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Results for “optimization, 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.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

High fidelity ultrasound imaging of concrete structures

As plans are made to extend licenses for the aging fleet of commercial nuclear power plants for periods of sixty years and beyond, research into the long-term integrity of their concrete structures has increased. Ultrasound tomography is a useful tool for nondestructive evaluation of these concrete structures. Typically, pulse-echo measurements are made over a large surface and are processed using a reconstruction algorithm, producing a 3D image of the structure that highlights embedded defects. These measurements are processed using a delay-and-sum algorithm such as the synthetic aperture focusing technique (SAFT). Oak Ridge National Laboratory is developing novel ultrasound model-based image reconstruction (U-MBIR) algorithms to improve the imaging capability of pulse-echo ultrasound array imagers. U-MBIR is an inversion technique that reconstructs the sample under test from the ultrasound measurements by formulating and solving a mathematical optimization problem using two sets of terms: one set ensures that the reconstruction matches measured data based on a model for the physics of beam propagation with the noise in the detector, and another set ensures that the reconstruction has certain properties based on a model for the object being scanned. This paper compares three techniques: SAFT, frequency-banded SAFT (FB-SAFT), and U-MBIR. The U-MBIR method produces higher quality images of the underlying concrete structures compared to the images produced using SAFT and FB-SAFT from the same set of measurements. This paper also illustrates the detection of various defects with higher confidence due to the lower noise and artifact-free U-MBIR images.

Ezell, N Dianne↗
DOE OSTI2024

Inverse design for waveguide dispersion with a differentiable mode solver

Inverse design of optical components based on adjoint sensitivity analysis has the potential to address the most challenging photonic engineering problems. However, existing inverse design tools based on finite-difference-time-domain (FDTD) models are poorly suited for optimizing waveguide modes for adiabatic transformation or perturbative coupling, which lies at the heart of many important photonic devices. Among these, dispersion engineering of optical waveguides is especially challenging in ultrafast and nonlinear optical applications involving broad optical bandwidths and frequency-dependent anisotropic dielectric material response. In this work, we develop gradient back-propagation through a general-purpose electromagnetic eigenmode solver and use it to demonstrate waveguide dispersion optimization for second harmonic generation with maximized phase-matching bandwidth. This optimization of three design parameters converges in eight steps, reducing the computational cost of optimization by ∼100x compared to exhaustive search and identifying new designs for broadband optical frequency doubling of laser sources in the 1.3–1.4 µm wavelength range. Furthermore, we demonstrate that the computational cost of gradient back-propagation is independent of the number of parameters, as required for optimization of complex geometries. This technique enables practical inverse design for a broad range of previously intractable photonic devices.

Gray, Dodd (ORCID:000000030469599X)↗
DOE OSTI2022

A Probabilistic Autoencoder for Type Ia Supernova Spectral Time Series

We construct a physically parameterized probabilistic autoencoder (PAE) to learn the intrinsic diversity of Type Ia supernovae (SNe Ia) from a sparse set of spectral time series. The PAE is a two-stage generative model, composed of an autoencoder that is interpreted probabilistically after training using a normalizing flow. We demonstrate that the PAE learns a low-dimensional latent space that captures the nonlinear range of features that exists within the population and can accurately model the spectral evolution of SNe Ia across the full range of wavelength and observation times directly from the data. By introducing a correlation penalty term and multistage training setup alongside our physically parameterized network, we show that intrinsic and extrinsic modes of variability can be separated during training, removing the need for the additional models to perform magnitude standardization. We then use our PAE in a number of downstream tasks on SNe Ia for increasingly precise cosmological analyses, including the automatic detection of SN outliers, the generation of samples consistent with the data distribution, and solving the inverse problem in the presence of noisy and incomplete data to constrain cosmological distance measurements. We find that the optimal number of intrinsic model parameters appears to be three, in line with previous studies, and show that we can standardize our test sample of SNe Ia with an rms of 0.091 ± 0.010 mag, which corresponds to 0.074 ± 0.010 mag if peculiar velocity contributions are removed.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1971

Users manual for the Variable dimension Automatic Synthesis Program (VASP)

A dictionary and some problems for the Variable Automatic Synthesis Program VASP are submitted. The dictionary contains a description of each subroutine and instructions on its use. The example problems give the user a better perspective on the use of VASP for solving problems in modern control theory. These example problems include dynamic response, optimal control gain, solution of the sampled data matrix Ricatti equation, matrix decomposition, and pseudo inverse of a matrix. Listings of all subroutines are also included. The VASP program has been adapted to run in the conversational mode on the Ames 360/67 computer.

White, J. S.↗
NASA NTRS1992

A boundary integral method for an inverse problem in thermal imaging

An inverse problem in thermal imaging involving the recovery of a void in a material from its surface temperature response to external heating is examined. Uniqueness and continuous dependence results for the inverse problem are demonstrated, and a numerical method for its solution is developed. This method is based on an optimization approach, coupled with a boundary integral equation formulation of the forward heat conduction problem. Some convergence results for the method are proved, and several examples are presented using computationally generated data.

Bryan, Kurt↗
DOE OSTI2015

Inconsistent Investment and Consumption Problems

In a traditional Black–Scholes market we develop a verification theorem for a general class of investment and consumption problems where the standard dynamic programming principle does not hold. The theorem is an extension of the standard Hamilton–Jacobi–Bellman equation in the form of a system of non-linear differential equations. We derive the optimal investment and consumption strategy for a mean-variance investor without pre-commitment endowed with labor income. In the case of constant risk aversion it turns out that the optimal amount of money to invest in stocks is independent of wealth. The optimal consumption strategy is given as a deterministic bang-bang strategy. In order to have a more realistic model we allow the risk aversion to be time and state dependent. Of special interest is the case were the risk aversion is inversely proportional to present wealth plus the financial value of future labor income net of consumption. Using the verification theorem we give a detailed analysis of this problem. It turns out that the optimal amount of money to invest in stocks is given by a linear function of wealth plus the financial value of future labor income net of consumption. The optimal consumption strategy is again given as a deterministic bang-bang strategy. We also calculate, for a general time and state dependent risk aversion function, the optimal investment and consumption strategy for a mean-standard deviation investor without pre-commitment. In that case, it turns out that it is optimal to take no risk at all.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Neural Networks to Find the Optimal Forcing for Offsetting the Anthropogenic Climate Change Effects

Abstract Of great relevance to climate engineering is the systematic relationship between the radiative forcing to the climate system and the response of the system, a relationship often represented by the linear response function (LRF) of the system. However, estimating the LRF often becomes an ill-posed inverse problem due to high-dimensionality and nonunique relationships between the forcing and response. Recent advances in machine learning make it possible to address the ill-posed inverse problem through regularization and sparse system fitting. Here, we develop a convolutional neural network (CNN) for regularized inversion. The CNN is trained using the surface temperature responses from a set of Green’s function perturbation experiments as imagery input data together with data sample densification. The resulting CNN model can infer the forcing pattern responsible for the temperature response from out-of-sample forcing scenarios. This promising proof of concept suggests a possible strategy for estimating the optimal forcing to negate certain undesirable effects of climate change. The limited success of this effort underscores the challenges of solving an inverse problem for a climate system with inherent nonlinearity. Significance Statement Predicting the climate response for a given climate forcing is a direct problem, while inferring the forcing for a given desired climate response is often an inverse, ill-posed, problem, posing a new challenge to the climate community. This study makes the first attempt to infer the radiative forcing for a given target pattern of global surface temperature response using a deep learning approach. The resulting deeply trained convolutional neural network inversion model shows promise in capturing the forcing pattern corresponding to a given surface temperature response, with a significant implication on the design of an optimal solar radiation management strategy for curbing global warming. This study also highlights the technical challenges that future research should prioritize in seeking feasible solutions to the inverse climate problem.

Ren, Huiying↗
NASA NTRS2017

Remote Sensing of Precipitation from Airborne and Spaceborne Radar

Weather radar measurements from airborne or satellite platforms can be an effective remote sensing tool for examining the three-dimensional structures of clouds and precipitation. This chapter describes some fundamental properties of radar measurements and their dependence on the particle size distribution (PSD) and radar frequency. The inverse problem of solving for the vertical profile of PSD from a profile of measured reflectivity is stated as an optimal estimation problem for single- and multi-frequency measurements. Phenomena that can change the measured reflectivity Z(sub m) from its intrinsic value Z(sub e), namely attenuation, non-uniform beam filling, and multiple scattering, are described and mitigation of these effects in the context of the optimal estimation framework is discussed. Finally, some techniques involving the use of passive microwave measurements to further constrain the retrieval of the PSD are presented.

cloud↗
NASA NTRS1990

Optimal impulsive time-fixed orbital rendezvous and interception with path constraints

Minimum-fuel, impulsive, time-fixed solutions are obtained for the problem of orbital rendezvous and interception with interior path constraints. Transfers between coplanar circular orbits in an inverse-square gravitational field are considered, subject to a circular path constraint representing a minimum or maximum permissible orbital radius. Primer vector theory is extended to incorporate path constraints. The optimal number of impulses, their times and positions, and the presence of initial or final coasting arcs are determined. The existence of constraint boundary arcs and boundary points is investigated as well as the optimality of a class of singular arc solutions. To illustrate the complexities introduced by path constraints, an analysis is made of optimal rendezvous in field-free space subject to a minimum radius constraint.

Taur, D.-R.↗
DOE OSTI2015

Optimizing Interacting Potentials to Form Targeted Materials Structures

Conventional applications of the principles of statistical mechanics (the "forward" problems), start with particle interaction potentials, and proceed to deduce local structure and macroscopic properties. Other applications (that may be classified as "inverse" problems), begin with targeted configurational information, such as low-order correlation functions that characterize local particle order, and attempt to back out full-system configurations and/or interaction potentials. To supplement these successful experimental and numerical "forward" approaches, we have focused on inverse approaches that make use of analytical and computational tools to optimize interactions for targeted self-assembly of nanosystems. The most original aspect of our work is its inherently inverse approach: instead of predicting structures that result from given interaction potentials among particles, we determine the optimal potential that most robustly stabilizes a given target structure subject to certain constraints. Our inverse approach could revolutionize the manner in which materials are designed and fabricated. There are a number of very tangible properties (e.g. zero thermal expansion behavior), elastic constants, optical properties for photonic applications, and transport properties.

36 MATERIALS SCIENCE↗
DOE OSTI2023

An asynchronous parallel high-throughput model calibration framework for crystal plasticity finite element constitutive models

Crystal plasticity finite element model (CPFEM) is a powerful numerical simulation in the integrated computational materials engineering toolboxes that relates microstructures to homogenized materials properties and establishes the structure–property linkages in computational materials science. However, to establish the predictive capability, one needs to calibrate the underlying constitutive model, verify the solution and validate the model prediction against experimental data. Bayesian optimization (BO) has stood out as a gradient-free efficient global optimization algorithm that is capable of calibrating constitutive models for CPFEM. Here in this paper, we apply a recently developed asynchronous parallel constrained BO algorithm to calibrate phenomenological constitutive models for stainless steel 304 L, Tantalum, and Cantor high-entropy alloy.

304L stainless steel↗
DOE OSTI2021

Bound Constrained Partial DifferentialEquation Inverse Problem Solution by theSemi-Smooth Newton Method

We present the mathematical derivation, software implementation details, and computational results for a semi-smooth Newton method applied to two inverse problems governed by partial differential equations with bound constraints. The two problems share mathematical structural similarities to density-based topology optimization problems. The semi-smooth Newton method provides a mesh independent solution computation for the two test problems. A key step is that the complementarity part of the necessary optimality conditions are reformulated with the use of a complementarity functionφsuch that the complementarity conditions are satisfied if and only if a zero of a nonsmooth function has been obtained. The modular finite element package MFEM is utilized for the software implementation. In addition we constructed a matrix-free Operator to enable the use of efficient Krylov subspace IterativeSolver of MFEM for the solution of our two target problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Pragmatic Uncertainty Quantification and Propagation in Inverse Estimation of Structural Dynamics Parameters given Material Property Uncertainties and Limited Sensor Data

In this report we demonstrate some relatively simple and inexpensive methods to effectively account for various sources of epistemic lack-of-knowledge type uncertainty in inverse problems. The demonstration problem involves inverse estimation of six parameters of a bolted joint that attaches a kettlebell shaped object to a thick plate. The parameters are efficiently inverted in a modal-based model calibration using gradient-based optimization. Two material properties of the kettlebell are treated as uncertain to within given epistemic uncertainty bounds. We apply and test interval and sparse-sample probabilistic approaches to account for uncertainty in the estimated parameters (and various scalar functionals of the parameters as generic quantities of interest, QOIs) due to uncertainties in the material properties. We also investigate the error effects of limited numbers of vibration sensors (accelerometers) on the kettlebell and plate, and therefore abbreviated excitation/response information in the parameter inversions. We propose and demonstrate a Leave-K-Sensors-Out “cross-prediction” UQ approach to estimate related uncertainties on the parameters and QOI functionals. We indicate how uncertainties from material properties and limited sensors are treated in a combined manner. The economical combined UQ approach involves just three to five samples (i.e. three to five inverse simulations), with no added complication or error/uncertainty from use of surrogate models for affordability. Finally, we describe a related economical UQ approach for handling potential parameter solution non-uniqueness and numerical optimization related precision uncertainties in the estimated parameter values. Indicated further research is identified.

36 MATERIALS SCIENCE↗
NASA NTRS1991

Inverse problems in the design, modeling and testing of engineering systems

Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.

Alifanov, Oleg M.↗
DOE OSTI2017

Prediction-Correction Algorithms for Time-Varying Constrained Optimization

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do not require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Improving the Quasi‐Biennial Oscillation via a Surrogate‐Accelerated Multi‐Objective Optimization

Accurate simulation of the quasi-biennial oscillation (QBO) is challenging due to uncertainties in representing convectively generated gravity waves. We develop an end-to-end uncertainty quantification workflow that calibrates these gravity wave processes in E3SM for a realistic QBO. Central to our approach is a domain knowledge-informed, compressed representation of high-dimensional spatio-temporal wind fields. By employing a parsimonious statistical model that learns the fundamental frequency from complex observations, we extract interpretable and physically meaningful quantities capturing key attributes. Building on this, we train a probabilistic surrogate model that approximates the fundamental characteristics of the QBO as functions of critical physics parameters governing gravity wave generation. Leveraging the Karhunen–Loève decomposition, our surrogate efficiently represents these characteristics as a set of orthogonal features, capturing cross-correlations among multiple physics quantities evaluated at different pressure levels and enabling rapid surrogate-based inference at a fraction of the computational cost of full-scale simulations. Finally, we analyze the inverse problem using a multi-objective approach. Our study reveals a tension between amplitude and period that constrains the QBO representation, precluding a single optimal solution. To navigate this, we quantify the bi-criteria trade-off and generate a set of Pareto optimal parameter values that balance the conflicting objectives. This integrated workflow improves the fidelity of QBO simulations and offers a versatile template for uncertainty quantification in complex geophysical models.

54 ENVIRONMENTAL SCIENCES↗
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↗