING↗
DOE OSTI2020

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve forward, inverse, and mixed stochastic problems in a unified manner based on a limited number of scattered measurements. Unlike standard GANs relying solely on data for training, here we encoded into the architecture of GANs the governing physical laws in the form of stochastic differential equations (SDEs) using automatic differentiation. In particular, we applied Wasserstein GANs with gradient penalty (WGAN-GP) for its enhanced stability compared to vanilla GANs. We first tested WGAN-GP in approximating Gaussian processes of different correlation lengths based on data realizations collected from simultaneous reads at sparsely placed sensors. We obtained good approximation of the generated stochastic processes to the target ones even if there is a mismatch between the input noise dimensionality and the effective dimensionality of the target stochastic processes. We also studied the overfitting issue for both the discriminator and the generator, and we found that overfitting occurs also in the generator in addition to the discriminator as previously reported. Subsequently, we considered the solution of elliptic SDEs requiring approximations of three stochastic processes, namely the solution, the forcing, and the diffusion coefficient. Here again, we assumed data collected from simultaneous reads at a limited number of sensors for the multiple stochastic processes. Furthermore, three generators were used for the PI-GANs: two of them were feed forward deep neural networks (DNNs), while the other one was the neural network induced by the SDE. For the case where we have one group of data, we employed one feed forward DNN as the discriminator, while for the case of multiple groups of data we employed multiple discriminators in PI-GANs. We solved forward, inverse, and mixed problems without changing the framework of PI-GANs, obtaining both the means and the standard deviations of the stochastic solution and the diffusion coefficient in good agreement with benchmarks. In this work, we have demonstrated the effectiveness of PI-GANs in solving SDEs for about 120 dimensions. In principle, PI-GANs could tackle very high dimensional problems given more sensor data with low-polynomial growth in computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Restoring the discontinuous heat equation source using sparse boundary data and dynamic sensors

Abstract This study focuses on addressing the inverse source problem associated with the parabolic equation. We rely on sparse boundary flux data as our measurements, which are acquired from a restricted section of the boundary. While it has been established that utilizing sparse boundary flux data can enable source recovery, the presence of a limited number of observation sensors poses a challenge for accurately tracing the inverse quantity of interest. To overcome this limitation, we introduce a sampling algorithm grounded in Langevin dynamics that incorporates dynamic sensors to capture the flux information. Furthermore, we propose and discuss two distinct dynamic sensor migration strategies. Remarkably, our findings demonstrate that even with only two observation sensors at our disposal, it remains feasible to successfully reconstruct the high-dimensional unknown parameters.

Mathematics↗
DOE OSTI2024

Augmenting a Simulation Campaign for Hybrid Computer Model and Field Data Experiments

The Kennedy and O’Hagan (KOH) calibration framework uses coupled Gaussian processes (GPs) to meta-model an expensive simulator (first GP), tune its “knobs” (calibration inputs) to best match observations from a real physical/field experiment and correct for any modeling bias (second GP) when predicting under new field conditions (design inputs). There are well-established methods for placement of design inputs for data-efficient planning of a simulation campaign in isolation, that is, without field data: space-filling, or via criterion like minimum integrated mean-squared prediction error (IMSPE). Analogues within the coupled GP KOH framework are mostly absent from the literature. Here, in this study, we derive a closed form IMSPE criterion for sequentially acquiring new simulator data for KOH. We illustrate how acquisitions space-fill in design space, but concentrate in calibration space. Closed form IMSPE precipitates a closed-form gradient for efficient numerical optimization. We demonstrate that our KOH-IMSPE strategy leads to a more efficient simulation campaign on benchmark problems, and conclude with a showcase on an application to equilibrium concentrations of rare earth elements for a liquid–liquid extraction reaction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Invertible Neural Networks for Airfoil Design

We report the airfoil design problem, in which an engineer seeks a shape with desired performance characteristics, is fundamental to aerodynamics. Design workflows traditionally rely on iterative optimization methods using low-fidelity integral boundary-layer methods as higher-fidelity adjoint-based computational fluid dynamics methods are computationally expensive. Surrogate-based approaches can accelerate the design process but still rely on some iterative inverse design procedure. In this work, we leverage emerging invertible neural network (INN) tools to enable the rapid inverse design of airfoil shapes for wind turbines. INNs are specialized deep-learning models with well-defined inverse mappings. When trained appropriately, INN surrogate models are capable of forward prediction of aerodynamic and structural quantities for a given airfoil shape as well as inverse recovery of airfoil shapes with specified aerodynamic and structural characteristics. The INN approach offers a roughly 100 times speed-up compared to adjoint-based methods for inverse design. We demonstrate the INN tool for inverse design on three test cases of 100 airfoils each that satisfy the performance characteristics close to those of airfoils used in wind-turbine blades. All generated shapes satisfy the desired aerodynamic characteristics, demonstrating the success of the INN approach for inverse design of airfoils.

17 WIND ENERGY↗
DOE OSTI2023

Forward sensitivity analysis and mode dependent control for closure modeling of Galerkin systems

Model reduction by projection-based approaches is often associated with losing some of the important features that contribute towards the dynamics of the retained scales. As a result, a mismatch occurs between the predicted trajectories of the original system and the truncated one. We put forth a framework to apply a continuous time control signal in the latent space of the reduced order model (ROM) to account for the effect of truncation. We set the control input using parameterized models by following energy transfer principles. Our methodology relies on observing the system behavior in the physical space and using the projection operator to restrict the feedback signal into the latent space. Then, we leverage the forward sensitivity method (FSM) to derive relationships between the feedback and the desired mode-dependent control. We test the performance of the proposed approach using two test cases, corresponding to viscous Burgers and vortex merger problems at high Reynolds number. Results show that the ROM trajectory with the applied FSM control closely matches its target values in both the data-dense and data-sparse regimes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Parallel physics-informed neural networks via domain decomposition

Here we develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in time-space, respectively. This domain decomposition endows cPINNs and XPINNs with several advantages over the vanilla PINNs, such as parallelization capacity, large representation capacity, efficient hyperparameter tuning, and is particularly effective for multi-scale and multi-physics problems. Here, we present a parallel algorithm for cPINNs and XPINNs constructed with a hybrid programming model described by MPI + X, where X ∈ {CPUs, GPUs}. The main advantage of cPINN and XPINN over the more classical data and model parallel approaches is the flexibility of optimizing all hyperparameters of each neural network separately in each subdomain. We compare the performance of distributed cPINNs and XPINNs for various forward problems, using both weak and strong scalings. Our results indicate that for space domain decomposition, cPINNs are more efficient in terms of communication cost but XPINNs provide greater flexibility as they can also handle time-domain decomposition for any differential equations, and can deal with any arbitrarily shaped complex subdomains. To this end, we also present an application of the parallel XPINN method for solving an inverse diffusion problem with variable conductivity on the United States map, using ten regions as subdomains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

From the Great Wave of Translation to the Force between Quarks

Here, the chance observation of a novel traveling wave in a canal led over time to the formulation of a nonlinear wave equation—the Korteweg–de Vries equation—that describes strikingly robust disturbances now called solitons. The figure of an isolated soliton corresponds to a reflectionless potential that supports a single bound state in the one-dimensional Schrödinger equation. An appropriate combination of individual solitons yields a symmetric reflectionless potential that supports multiple bound states. Thus, the KdV equation opens the path to solving the inverse scattering problem for a collection of bound states. Applied to the quarkonium spectra, this formalism allows the construction of reflectionless approximations to the confining potentials that account for the force between quarks, and to tests of the flavor-independence of the interquark interaction.

Inverse Scattering↗
DOE OSTI2024

Protorheology in practice: Avoiding misinterpretation

Protorheology is the paradigm that any observed flow or deformation is a chance to infer quantitative rheological properties. While this creates many opportunities for insight, there is significant risk of misunderstanding the physics involved, e.g. misinterpreting a liquid as a solid or mistaking viscous flow time as viscoelastic relaxation time. We describe these and other potential mistakes, use case studies to show how serious the problems can be, and contrast misinterpretations with correct approaches and interpretations. Some issues are especially important with materials involving colloidal particles and flows involving surface tension. Whether the reader is making inference from a tilted vial, time-lapse gravity-driven flow, a bounce test, die swell, or any other protorheology observation, the examples here serve as a guide for avoiding bad data in protorheology.

42 ENGINEERING↗
DOE OSTI2021

Watch and learn—a generalized approach for transferrable learning in deep neural networks via physical principles

Transfer learning refers to the use of knowledge gained while solving a machine learning task and applying it to the solution of a closely related problem. Such an approach has enabled scientific breakthroughs in computer vision and natural language processing where the weights learned in state-of-the-art models can be used to initialize models for other tasks which dramatically improve their performance and save computational time. Here we demonstrate an unsupervised learning approach augmented with basic physical principles that achieves fully transferrable learning for problems in statistical physics across different physical regimes. By coupling a sequence model based on a recurrent neural network to an extensive deep neural network, we are able to learn the equilibrium probability distributions and inter-particle interaction models of classical statistical mechanical systems. Our approach, distribution-consistent learning, DCL, is a general strategy that works for a variety of canonical statistical mechanical models (Ising and Potts) as well as disordered interaction potentials. Using data collected from a single set of observation conditions, DCL successfully extrapolates across all temperatures, thermodynamic phases, and can be applied to different length-scales. This constitutes a fully transferrable physics-based learning in a generalizable approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Dealing with Measurement Uncertainties as Nuisance Parameters in Bayesian Model Calibration

In the presence of model discrepancy, the calibration of physics-based models for physical parameter inference is a challenging problem. Lack of identifiability between calibration parameters and model discrepancy requires additional identifiability constraints to be placed on the model discrepancy to obtain unique physical parameter estimates. If these assumptions are violated, the inference for the calibration parameters can be systematically biased. In many applications, such as in dynamic material property experiments, many of the calibration inputs refer to measurement uncertainties. Here, we develop a metric for identifying overfitting of these measurement uncertainties, propose a prior capable of reducing this overfitting, and show how this leads to a diagnostic tool for validation of physical parameter inference. The approach is demonstrated for a benchmark example and applied for a material property application to perform inference on the equation of state parameters of tantalum.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Chapter 4 - Recent Advances in Identification of Differential Equations from Noisy Data: IDENT Review

Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of time-dependent data. If we assume that the differential equation is a linear combination of various linear and nonlinear differential terms, then the identification problem can be formulated as solving a linear system. The goal then reduces to finding the optimal coefficient vector that best represents the time derivative of the given data. We review some recent works on the identification of differential equations. We find some common themes for the improved accuracy: (i) The formulation of linear system with proper denoising is important, (ii) how to utilize sparsity and model selection to find the correct coefficient support needs careful attention, and (iii) there are ways to improve the coefficient recovery. We present an overview and analysis of recent developments on the topic.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Bayesian-based response expansion and uncertainty quantification using sparse measurement sets

Systems subjected to dynamic loads often require monitoring of their vibrational response, but limitations on the total number and placement of the measurement sensors can hinder the data-collection process. Here, we present an indirect approach to estimate a system’s full-field dynamic response, including all uninstrumented locations, using response measurements from sensors sparsely located on the system. This approach relies on Bayesian inference that utilizes a system model to estimate the full-field response and quantify the uncertainty in these estimates. By casting the estimation problem in the frequency domain, this approach utilizes the modal frequency response functions as a natural, frequency-dependent weighting scheme for the system mode shapes to perform the expansion. This frequency-dependent weighting scheme enables an accurate expansion, even with highly correlated mode shapes that may arise from spatial aliasing due to the limited number of sensors, provided these correlated modes do not have natural frequencies that are closely spaced. Furthermore, the inherent regularization mechanism that arises in this Bayesian-based procedure enables the utilization of the full set of system mode shapes for the expansion, rather than any reduced subset. This approach can produce estimates when considering a single realization of the measured responses, and with some modification, it can also produce estimates for power spectral density matrices measured from many realizations of the responses from statistically stationary random processes. A simply supported beam provides an initial numerical validation, and a cylindrical test article excited by acoustic loads in a reverberation chamber provides experimental validation.

42 ENGINEERING↗
DOE OSTI2026

Efficient Optimization of Plasma Radiation Detector Configurations using Imperfect Inference Models

The configurations of instruments fielded on an experiment affect the amount of information captured and the quality of subsequent inference. Here, we investigate the problem of optimizing plasma x-ray radiation detectors in a magneto-inertial fusion experiment at Sandia National Laboratories. It is impossible to directly measure properties such as the temperature of the thermonuclear fusion plasma produced in these experiments because of the extreme environment and destructive nature of the experiment. Among other diagnostics, several detectors are placed with significant standoff from the fusion target to capture the x-rays emitted by the fusion plasma, which can be used to infer some of its properties. To optimize the configuration of these detectors, a high-fidelity model (HFM) is used for simulating outputs and a low-fidelity model (LFM) is used for inference. We develop methods based on A- and L-optimality criteria that are efficient to compute while explicitly accounting for the discrepancy between the HFM and the LFM. The method allows us to find detector configurations that perform similarly to or better than the configuration obtained using an existing sampling-based optimization method while decreasing computational time by a factor of 50. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Bayesian optimization↗
DOE OSTI2021

Reinforcement learning in discrete action space applied to inverse defect design

Abstract Reinforcement learning (RL) algorithms that include Monte Carlo Tree Search (MCTS) have found tremendous success in computer games such as Go, Shiga and Chess. Such learning algorithms have demonstrated super-human capabilities in navigating through an exhaustive discrete action search space. Motivated by their success in computer games, we demonstrate that RL can be applied to inverse materials design problems. We deploy RL for a representative case of the optimal atomic scale inverse design of extended defects via rearrangement of chalcogen (e.g. S) vacancies in 2D transition metal dichalcogenides (e.g. MoS 2 ). These defect rearrangements and their dynamics are important from the perspective of tunable phase transition in 2D materials i.e. 2H (semi-conducting) to 1T (metallic) in MoS 2 . We demonstrate the ability of MCTS interfaced with a reactive molecular dynamics simulator to efficiently sample the defect phase space and perform inverse design—starting from randomly distributed S vacancies, the optimal defect rearrangement of defects corresponds a line defect of S vacancies. We compare MCTS performance with evolutionary optimization i.e. genetic algorithms and show that MCTS converges to a better optimal solution (lower objective) and in fewer evaluations compared to GA. We also comprehensively evaluate and discuss the effect of MCTS hyperparameters on the convergence to solution. Overall, our study demonstrates the effectives of using RL approaches that operate in discrete action space for inverse defect design problems.

42 ENGINEERING↗
DOE OSTI2021

Deep Learning the Electromagnetic Properties of Metamaterials—A Comprehensive Review

Deep neural networks (DNNs) are empirically derived systems that have transformed traditional research methods, and are driving scientific discovery. Here, artificial electromagnetic materials (AEMs)—including electromagnetic metamaterials, photonic crystals, and plasmonics—are research fields where DNN results valorize the data driven approach; especially in cases where conventional methods have failed. In view of the great potential of deep learning for the future of artificial electromagnetic materials research, the status of the field with a focus on recent advances, key limitations, and future directions is reviewed. Strategies, guidance, evaluation, and limits of using deep networks for both forward and inverse AEM problems are presented.

14 SOLAR ENERGY↗
DOE OSTI2021

Machine-Learning Microstructure for Inverse Material Design

Metallurgy and material design have thousands of years’ history and have played a critical role in the civilization process of humankind. The traditional trial-and-error method has been unprecedentedly challenged in the modern era when the number of components and phases in novel alloys keeps increasing, with high-entropy alloys as the representative. New opportunities emerge for alloy design in the artificial intelligence era. Here a successful machine-learning (ML) method is developed to identify the microstructure images with eye-challenging morphology for a number of martensitic and ferritic steels. Assisted by it, a new neural-network method is proposed for the inverse design of alloys with 20 components, which can accelerate the design process based on microstructure. The method is also readily applied to other material systems given sufficient microstructure images. This work lays the foundation for inverse alloy design based on microstructure images with extremely similar features.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Quantifying the impact of temporal analysis of products reactor initial state uncertainties on kinetic parameters

The temporal analysis of products (TAP) reactor, a transient kinetic tool, provides users with information as the catalyst state evolves. However, the state of the art for TAP uncertainty quantification only considers the experimental noise present in the outlet flow signal. Additional sources of uncertainty, including, but not limited to, initial surface coverages, the catalyst zone location, the inert void fraction, and the gas pulse intensity and pulse delay, are not included. For this reason, a framework for quantifying all uncertainty sources present in TAP experiments is presented and applied to a carbon monoxide oxidation case study. Herein, two methods for quantifying these sources of uncertainty are introduced. The first utilizes initial state sensitivities to approximate the parameter variances, as well as to provide insights into the structural certainty of the model. The second generates parameter confidence distributions through an ensemble-based sampling algorithm. This initial state covariance matrix can ultimately be merged with the experimental noise covariance matrix, providing a unified description of the parameter uncertainties for a single TAP experiment.

36 MATERIALS SCIENCE↗