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Results for “partial least squares”

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.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs. It is shown that quantities that are necessary for the error estimator can be either obtained exactly as the solutions of least-squares problems in a non-intrusive way from data such as initial conditions, control inputs, and high-dimensional solution trajectories or bounded in a probabilistic sense. Here, the computational procedure follows an offline/online decomposition. In the offline (training) phase, the high-dimensional system is judiciously solved in a black-box fashion to generate data and to set up the error estimator. In the online phase, the estimator is used to bound the error of the reduced-model predictions for new initial conditions and new control inputs without recourse to the high-dimensional system. Numerical results demonstrate the workflow of the proposed approach from data to reduced models to certified predictions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Abridged spectral matrix inversion: parametric fitting of X-ray fluorescence spectra following integrative data reduction

Recent improvements in both X-ray detectors and readout speeds have led to a substantial increase in the volume of X-ray fluorescence data being produced at synchrotron facilities. This in turn results in increased challenges associated with processing and fitting such data, both temporally and computationally. Herein an abridging approach is described that both reduces and partially integrates X-ray fluorescence (XRF) data sets to obtain a fivefold total improvement in processing time with negligible decrease in quality of fitting. The approach is demonstrated using linear least-squares matrix inversion on XRF data with strongly overlapping fluorescent peaks. This approach is applicable to any type of linear algebra based fitting algorithm to fit spectra containing overlapping signals wherein the spectra also contain unimportant (non-characteristic) regions which add little (or no) weight to fitted values, e.g. energy regions in XRF spectra that contain little or no peak information.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Radiation-induced bowing of SiC/SiC composites under neutron flux gradients—integral experimental data for model validation

Here, the radiation-induced swelling of SiC and its composites, including strong dependencies on temperature and dose, can drive significant lateral bowing in the presence of temperature and/or dose gradients. In recent years, simulations have been performed to assess the extent of bowing in SiC composite light-water reactor (LWR) fuel cladding and boiling water reactor (BWR) channel boxes. However, to date, no integral experimental data exist to validate these models. This work provides the first experimental bowing evaluation of three ∼380 mm long SiC composite specimens irradiated under varying neutron dose gradients (∼50°C–60°C, 0.03–0.06 dpa): two tubes (∼9.8 mm diameter) and a miniature BWR channel box (∼30 mm square). The measured radiation-induced length swelling (∼0.3%–0.7% linear) was consistently 10%–21% higher than values obtained from 3D finite element structural analyses with inputs from 3D radiation transport calculations. This discrepancy could be at least partially explained by differences in dose rate (∼10 -8 dpa/s) compared to the literature data (∼10-6 dpa/s) used to establish the dose-to-swelling correlations in the model. Nevertheless, the modeled bowing magnitudes (<2 mm) obtained from finite element analyses and simple analytical equations were within the bounds of the experimental measurements for all specimens. With improved confidence in the ability to predict the structural response and measure the macroscopic deformations, future experiments will target transient bowing under neutron flux gradients at representative LWR temperatures and assess whether grid spacers can mitigate the tens of millimeters of bowing that would otherwise be expected in ∼4 m long LWR components.

bowing↗
DOE OSTI2020

Retrieval of Cloud Liquid Water Using Microwave Signals from LEO Satellites: A Feasibility Study through Simulations

A novel method, using low Earth orbit (LEO) satellite microwave communication links for cloud liquid water measurements, is introduced in this paper. The feasibility of this approach is studied through simulations of the retrieval system including a LEO satellite communicating with a group of ground receivers equipped with signal-to-noise ratio (SNR) estimators, a synthetic cloud attenuation field and a tomographic retrieval algorithm. Rectangular and Gaussian basis functions are considered to define the targeted field. Simulation results suggest that the proposed least-squares based retrieval algorithm produces satisfactory outcomes for both types of basis functions. The root-mean-square error of the retrieved field is around 0.2 dB/km, with the range of the reference field as 0 to 2.35 dB/km. It is also confirmed that the partial retrieval of the cloud field is achievable when a limited number of receivers with restricted locations are available. The retrieval outcomes exhibit properties of high resolution and low error, indicating that the proposed approach has great potential for cloud observations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Parameter dependencies of the experimental nitrogen concentration required for detachment on ASDEX Upgrade and JET

While current tokamak experiments are beginning to use real-time feedback control systems to manage the plasma exhaust, future tokamaks still require validation of theoretical models used to predict the threshold impurity concentration required to sufficiently reduce the power and particle fluxes to the divertor. This work exploits new spectroscopic measurements of the divertor nitrogen concentration, c n , in partially detached N 2 -seeded H-mode plasmas on ASDEX Upgrade (AUG) and JET with the ITER-Like Wall (JET-ILW) to test the parameter dependencies of the power flowing to the outer divertor, P div,outer , and the separatrix electron density, n e.sep . A least-squares regression of the AUG measurements demonstrates that the threshold c n required for detachment scales as $c_n∝P^{1.19±0.32}_{div,outer}n^{-2.77±0.36}_{e,sep}$. This scaling of n e,sep is also consistent with the measurements from JET which, at constant P div,outer , show $c_n∝n^{-2.43±0.27}_{e,sep}$. The dependencies of P div,outer and n e.sep is demonstrated over at least a factor of two change in both parameters and indicates a stronger dependence on n e.sep in comparison to the Lengyel model, which could be due to the assumption in this model that the heat flux channel width is independent of density. This first assessment of detachment scaling with impurity seeding highlights the need for further analysis of the systematic uncertainties of the measurement and more consistent scenarios from more tokamaks to investigate the machine size scaling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained “blind” ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗
DOE OSTI2020

Absolute Band Intensity of the Iodine Monochloride Fundamental Mode for Infrared Sensing and Quantitative Analysis

Iodine monochloride (ICl) is a gaseous off-product of molten salt reactors; monitoring this heteronuclear diatomic is of great interest for both environmental and safety purposes. In this paper we investigate the possibility of infrared monitoring of ICl by measuring the far-infrared absorption cross section of its fundamental band near 381 cm -1 . We have performed quantitative studies of the neat gas in a 20 cm cell at 25, 35, 50 and 70 oC at multiple pressures up to ~ 9 Torr and investigated the temperature and pressure dependence of the band’s infrared cross section. Quantitative measurements were problematic due to sample adhesion to the cell walls and windows as well as reactions/possible hydrolysis of ICl to form HCl gas. Effects were mitigated by measuring only the neat gas, using short measurement times and subtracting out the partial pressure of the HCl(g). The integrated band strength is shown to be temperature independent and was found to be equal to 9.1 x 10 -19 (cm 2 /molecule) cm-1. As expected, the temperature dependence of the band profile showed only a small effect over this limited temperature range. Furthermore, we have also investigated using the absorption data along with inverse least squares multivariate methods for the quantitative monitoring of ICl effluent concentrations under different scenarios using infrared (standoff) sensing and compare these results with traditional Beer’s Law (univariate) techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Uncertainty Quantification Enabled by Automatic Differentiation for Hydrodynamic Simulation of Shock‐to‐Detonation Transition in High Explosives

Quantifying the effects of uncertainty in a reactive burn model on the run-to-detonation time in high explosives (HEs) provides a robust methodology for assessing the probability of an HE failing the IHE qualification standard. Moreover, uncertainty quantification helps evaluate whether the model calibration accurately represents data outside the calibration set. This study uses a specialized hydrodynamic simulation code for modeling detonation to determine the run-to-detonation time of the HE PBX 9502 for various impact velocities. To quickly approximate uncertainties in the model, a surrogate was constructed using a Taylor series expansion centered at the mean of the input parameters. To obtain the sensitivities required for constructing the Taylor series, HYP-percomplex Automatic Differentiation (HYPAD) was implemented. HYPAD is a methodology for infusing existing codes with automatic differentiation capabilities by augmenting variables with one or more imaginary units to compute step-size independent partial derivatives. These derivatives are accurate to machine precision with respect to the implemented numerical algorithm, meaning their accuracy reflects that of the underlying method (e.g., integration or discretization schemes). Using reduced order modeling techniques, the mean and standard deviation of the run-to-detonation time of a shock within PBX 9502 were computed for a number of initial impact velocities. A weighted least squares regression was then performed to obtain a best fit curve and prediction interval for the computed statistics. Historical data points from explosively driven wedge tests were utilized to validate the prediction interval, ensuring its reliability in predicting future outcomes. With this prediction interval and a known safety constraint curve, the most probable point of failure and the probability of failure for the HE PBX 9502 were determined.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

We evaluate the performance of the Karhunen-Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen-Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log-predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

Approximate Bayesian inference↗
DOE OSTI2026

Transient Catalytic Reaction Analysis Through Signal Defragmentation

The Temporal Analysis of Products (TAP) pulse response technique provides valuable insights into catalytic function and reaction kinetics. However, complex fragmentation patterns in the TAP mass spectrometry signals can complicate precise quantification, particularly when analyzing transient gas flux data typical of TAP experiments. This work demonstrates a standard defragmentation method that deconvolves transient TAP signals while maintaining the temporal resolution of the experiment. First, the integrals of calibration gas fluxes are used to determine the fingerprint fragmentation pattern and construct a fragmentation matrix. This matrix is then used to defragment experimental flux data at each recorded time point via a non-negative least squares regression. The effectiveness of this method is demonstrated using virtual data and control experiments with a TAP reactor system. The defragmentation is then applied to the more complex propane dehydrogenation reaction on a chromia/alumina catalyst, which can contain up to ten significant gas species in the reactor outlet. Initial propane pulsing reveals an induction period during which propane is fully oxidized to CO2, followed by partial reduction to CO. Afterwards, there is a transition in chemistries towards coking and propylene production. Our example illustrates a practical method for the accurate determination of the time-dependent reactant/product concentrations and rates for a thorough analysis of the propane dehydrogenation kinetics. This approach can be broadly applied to any transient mass spectrometry experiment for a better understanding of catalyst-reaction dynamics.

36 - MATERIALS SCIENCE↗
DOE OSTI2021

A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks

We employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) for learning a forward and an inverse solution operator of partial differential equations (PDEs). We focus on steady-state solutions of coupled hydromechanical processes in heterogeneous porous media and present the parameterization of the spatially heterogeneous coefficients, which is exceedingly difficult using standard reduced-order modeling techniques. We show that our framework provides a speed-up of at least 2,000 times compared to a finite-element solver and achieves a relative root-mean-square error (r.m.s.e.) of less than 2% for forward modeling. For inverse modeling, the framework estimates the heterogeneous coefficients, given an input of pressure and/or displacement fields, with a relative r.m.s.e. of less than 7%, even for cases where the input data are incomplete and contaminated by noise. The framework also provides a speed-up of 120,000 times compared to a Gaussian prior-based inverse modeling approach while also delivering more accurate results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Rapid subsurface analysis of frequency-domain thermoreflectance images with K-means clustering

K-means clustering analysis is applied to frequency-domain thermoreflectance (FDTR) hyperspectral image data to rapidly screen the spatial distribution of thermophysical properties at material interfaces. Performing FDTR while raster scanning a sample consisting of 8.6 μm of doped-silicon (Si) bonded to a doped-Si substrate identifies spatial variation in the subsurface bond quality. Routine thermal analysis at select pixels quantifies this variation in bond quality and allows assignment of bonded, partially bonded, and unbonded regions. Performing this same routine thermal analysis across the entire map, however, becomes too computationally demanding for rapid screening of bond quality. To address this, K-means clustering was used to reduce the dimensionality of the dataset from more than 20 000 pixel spectra to just K = 3 component spectra. The three component spectra were then used to express every pixel in the image through a least-squares minimized linear combination providing continuous interpolation between the components across spatially varying features, e.g., bonded to unbonded transition regions. Fitting the component spectra to the thermal model, thermal properties for each K cluster are extracted and then distributed according to the weighting established by the regressed linear combination. Thermophysical property maps are then constructed and capture significant variation in bond quality over 25 μm length scales. The use of K-means clustering to achieve these thermal property maps results in a 74-fold speed improvement over explicit fitting of every pixel.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

In this paper we present a non-intrusive data-driven approach for model reduction of nonlinear systems. The approach considers the particular case of nonlinear partial differential equations (PDEs) that form systems of partial differential–algebraic equations (PDAEs) when lifted to polynomial form. Such systems arise, for example, when the governing equations include Arrhenius reaction terms (e.g., in reacting flow models) and thermodynamic terms (e.g., the Helmholtz free energy terms in a phase-field solidification model). Using the known structured form of the lifted algebraic equations, the approach computes the reduced operators for the algebraic equations explicitly, using straightforward linear algebra operations on the basis matrices. The reduced operators for the differential equations are inferred from lifted snapshot data using operator inference, which solves a linear least squares regression problem. The approach is illustrated for the nonlinear model of solidification of a pure material. The lifting transformations reformulate the solidification PDEs as a system of PDAEs that have cubic structure. The operators of the lifted system for this solidification example have affine dependence on key process parameters, permitting us to learn a parametric reduced model with operator inference. Numerical experiments show the effectiveness of the resulting reduced models in capturing key aspects of the solidification dynamics.

42 ENGINEERING↗
DOE OSTI2020

Physics-Informed Deep Neural Network Method for Limited Observability State Estimation

The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable energy sources are connected directly into the distribution network, increasing the fluctuations of the injected power. In this paper, we consider the case when the distribution grid becomes partially observable, due to for example cyber attacks, and the state estimation problem is under-determined. We present a new methodology that leverages a deep neural network (DNN) to estimate the grid state. The standard DNN training method is modified to explicitly incorporate the physical information of the grid topology and line/shunt admittance. We show that our method leads to a superior accuracy of the estimation when compared to the case when no physical information is provided. Finally, we compare the performance of our method to the standard state estimation approach, which is based on the weighted least squares with pseudo-measurements, and show that our method performs significantly better with respect to the estimation accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Train Like a (Var)Pro: Efficient Training of Neural Networks with Variable Projection

Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and segmentation. The ability of DNNs to efficiently approximate high-dimensional functions has also motivated their use in scientific applications, e.g., to solve partial differential equations and to generate surrogate models. In this paper, we consider the supervised training of DNNs, which arises in many of the above applications. We focus on the central problem of optimizing the weights of the given DNN such that it accurately approximates the relation between observed input and target data. Devising effective solvers for this optimization problem is notoriously challenging due to the large number of weights, nonconvexity, data sparsity, and nontrivial choice of hyperparameters. To solve the optimization problem more efficiently, we propose the use of variable projection (VarPro), a method originally designed for separable nonlinear least-squares problems. Our main contribution is the Gauss--Newton VarPro method (GNvpro) that extends the reach of the VarPro idea to nonquadratic objective functions, most notably cross-entropy loss functions arising in classification. These extensions make GNvpro applicable to all training problems that involve a DNN whose last layer is an affine mapping, which is common in many state-of-the-art architectures. In our four numerical experiments from surrogate modeling, segmentation, and classification, GNvpro solves the optimization problem more efficiently than commonly used stochastic gradient descent (SGD) schemes. Finally, GNvpro finds solutions that generalize well, and in all but one example better than well-tuned SGD methods, to unseen data points.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Thermal Dehydration of Aluminum (Oxy)hydroxides on Fuel Cladding Material - 20200

The aluminum cladding of research-reactor fuel undergoes general corrosion with resulting formation of adherent aluminum (oxy)hydroxide films during in-reactor and post-discharge exposure to water under various conditions and temperatures. These (oxy)hydroxides contain chemically-bound water that poses challenges for extended dry storage due to the risk of thermal or radiolytic decomposition releasing free water and/or hydrogen and oxygen gases. This study comprised laboratory experiments of thermal drying behavior of aluminum (oxy)hydroxides to identify approaches for reducing bound water on fuel cladding prior to sealed dry storage. Effective drying strategies for adherent (oxy)hydroxides on fuel cladding will improve the safety of dry storage by mitigating potential avenues for additional corrosion and/or generation of flammable gases inside the storage canister. This work is part of a broader investigation to address knowledge gaps and technical data needs for dry storage of aluminum-clad spent nuclear fuel (ASNF), which included investigation of (oxy)hydroxide formation on aluminum alloy substrates immersed in water, characterization of service-grown films from ASNF, and radiolytic yield of hydrogen from (oxy)hydroxide powders and films. The current work comprises experimental thermal dehydration of aluminum trihydroxides (bayerite and gibbsite) characteristic of low-temperature (<80 deg. C) corrosion in water and aluminum oxyhydroxide (boehmite) characteristic of high temperature (>80 deg. C) corrosion in water. First, commercially produced (oxy)hydroxide powders (boehmite and gibbsite) were tested via thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). The effort aimed to identify or confirm key temperature ranges/thresholds for the thermal decomposition reactions, as well as impacts of ramp rate and hold times, for drying of isolated, high-surface-area (oxy)hydroxides. The information gleaned from powder tests was used to guide subsequent drying tests on adherent (oxy)hydroxide films grown on aluminum alloy substrates. TGA was used to analyze small samples of the aluminum coupons with adherent (oxy)hydroxide films. Specimens were characterized both pre- and post-drying using X-ray diffraction (XRD) to determine the film composition and scanning electron microscopy (SEM) to determine its morphology. Drying of adherent (oxy)hydroxide films was anticipated to pose additional complications relative to drying of (oxy)hydroxide powders. Anticipated challenges include achieving sufficient drying of the (oxy)hydroxide at low-enough temperature to avoid melting or other undesirable phase changes in the aluminum substrate and overcoming transport limitations of water through the thickness of a dense film or through a tortuous pore structure to reach the outer surface of the film. Inn addition, dehydration of (oxy)hydroxides significantly changes the film density, which may lead to substantial alterations in the morphology, including potential cracking and spalling of the film. TGA/DSC tests of gibbsite powders resulted in successful conversion to boehmite or alumina, depending on the maximum temperature reached. At low ramp rates (≤5 deg. C/min), the conversion to boehmite occurred around 300 deg. C (210-340 deg. C). XRD confirmed that boehmite was the only phase detected after tests reaching 450 deg. C. The transition to alumina occurred around 510 deg. C (470-550 deg. C), with XRD detecting only alumina after tests reaching at least 600 deg. C. Boehmite powders dehydrated to alumina at about 400 deg. C (330-460 deg. C) for coarse (77-μm particle diameter) powder and about 490 deg. C (420-520 deg. C) for fine (0.7-μm particle diameter) powder. For all powders tested, the maximum percent mass loss after drying to high temperature slightly exceeded the theoretical mass loss for complete dehydration of the stoichiometric (oxy)hydroxide to alumina, which is likely attributable to physisorbed water in the powder. Drying of a thick (∼8.6 μm), predominantly bayerite adherent film displayed a dramatic change in film morphology, with the initially continuous trihydroxide film cracking into sections on the order of 50 μm square and partially delaminating. The outermost layer of the film completely faked of in some regions. The layer exposed under the spalled oxide also displayed prominent cracking, with spacing on the order of 10 μm, but this surface layer appeared to remain completely adhered to the aluminum substrate. TGA showed mass losses per unit surface area up to ∼1.0 mg/cm{sup 2}. XRD characterization of the remaining oxide was inconclusive, with no crystalline phases detected. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗