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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Smoothing by cubic spline modified applied to solve inverse thermal problem

This paper presents an alternative to cubic spline regularization and its weighted form applied in solving inverse thermal problems. The inverse heat transfer problems are classified as ill-posed, that is, the solution may become unstable, mainly because they are sensitive to random errors deriving from the input data, necessitating a regularization method to soften these effects. The smoothing technique proposed by cubic spline regularization ensures that the global data tend to be more stable, with fewer data oscillations and dependent on a single arbitrary parameter input. It also shows that the weighted cubic spline is able to enhance filter action. The methods have been implemented in order for the search engine to optimize the choice of parameters and weight and, thus, the smoothing gains more flexibility and accuracy. The simulated and experimental tests confirm that the techniques are effective in reducing the amplified noise by inverse thermal problem presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Optimal Estimation Retrievals and Their Uncertainties: What Every Atmospheric Scientist Should Know

Remote sensing instruments are heavily used to provide observations for both the operational and research communities. These sensors do not provide direct observations of the desired atmospheric variables, but instead, retrieval algorithms are necessary to convert the indirect observations into the variable of interest. It is critical to be aware of the underlying assumptions made by many retrieval algorithms, including that the retrieval problem is often ill posed and that there are various sources of uncertainty that need to be treated properly. In short, the retrieval challenge is to invert a set of noisy observations to obtain estimates of atmospheric quantities. The problem is often complicated by imperfect forward models, by imperfect prior knowledge, and by the existence of nonunique solutions. Optimal estimation (OE) is a widely used physical retrieval method that combines measurements, prior information, and the corresponding uncertainties based on Bayes’s theorem to find an optimal solution for the atmospheric state. Furthermore, OE also allows the relative contributions of the different sources of error to the uncertainty in the final retrieved atmospheric state to be understood. Here, we provide a novel Python library to illustrate the use of OE for inverse problems in the atmospheric sciences. We introduce two example problems: how to retrieve drop size distribution parameters from radar observations and how to retrieve the temperature profile from ground-based microwave sensors. Using these examples, we discuss common pitfalls, how the various error sources impact the retrieval, and how the quality of the retrieval results can be quantified.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1995

Contribution to the optimal shape design of two-dimensional internal flows with embedded shocks

We explore the practicability of optimal shape design for flows modeled by the Euler equations. We define a functional whose minimum represents the optimality condition. The gradient of the functional with respect to the geometry is calculated with the Lagrange multipliers, which are determined by solving a co-state equation. The optimization problem is then examined by comparing the performance of several gradient-based optimization algorithms. In this formulation, the flow field can be computed to an arbitrary order of accuracy. Finally, some results for internal flows with embedded shocks are presented, including a case for which the solution to the inverse problem does not belong to the design space.

Iollo, Angelo↗
NASA NTRS1996

Design of Robust Adaptive Unbalance Response Controllers for Rotors with Magnetic Bearings

Experimental results have recently demonstrated that an adaptive open loop control strategy can be highly effective in the suppression of unbalance induced vibration on rotors supported in active magnetic bearings. This algorithm, however, relies upon a predetermined gain matrix. Typically, this matrix is determined by an optimal control formulation resulting in the choice of the pseudo-inverse of the nominal influence coefficient matrix as the gain matrix. This solution may result in problems with stability and performance robustness since the estimated influence coefficient matrix is not equal to the actual influence coefficient matrix. Recently, analysis tools have been developed to examine the robustness of this control algorithm with respect to structured uncertainty. Herein, these tools are extended to produce a design procedure for determining the adaptive law's gain matrix. The resulting control algorithm has a guaranteed convergence rate and steady state performance in spite of the uncertainty in the rotor system. Several examples are presented which demonstrate the effectiveness of this approach and its advantages over the standard optimal control formulation.

Knospe, Carl R.↗
DOE OSTI2017

A First-order Prediction-Correction Algorithm for Time-varying (Constrained) Optimization: Preprint

This paper focuses on the design of online algorithms based on prediction-correction steps to track the optimal solution of a time-varying constrained problem. Existing prediction-correction methods have been shown to work well for unconstrained convex problems and for settings where obtaining the inverse of the Hessian of the cost function can be computationally affordable. The prediction-correction algorithm proposed in this paper addresses the limitations of existing methods by tackling constrained problems and by designing a first-order prediction step that relies on the Hessian of the cost function (and do not require the computation of its inverse). Analytical results are established to quantify the tracking error. Numerical simulations corroborate the analytical results and showcase performance and benefits of the algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Distributed Stochastic Optimization of a Neural Representation Network for Time-Space Tomography Reconstruction

4D time-space reconstruction of dynamic events or deforming objects using X-ray computed tomography (CT) is an important inverse problem in non-destructive evaluation. Conventional back-projection based reconstruction methods assume that the object remains static for the duration of several tens or hundreds of X-ray projection measurement images (reconstruction of consecutive limited-angle CT scans). However, this is an unrealistic assumption for many in-situ experiments that causes spurious artifacts and inaccurate morphological reconstructions of the object. To solve this problem, we propose to perform a 4D time-space reconstruction using a distributed implicit neural representation (DINR) network that is trained using a novel distributed stochastic training algorithm. Our DINR network learns to reconstruct the object at its output by iterative optimization of its network parameters such that the measured projection images best match the output of the CT forward measurement model. Here, we use a forward measurement model that is a function of the DINR outputs at a sparsely sampled set of continuous valued 4D object coordinates. Unlike previous neural representation architectures that forward and back propagate through dense voxel grids that sample the object's entire time-space coordinates, we only propagate through the DINR at a small subset of object coordinates in each iteration resulting in an order-of-magnitude reduction in memory and compute for training. DINR leverages distributed computation across several compute nodes and GPUs to produce high-fidelity 4D time-space reconstructions. We use both simulated parallel-beam and experimental cone-beam X-ray CT datasets to demonstrate the superior performance of our approach.

36 MATERIALS SCIENCE↗
DOE OSTI2022

$\mathrm{IH}$-$\mathrm{GAN}$: A conditional generative model for implicit surface-based inverse design of cellular structures

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignoring the effects of unit cell geometry on properties, or considers the geometry–property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from properties to geometries. Here we further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (R 2 -scores between target properties and properties of generated unit cells >98%) and 2) improve the optimized structural performance over the conventional variable-density single-type structure. In the minimum compliance example, our IH-GAN generated structure achieves a 79.7% reduction in concentrated stress and an extra 3.03% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 86.4% and 79.6% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending.

42 ENGINEERING↗
NASA NTRSDate not supplied

A Comparison of Control Allocation Methods in the Presence of Parametric Model Uncertainty

When allocating redundant effectors to virtual control commands, linear (generalized inverse) allocators have historically been used on aircraft and spacecraft. While simple to implement, generalized inverses are unable to realize a significant portion of the attainable moments. To address this drawback, the control allocation problem can also be formulated as a linear programming or quadratic programming problem and solved using convex optimization based solvers. These approaches have been shown to access a larger set of attainable moments, however, little work has been done to understand the performance of convex optimization-based control allocation in the presence of parametric model uncertainty. This paper seeks to compare the performance of several control allocation approaches, including two forms of generalized inverse allocators, the pseudo inverse and minimum-variance, and the linear programming and quadratic programming approach in the presence of parametric model uncertainty. The performance of these four allocators were tested on an aircraft model in the presence of realistic parametric model uncertainty and the convex optimization approaches were shown to outperform the generalized inverses.

Luke J Miller↗
DOE OSTI2020

A Nonlocal-Gradient Descent Method for Inverse Design in Nanophotonics

Local-gradient-based optimization approaches lack nonlocal exploration abilityrequired for escaping from local minima when searching non-convex landscapes.A directional Gaussian smoothing (DGS) approach was recently proposed in [29]and used to define a truly nonlocal gradient, referred to as the DGS gradient, inorder to enable nonlocal exploration in high-dimensional black-box optimization.Promising results show that replacing the traditional local gradient with the nonlocalDGS gradient can significantly improve the performance of gradient-based methodsin optimizing highly multi-modal loss functions. However, the current DGS methodis designed for unbounded and uncontrained optimization problems, making itinapplicable to real-world engineering optimization problems where the tuningparameters are often bounded and the loss function is usually constrained byphysical processes. In this work, we propose to extend to the DGS approachto the constrained inverse design framework in order to find better optima ofmulti-modal loss functions. A series of adaptive strategies for smoothing radiusand learning rate updating are developed to improve the computational efficiencyand robustness. Our methodology is demonstrated by an example of designing ananoscale wavelength demultiplexer, and shows superior performance compared tothe state-of-the-art approaches. By incorporating volume constraints, the optimizeddesign achieves an equivalently high performance but significantly reduces theamount of material usage.

Bi, Sirui↗
DOE OSTI2016

Optimization-Based Approach for Joint X-Ray Fluorescence and Transmission Tomographic Inversion

Fluorescence tomographic reconstruction, based on the detection of photons coming from fluorescent emission, can be used for revealing the internal elemental composition of a sample. On the other hand, conventional X-ray transmission tomography can be used for reconstructing the spatial distribution of the absorption coefficient inside a sample. In this work, we integrate both X-ray fluorescence and X-ray transmission data modalities and formulate a nonlinear optimization-based approach for reconstruction of the elemental composition of a given object. This model provides a simultaneous reconstruction of both the quantitative spatial distribution of all elements and the absorption effect in the sample. Mathematically speaking, we show that compared with the single-modality inversion (i.e., the X-ray transmission or fluorescence alone), the joint inversion provides a better-posed problem, which implies a better recovery. Therefore, the challenges in X-ray fluorescence tomography arising mainly from the effects of self-absorption in the sample are partially mitigated. The use of this technique is demonstrated on the reconstruction of several synthetic samples.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Scientific Computational Imaging Code (SCICO)

Scientific Computational Imaging Code (SCICO) is a Python package for solving the inverse problems that arise in scientific imaging applications. Its primary focus is providing methods for solving ill-posed inverse problems by using an appropriate prior model of the reconstruction space. SCICO includes a growing suite of operators, cost functionals, regularizers, and optimization routines that may be combined to solve a wide range of problems, and is designed so that it is easy to add new building blocks. SCICO is built on top of JAX rather than NumPy, enabling GPU/TPU acceleration, just-in-time compilation, and automatic gradient functionality, which is used to automatically compute the adjoints of linear operators. An example of how to solve a multi-channel tomography problem with SCICO is shown in Figure 1. The SCICO source code is available from GitHub, and pre-built packages are available from PyPI. It has extensive online documentation, including API documentation and usage examples, which can be run online at Google Colab and binder.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Application of a stochastic inverse to the geophysical inverse problem

The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.

Jordan, T. H.↗
DOE OSTI2023

Solving multiphysics-based inverse problems with learned surrogates and constraints

Abstract Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. Not only does this combination lead to vastly improved inversions for the important fluid-flow property, permeability, it also provides a natural platform for inverting multimodal data including well measurements and active-source time-lapse seismic data. By adding a learned constraint, we arrive at a computationally feasible inversion approach that remains accurate. This is accomplished by including a trained deep neural network, known as a normalizing flow, which forces the model iterates to remain in-distribution, thereby safeguarding the accuracy of trained Fourier neural operators that act as surrogates for the computationally expensive multiphase flow simulations involving partial differential equation solves. By means of carefully selected experiments, centered around the problem of geological carbon storage, we demonstrate the efficacy of the proposed constrained optimization method on two different data modalities, namely time-lapse well and time-lapse seismic data. While permeability inversions from both these two modalities have their pluses and minuses, their joint inversion benefits from either, yielding valuable superior permeability inversions and CO 2 plume predictions near, and far away, from the monitoring wells.

Yin, Ziyi (ORCID:0000000250248771)↗
DOE OSTI2020

Novel strategies for modal-based structural material identification

Here, we present modal-based methods for model calibration in structural dynamics, and address several key challenges in the solution of gradient-based optimization problems with eigenvalues and eigenvectors, including the solution of singular Helmholtz problems encountered in sensitivity calculations, non-differentiable objective functions caused by mode swapping during optimization, and cases with repeated eigenvalues. Unlike previous literature that relied on direct solution of the eigenvector adjoint equations, we present a parallel iterative domain decomposition strategy (Adjoint Computation via Modal Superposition with Truncation Augmentation) for the solution of the singular Helmholtz problems. For problems with repeated eigenvalues we present a novel Mode Separation via Projection algorithm, and in order to address mode swapping between inverse iterations we present a novel Injective mode ordering metric. We present the implementation of these methods in a massively parallel finite element framework with the ability to use measured modal data to extract unknown structural model parameters from large complex problems. A series of increasingly complex numerical examples are presented that demonstrate the implementation and performance of the methods in a massively parallel finite element framework [7], [5], using gradient-based optimization techniques in the Rapid Optimization Library (ROL) [21].

36 MATERIALS SCIENCE↗
DOE OSTI2017

Accurate Holdup Calculations with Predictive Modeling & Data Integration

In facilities that process special nuclear material (SNM) it is important to account accurately for the fissile material that enters and leaves the plant. Although there are many stages and processes through which materials must be traced and measured, the focus of this project is material that is “held-up” in equipment, pipes, and ducts during normal operation and that can accumulate over time into significant quantities. Accurately estimating the holdup is essential for proper SNM accounting (vis-à-vis nuclear non-proliferation), criticality and radiation safety, waste management, and efficient plant operation. Usually it is not possible to directly measure the holdup quantity and location, so these must be inferred from measured radiation fields, primarily gamma and less frequently neutrons. Current methods to quantify holdup, i.e. Generalized Geometry Holdup (GGH), primarily rely on simple source configurations and crude radiation transport models aided by ad hoc correction factors. This project seeks an alternate method of performing measurement-based holdup calculations using a predictive model that employs state-of-the-art radiation transport codes capable of accurately simulating such situations. Inverse and data assimilation methods use the forward transport model to search for a source configuration that best matches the measured data and simultaneously provide an estimate of the level of confidence in the correctness of such configuration. In this work the holdup problem is re-interpreted as an inverse problem that is under-determined, hence may permit multiple solutions. A probabilistic approach is applied to solving the resulting inverse problem. This approach rates possible solutions according to their plausibility given the measurements and initial information. This is accomplished through the use of Bayes’ Theorem that resolves the issue of multiple solutions by giving an estimate of the probability of observing each possible solution. To use Bayes’ Theorem, one must have a model y(x) that maps the state variables x (the solution in this case) to the measurements y. In this case, the unknown state variables are the configuration and composition of the heldup SNM. The measurements are the detector readings. Thus, the natural model is neutral-particle radiation transport where a wealth of computational tools exists for performing these simulations accurately and efficiently. The combination of predictive model and Bayesian inference forms the Data Integration with Modeled Predictions (DIMP) method that serves as foundation for this project. The cost functional describing the model-to-data misfit is computed via a norm created by the inverse of the covariance matrix of the model parameters and responses. Since the model y(x) for the holdup problem is nonlinear, a nonlinear optimization on Q is conducted via Newton-type iterative methods to find the optimal values of the model parameters x. This project comprised a collaboration between NC State University (NCSU), the University of South Carolina (USC), and Oak Ridge National Laboratory (ORNL). The project was originally proposed in seven main tasks with an eighth contingency task to be performed if time and funding permitted; in fact time did not permit commencement of the contingency task and it was not performed. The remaining tasks involved holdup analysis with gamma detection strategies and separately with neutrons based on coincidence counting. Early in the project, and upon consultation with experts in coincidence counting it became evident that this approach is not viable for holdup applications and this task was replaced with an alternative, but valuable investigation that was carried out by the USC partner. Nevertheless, the experimental 4 measurements at ORNL of both gamma and neutron sources for the purpose of constructing Detector Response Functions (DRFs) with the associated uncertainties were indeed completed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2018

A genetic meta-algorithm-assisted inversion approach: hydrogeological study for the determination of volumetric rock properties and matrix and fluid parameters in unsaturated formations

An evolutionary inversion approach is suggested for the interpretation of nuclear and resistivity logs measured by direct-push tools in shallow unsaturated sediments. The efficiency of formation evaluation is improved by estimating simultaneously (1) the petrophysical properties that vary rapidly along a drill hole with depth and (2) the zone parameters that can be treated as constant, in one inversion procedure. In the workflow, the fractional volumes of water, air, matrix and clay are estimated in adjacent depths by linearized inversion, whereas the clay and matrix properties are updated using a float-encoded genetic meta-algorithm. The proposed inversion method provides an objective estimate of the zone parameters that appear in the tool response equations applied to solve the forward problem, which can significantly increase the reliability of the petrophysical model as opposed to setting these parameters arbitrarily. The global optimization meta-algorithm not only assures the best fit between the measured and calculated data but also gives a reliable solution, practically independent of the initial model, as laboratory data are unnecessary in the inversion procedure. The feasibility test uses engineering geophysical sounding logs observed in an unsaturated loessy-sandy formation in Hungary. The multi-borehole extension of the inversion technique is developed to determine the petrophysical properties and their estimation errors along a profile of drill holes. The genetic meta-algorithmic inversion method is recommended for hydrogeophysical logging applications of various kinds to automatically extract the volumetric ratios of rock and fluid constituents as well as the most important zone parameters in a reliable inversion procedure.

58 GEOSCIENCES↗
DOE OSTI2018

Applying a predictive modeling methodology to a radiation transport inverse problem - 25588

In this paper, the predictive modeling of coupled multiphysics systems (PM-CMPS) procedure, developed by Cacuci and embodied in the software package MULTIPRED, has been applied to determine unknown parameters of a radioactive system from its gamma-ray and neutron signature. PM-CMPS has been integrated in two different ways with the inverse transport code INVERSE to determine the parameters. The first uses PM-CMPS in the inverse mode to directly estimate the parameters while the second mode uses a traditional nonlinear optimization routine and has PMCMPS complete a final iteration to estimate the uncertainty in the parameter best estimates. A test problem has been created and used to test both methods for varying numbers and types of responses and parameters. The first method was capable of accurately determining parameters but had a number of drawbacks. The second method functioned well at determining the correct parameter values in cases with limited numbers of parameters. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗