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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Inference of phase field fracture models

The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). Furthermore, in this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Invertible neural networks for real-time control of extrusion additive manufacturing

Material extrusion additive manufacturing (AM) has enabled an elegant fabrication pathway for a vast material library. Nonetheless, each material requires optimization of printing parameters generally determined through significant trial-and-error testing. To eliminate arduous, iteration-based optimization approaches, many researchers have used machine learning (ML) algorithms which provide opportunities for automated process optimization. Here, in this work, we demonstrate the use of an ML-driven approach for real-time material extrusion print-parameter optimization through in-situ monitoring of printed line geometry. To do this, we use deep invertible neural networks (INNs) which can solve both forward and inverse, or optimization, problems using a single network. By combining in-situ computer vision and deep INNs, the printing parameters can be autonomously optimized to print a target line width in 1.2 s. Furthermore, defects that occur during printing can be rapidly identified and corrected autonomously. The methods developed and presented in this work eliminate user-intensive, time-consuming, and iterative parameter discovery approaches that currently limit accelerated implementation of extrusion-based AM processes. Furthermore, the presented approach can be generalized to provide real-time monitoring and optimization pathways for increasingly complex AM environments.

36 MATERIALS SCIENCE↗
DOE OSTI2015

A stochastic approach to quantifying the blur with uncertainty estimation for high-energy X-ray imaging systems

One of the primary causes of blur in a high-energy X-ray imaging system is the shape and extent of the radiation source, or ‘spot’. It is important to be able to quantify the size of the spot as it provides a lower bound on the recoverable resolution for a radiograph, and penumbral imaging methods – which involve the analysis of blur caused by a structured aperture – can be used to obtain the spot’s spatial profile. We present a Bayesian approach for estimating the spot shape that, unlike variational methods, is robust to the initial choice of parameters. The posterior is obtained from a normal likelihood, which was constructed from a weighted least squares approximation to a Poisson noise model, and prior assumptions that enforce both smoothness and non-negativity constraints. A Markov chain Monte Carlo algorithm is used to obtain samples from the target posterior, and the reconstruction and uncertainty estimates are the computed mean and variance of the samples, respectively. Lastly, synthetic data-sets are used to demonstrate accurate reconstruction, while real data taken with high-energy X-ray imaging systems are used to demonstrate applicability and feasibility.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A memory-distributed quasi-Newton solver for nonlinear programming problems with a small number of general constraints

We approach the problem of parallelizing state-of-the-art nonlinear programming optimization algorithms.Specifically, we focus on parallelizing quasi-Newton interior-point methods that use limited-memory secant Hessian approximations. Such interior-point methods are known to have better convergence properties and to be more effective on large-scale problems than gradient-based and derivative-free optimization algorithms. We target nonlinear and potentially nonconvex optimization problems with an arbitrary number of bound constraints and a small number of general equality and inequality constraints on the optimization variables. These problems occur for example in the form of optimal control, optimal design, and inverse problems governed by ordinary or partial differential equations, whenever they are expressed in a “reduced-space” optimization approach. We introduce and analyze the time and space complexity of a decomposition method for solving the quasi-Newton linear systems that leverages the fact that the quasi-Newton Hessian matrix has a small number of dense blocks that border a low-rank update of a diagonal matrix. This enables an efficient parallelization on memory-distributed computers of the iterations of the optimization algorithm, a state-of-the-art filter line-search interior-point algorithm by Wächter et. al. We illustrate the efficiency of the proposed method by solving structural topology optimization problems on up to 4608 cores on a parallel machine.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

42 ENGINEERING↗
DOE OSTI2015

A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by three steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Local convergence analysis of an inexact trust-region method for nonsmooth optimization

In Baraldi, we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function in Hilbert space—a class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. Furthermore, this algorithm has demonstrated excellent performance and scalability with problem size. In this paper, we enrich the convergence analysis for this algorithm, proving strong convergence of the iterates with guaranteed rates. In particular, we demonstrate that the trust-region algorithm recovers superlinear, even quadratic, convergence rates when using a second-order Taylor approximation of the smooth objective function term.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks for approximating the gradient of an objective functional constrained by the nonlinear Boltzmann equation. While the forward problem can be solved by the DSMC method, it is difficult to efficiently solve the high-dimensional continuous adjoint equation obtained by the “optimize-then-discretize” approach. This challenge motivates us to propose an adjoint DSMC method following the “discretize-then-optimize” approach for Boltzmann-constrained optimization. We also analyze the properties of the two frameworks and their connections. Here, several numerical examples are presented to demonstrate their accuracy and efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Stochastic Learning Approach for Binary Optimization: Application to Bayesian Optimal Design of Experiments

Here, we present a novel stochastic approach to binary optimization suited for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the regularized optimality criterion, is cast into a stochastic objective function in the form of an expectation over a multivariate Bernoulli distribution. The probabilistic objective is then solved by using a stochastic optimization routine to find an optimal observational policy. This formulation (a) is generally applicable to binary optimization problems with soft constraints and is ideal for OED and sensor placement problems; (b) does not require differentiability of the original objective function (e.g., a utility function in OED applications) with respect to the design variable, and thus it enables direct employment of sparsity-enforcing penalty functions such as $\ell_0$, without needing to utilize a continuation procedure or apply a rounding technique; (c) exhibits much lower computational cost than traditional gradient-based relaxation approaches; and (d) can be applied to both linear and nonlinear OED problems with proper choice of the utility function. The proposed approach is analyzed from an optimization perspective with detailed convergence analysis of the optimization approach and is also analyzed from a machine learning perspective with correspondence to policy gradient reinforcement learning. The approach is demonstrated numerically by using an idealized two-dimensional Bayesian linear inverse problem and validated by extensive numerical experiments carried out for sensor placement in a parameter identification setup.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Rapid Optimization of Total Variation with Applications in Imaging, Additive Manufacturing, and Qualification

Total Variation optimization penalizes the gradient of a control variable or state. While this work focuses on image processing in particular, it has also found applications in inverse problems and topology optimization. In image processing, the goal is to maintain faithfulness to the original image while denoising and/or deblurring. Additionally, bilevel optimization over the spatially varying regularization weights can illuminate interfaces such as damage regions and other anomalies. We will address two fundamental challenges with TV-optimization: (i) the typical slow convergence of existing TV-optimization methods, and (ii) the selection of spatially varying TV parameters to promote interface detection. Additionally, we will apply such techniques to image data collected in additive manufacturing. In said context, stochasticity in build events induces flaws in the manufactured piece, compromising the integrity of said part. There is a critical need for in-situ monitoring to spot anomalies once they form, and in this setting we apply our total variation and hyperparameter solvers. We will develop a customized algorithm based on for extreme-scale TV-optimization that achieves super-linear or quadratic-convergence, a critical property for real-time, image-by-image analysis. A worst-case outcome is a preprocessing step that enhances image quality in-situ, specifically for out-of-focus and noisy images.

36 MATERIALS SCIENCE↗
DOE OSTI2024

PyOED: An Extensible Suite for Data Assimilation and Model-Constrained Optimal Design of Experiments

This article describes PyOED, a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-constrained OED. The package targets scientists and researchers interested in understanding the details of OED formulations and approaches. It is also meant to enable researchers to experiment with standard and innovative OED technologies with a wide range of test problems (e.g., simulation models). OED, inverse problems (e.g., Bayesian inversion), and data assimilation (DA) are closely related research fields, and their formulations overlap significantly. Thus, PyOED is continuously being expanded with a plethora of Bayesian inversion, DA, and OED methods as well as new scientific simulation models, observation error models, and observation operators. These pieces are added such that they can be permuted to enable testing OED methods in various settings of varying complexities. The PyOED core is completely written in Python and utilizes the inherent object-oriented capabilities; however, the current version of PyOED is meant to be extensible rather than scalable. Specifically, PyOED is developed to “enable rapid development and benchmarking of OED methods with minimal coding effort and to maximize code reutilization.” This article provides a brief description of the PyOED layout and philosophy and provides a set of exemplary test cases and tutorials to demonstrate the potential of the package.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the underlying partial differential equation is a Laplace-like operator. In this paper, we extend some of the prior convergence results to Helmholtz-based optimization applications. Our analysis examines situations where control variables and observations are restricted to subregions of the computational domain. We prove that solver convergence rates do not deteriorate as the mesh is refined or as the wavenumber increases. More specifically, for one of the preconditioners we prove accelerated convergence as the wavenumber increases. Additionally, in situations where the control and observation subregions are disjoint, we observe that solver convergence rates have a weak dependence on the regularization parameter. We give a partial analysis of this behavior. We illustrate the performance of the preconditioners on control problems motivated by acoustic testing.

97 MATHEMATICS AND COMPUTING↗