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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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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Topology optimization of 3D photonic crystals with complete bandgaps

The design of photonic crystals with complete bandgaps has recently received considerable research focus for numerous reasons. This work leverages well-known nonlinear programming techniques to alleviate the non-smoothness caused by degenerate eigenvalues such that topology optimization problems can be solved with the open-source IPOPT software. A fully-vectorial plane wave expansion technique is used with an iterative eigensolver to efficiently predict dispersion properties of candidate structures. Nonlinear programming is employed to solve the inverse problem of designing three-dimensional periodic structures that exhibit complete two-dimensional (2D) and three-dimensional (3D) photonic bandgaps. Mesh refinement is performed to alleviate the large computational burden of designing and analyzing photonic crystals, and a periodic density filter is implemented to impose a minimum feature size for manufacturability considerations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

A methodology for designing robust multivariable nonlinear feedback control systems

This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.

Grunberg, D. B.↗
DOE OSTI2021

Rapid 3D nanoscale coherent imaging via physics-aware deep learning

Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of phase recovery is iterative in nature. As a result, the image formation is time consuming and computationally expensive, precluding real-time imaging. Here, we use 3D nanoscale X-ray imaging as a representative example to develop a deep learning model to address this phase retrieval problem. We introduce 3D-CDI-NN, a deep convolutional neural network and differential programing framework trained to predict 3D structure and strain, solely from input 3D X-ray coherent scattering data. Our networks are designed to be “physics-aware” in multiple aspects; in that the physics of the X-ray scattering process is explicitly enforced in the training of the network, and the training data are drawn from atomistic simulations that are representative of the physics of the material. We further refine the neural network prediction through a physics-based optimization procedure to enable maximum accuracy at lowest computational cost. 3D-CDI-NN can invert a 3D coherent diffraction pattern to real-space structure and strain hundreds of times faster than traditional iterative phase retrieval methods. Our integrated machine learning and differential programing solution to the phase retrieval problem is broadly applicable across inverse problems in other application areas.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Multimodal parameter spaces of a complex multi-channel neuron model

One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin–Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Physics constrained learning for data-driven inverse modeling from sparse observations

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Interpretation of lightcurves of atmosphereless bodies. I - General theory and new inversion schemes

Theoretical models of light-curve inversion that can be used in photomorphography, i.e., determination of the 3D shape and/or the light-scattering behavior of the surface of a body from disk-integrated photometry. These methods can be applied to atmosphereless bodies, mainly asteroids and planetary satellites, in the solar system. The inversion comprises three steps. First, a function containing data on the shape and the albedo variegation of an asteroid is determined. In the second step, separate expressions for the inverse of the Gaussian curvature and the albedo distribution are derived from the information obtained in the first step. In the third step, the nontrivial problem of determining the radius vector of the surface from the Gaussian curvature is solved by using iterative optimization procedures.

Kaasalainen, M.↗
DOE OSTI2023

MOOSE Optimization Module Overview: Application to Residual Stress Inversion in Nuclear Fuel Plates

Manufacturing methods, material selections and unique plate geometries used in low enriched uranium plate fuels for the High Performance Research Reactor (HPRR) have led to concerns about the residual stresses effect on bond strength of the fuel/cladding interfaces and overall fuel performance under irradiation. The current HPRR plate fuel test program performed residual stress calculations using the contour method with experimental displacement data obtained by incrementally cutting the plate fuel. In this work, we use a gradient based inverse optimization module developed within the MOOSE framework to estimate normal and shear residual stresses within the plate fuels using displacement data taken from a cut placed in the HPRR fuel plate. These results are verified against residual stress calculations obtained from the contour method. The inversion protocol used in this work utilizes two meshes to separately discretize the physics and parameter space. This allows a fine mesh to be used to fully resolve the physics and geometry of the forward problem. A coarser mesh is used to resolve the parameter space with spatially varying mesh density determined from a sensitivity analysis. The adaptive resolution of the parameter space essentially has the effect of regularization as it is designed to achieve the bias-variance tradeoff.

42 ENGINEERING↗
DOE OSTI2021

A persistent adjoint method with dynamic time-scaling and an application to mass action kinetics

In this article, we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since the derivative of the fixed-point with respect to the parameter can usually not be evaluated exactly, an adjoint dynamical system can be used to estimate gradients. Using this estimation procedure, the optimization algorithm alternates between derivative estimation and an approximate gradient descent step. We analyze a variant of this approach involving dynamic time-scaling, where after each parameter update the adjoint system is iterated until a convergence threshold is passed. Here, we prove that, under certain conditions, the algorithm can find approximate stationary points of the objective function. We demonstrate the approach in the settings of an inverse problem in chemical kinetics, and learning in attractor networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains. The proposed framework, named eXtended PINNs ( X P I N N s ), further pushes the boundaries of both PINNs as well as conservative PINNs (cPINNs), which is a recently proposed domain decomposition approach in the PINN framework tailored to conservation laws. Compared to PINN, the XPINN method has large representation and parallelization capacity due to the inherent property of deployment of multiple neural networks in the smaller subdomains. Unlike cPINN, XPINN can be extended to any type of PDEs. Moreover, the domain can be decomposed in any arbitrary way (in space and time), which is not possible in cPINN. Thus, XPINN offers both space and time parallelization, thereby reducing the training cost more effectively. In each subdomain, a separate neural network is employed with optimally selected hyperparameters, e.g., depth/width of the network, number and location of residual points, activation function, optimization method, etc. A deep network can be employed in a subdomain with complex solution, whereas a shallow neural network can be used in a subdomain with relatively simple and smooth solutions. We demonstrate the versatility of XPINN by solving both forward and inverse PDE problems, ranging from one-dimensional to three-dimensional problems, from time-dependent to time-independent problems, and from continuous to discontinuous problems, which clearly shows that the XPINN method is promising in many practical problems. The proposed XPINN method is the generalization of PINN and cPINN methods, both in terms of applicability as well as domain decomposition approach, which efficiently lends itself to parallelized computation. The XPINN code is available on h t t p s : / / g i t h u b . c o m / A m e y a J a g t a p / X P I N N s .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Inverse Design of Two-Dimensional Airfoils Using Conditional Generative Models and Surrogate Log-Likelihoods

Abstract This paper shows how to use conditional generative models in two-dimensional (2D) airfoil optimization to probabilistically predict good initialization points within the vicinity of the optima given the input boundary conditions, thus warm starting and accelerating further optimization. We accommodate the possibility of multiple optimal designs corresponding to the same input boundary condition and take this inversion ambiguity into account when designing our prediction framework. To this end, we first employ the conditional formulation of our previous work BézierGAN–Conditional BézierGAN (CBGAN)—as a baseline, then introduce its sibling conditional entropic BézierGAN (CEBGAN), which is based on optimal transport regularized with entropy. Compared with CBGAN, CEBGAN overcomes mode collapse plaguing conventional GANs, improves the average lift-drag (Cl/Cd) efficiency of airfoil predictions from 80.8% of the optimal value to 95.8%, and meanwhile accelerates the training process by 30.7%. Furthermore, we investigate the unique ability of CEBGAN to produce a log-likelihood lower bound that may help select generated samples of higher performance (e.g., aerodynamic performance). In addition, we provide insights into the performance differences between these two models with low-dimensional toy problems and visualizations. These results and the probabilistic formulation of this inverse problem justify the extension of our GAN-based inverse design paradigm to other inverse design problems or broader inverse problems.

Engineering↗
DOE OSTI2022

Three-dimensional Skyrme Hartree-Fock-Bogoliubov solver in coordinate-space representation

The coordinate-space representation of the Hartree-Fock-Bogoliubov theory is the method of choice to study weakly bound nuclei whose properties are affected by the quasiparticle continuum space. To describe such systems, we developed a three-dimensional Skyrme-Hartree-Fock-Bogoliubov solver HFBFFT based on the existing, highly optimized and parallelized Skyrme-Hartree-Fock code Sky3D. The code does not impose any self-consistent spatial symmetries such as mirror inversions or parity. The underlying equations are solved in HFBFFT directly in the canonical basis using the fast Fourier transform. To remedy the problems with pairing collapse, we implemented the soft energy cutoff and pairing annealing. The convergence of HFB solutions was improved by a sub-iteration method. The Hermiticity violation of differential operators brought by Fourier-transform-based differentiation has also been solved. Furthermore, the accuracy and performance of HFBFFT were tested by benchmarking it against other HFB codes, both spherical and deformed, for a set of nuclei, both well-bound and weakly-bound.

3D coordinate-space representation↗
DOE OSTI2025

Estimating QSVT angles for matrix inversion with large condition numbers

Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a sequence of angles that must be pre-calculated classically, with the number of angles increasing as the matrix condition number grows. Computing QSVT angles for ill-conditioned problems is a numerically challenging task. Here, we propose a numerical technique for estimating QSVT angles for large condition numbers. This technique allows one to avoid expensive numerical computations of QSVT angles and to emulate QSVT circuits for solving ill-conditioned problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Application and performance of an ML-EM algorithm in NEXT

The goal of the NEXT experiment is the observation of neutrinoless double beta decay in (136)Xe using a gaseous xenon TPC with electroluminescent amplification and specialized photodetector arrays for calorimetry and tracking. The NEXT Collaboration is exploring a number of reconstruction algorithms to exploit the full potential of the detector. This paper describes one of them: the Maximum Likelihood Expectation Maximization (ML-EM) method, a generic iterative algorithm to find maximum-likelihood estimates of parameters that has been applied to solve many different types of complex inverse problems. In particular, we discuss a bi-dimensional version of the method in which the photosensor signals integrated over time are used to reconstruct a transverse projection of the event. First results show that, when applied to detector simulation data, the algorithm achieves nearly optimal energy resolution (better than 0.5% FWHM at the Q value of (136)Xe) for events distributed over the full active volume of the TPC.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Lossy checkpoint compression in full waveform inversion: a case study with ZFPv0.5.5 and the overthrust model

This paper proposes a new method that combines checkpointing methods with error-controlled lossy compression for large-scale high-performance full-waveform inversion (FWI), an inverse problem commonly used in geophysical exploration. This combination can significantly reduce data movement, allowing a reduction in run time as well as peak memory. In the exascale computing era, frequent data transfer (e.g., memory bandwidth, PCIe bandwidth for GPUs, or network) is the performance bottleneck rather than the peak FLOPS of the processing unit. Like many other adjoint-based optimization problems, FWI is costly in terms of the number of floating-point operations, large memory footprint during backpropagation, and data transfer overheads. Past work for adjoint methods has developed checkpointing methods that reduce the peak memory requirements during backpropagation at the cost of additional floating-point computations. Combining this traditional checkpointing with error-controlled lossy compression, we explore the three-way tradeoff between memory, precision, and time to solution. We investigate how approximation errors introduced by lossy compression of the forward solution impact the objective function gradient and final inverted solution. Empirical results from these numerical experiments indicate that high lossy-compression rates (compression factors ranging up to 100) have a relatively minor impact on convergence rates and the quality of the final solution.

58 GEOSCIENCES↗
NASA NTRS2002

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine and compared to earlier methods. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗
NASA NTRS2002

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗
NASA NTRS2022

Simultaneous Retrieval of Selected Optical Water Quality Indicators From Landsat-8, Sentinel-2, and Sentinel-3

Constructing multi-source satellite-derived water quality (WQ) products in inland and nearshore coastal waters from the past, present, and future missions is a long-standing challenge. Despite inherent differences in sensors’ spectral capability, spatial sampling, and radiometric performance, research efforts focused on formulating, implementing, and validating universal WQ algorithms continue to evolve. This research extends a recently developed machine-learning (ML) model, i.e., Mixture Density Networks (MDNs) (Pahlevan et al., 2020; Smith et al., 2021), to the inverse problem of simultaneously retrieving WQ indicators, including chlorophyll-a (Chla), Total Suspended Solids (TSS), and the absorption by Colored Dissolved Organic Matter at 440 nm (a cdom (440)), across a wide array of aquatic ecosystems. We use a database of in situ measurements to train and optimize MDN models developed for the relevant spectral measurements (400–800 nm) of the Operational Land Imager (OLI), MultiSpectral Instrument (MSI), and Ocean and Land Color Instrument (OLCI) aboard the Landsat-8, Sentinel-2, and Sentinel-3 missions, respectively. Our two performance assessment approaches, namely hold-out and leave-one-out, suggest significant, albeit varying degrees of improvements with respect to second-best algorithms, depending on the sensor and WQ indicator (e.g., 68%, 75%, 117% improvements based on the hold-out method for Chla, TSS, and a cdom (440), respectively from MSI-like spectra). Using these two assessment methods, we provide theoretical upper and lower bounds on model performance when evaluating similar and/or out-of-sample datasets. To evaluate multi-mission product consistency across broad spatial scales, map products are demonstrated for three near-concurrent OLI, MSI, and OLCI acquisitions. Overall, estimated TSS and a cdom (440) from these three missions are consistent within the uncertainty of the model, but Chla maps from MSI and OLCI achieve greater accuracy than those from OLI. By applying two different atmospheric correction processors to OLI and MSI images, we also conduct matchup analyses to quantify the sensitivity of the MDN model and best-practice algorithms to uncertainties in reflectance products. Our model is less or equally sensitive to these uncertainties compared to other algorithms. Recognizing their uncertainties, MDN models can be applied as a global algorithm to enable harmonized retrievals of Chla, TSS, and a cdom (440) in various aquatic ecosystems from multi-source satellite imagery. Local and/or regional ML models tuned with an apt data distribution (e.g., a subset of our dataset) should nevertheless be expected to outperform our global model.

Machine learning↗
DOE OSTI2021

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗