Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “adjoint optimization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

An optimization method for chaotic turbulent flow

Evidence indicates that quantities-of-interest in some turbulent flows can be controlled despite the overall chaotic dynamics. It is typically thought that this is via relatively deterministic, larger-scale components of the turbulence. However, finding such controls, if they exist, is challenging because chaos causes sensitivity gradients to explode and the search space to become intractably non-convex. This challenge is analyzed, and a penalty method is introduced to cope with it. In the new approach, the time domain is broken into segments approximately matching the chaos time scales, so that the solution within each segment is both physical and relatively deterministic. The initial condition of each segment is included in an adjoint-based gradient optimization, which temporarily introduces artificial Δq discontinuities in the overall solution. The optimization then proceeds in stages with increasing penalization of Δq. The method is developed and illustrated for a logistic map, the Lorenz Equation, and an advection augmented Kuramoto–Sivashinsky Equation. These examples show how the Δq temporarily increases the search scale prior to the strong Δq → 0 penalization that recovers a physical solution. It is then applied to turbulent Kolmogorov flow, for which it also far outperforms a standard adjoint-based gradient search. Finally, the utility of such an optimized chaotic solution is discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

PETSc TSAdjoint: A Discrete Adjoint ODE Solver for First-Order and Second-Order Sensitivity Analysis

Here, we present a new software system PETSc TSAdjoint for first-order and second order adjoint sensitivity analysis of time-dependent nonlinear differential equations. The derivative calculation in PETSc TSAdjoint is essentially a high-level algorithmic differentiation process. The adjoint models are derived by differentiating the timestepping algorithms and implementing them based on the parallel infrastructure in PETSc. Full differentiation of the library code, including MPI routines, is avoided, and users do not need to derive their own adjoint models for their specific applications. PETSc TSAdjoint can compute the first-order derivative, that is, the gradient of a scalar functional, and the Hessian-vector product, which carries second-order derivative information, while requiring minimal input (a few callbacks) from the users. The adjoint model employs optimal checkpointing schemes in a manner that is transparent to users. Finally, usability, efficiency, and scalability are demonstrated through examples from a variety of applications.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A general approach to seismic inversion with automatic differentiation

Imaging Earth structure or seismic sources from seismic data involves minimizing a target misfit function, and is commonly solved through gradient-based optimization. The adjoint-state method has been developed to compute the gradient efficiently; however, its implementation can be time-consuming and difficult. We develop a general seismic inversion framework to calculate gradients using reverse-mode automatic differentiation. The central idea is that adjoint-state methods and reverse-mode automatic differentiation are mathematically equivalent. Here, the mapping between numerical PDE simulation and deep learning allows us to build a seismic inverse modeling library, ADSeismic, based on deep learning frameworks, which supports high performance reverse-mode automatic differentiation on CPUs and GPUs. We demonstrate the performance of ADSeismic on inverse problems related to velocity model estimation, rupture imaging, earthquake location, and source time function retrieval. ADSeismic has the potential to solve a wide variety of inverse modeling applications within a unified framework.

58 GEOSCIENCES↗
DOE OSTI2021

Juqbox.jl

The Juqbox.jl package implements functionality for solving the quantum optimal control problem for realizing logical gates in closed quantum systems. The dynamics of the quantum system is modeled by Schroedinger's equation, which takes to form of a linear system of ordinary differential equations (ODE). Juqbox.jl solves this ODE by numerical time stepping and applies a gradient-based optimization technique to determine control pulses for driving an initial state to a final state, according to the desired logical gate transformation. To evaluate the gradient, Juqbox.jl applies the ``first discretize, then optimize'' approach based on a discrete adjoint time stepping technique. The actual optimization is performed by the open source Ipopt libaray. Juqbox.jl is written in the Julia programming language which, among many other features, provides a convenient interface to the Ipopt library.

PETERSSON, NILSA.↗
DOE OSTI2022

Automatic Calibration of a Geomechanical Model from Sparse Data for Estimating Stress in Deep Geological Formations

Summary In this study, we demonstrate geomechanical modeling with fully automatic parameter calibration to estimate the full geomechanical stress fields of a prospective US carbon dioxide (CO2) storage site, based on sparse measurement data. The goal is to compute full stress tensor field estimates (principal stresses and orientations) that are maximally compatible with observations within the constraints of the model assumptions, thereby extending pointwise, incomplete partial stress measurement to a simulated full formation stress field, as well as a rough assessment of the associated error. We use the Perch site, located in Otsego County, Michigan, USA, as our case study. The input data consist of partial stress tensor information inferred from in-situ borehole tests, geophysical well logs, and processing of seismic data. A static earth model (SEM) of the site was developed, and geomechanical simulation functionality of the open-source MATLAB Reservoir Simulation Toolbox (MRST) was used to model the stress field. Adjoint-based nonlinear optimization was used to adjust boundary conditions and material properties to calibrate simulated results of observations. Results were interpreted through a Bayesian framework. The focus of this paper is to demonstrate how the fully automatic calibration procedure works and discuss the results obtained; it does not attempt a detailed analysis of the stress field in the context of the proposed CO2 storage initiatives. Our work is part of a larger effort to noninvasively determine in-situ stresses in deep formations considered for CO2 storage. Guided by previously published research on geomechanical model calibration, our work presents a novel calibration approach supporting a potentially large number of linear or nonlinear calibration parameters to produce results optimally agreeing with available measurements and thus extend partial pointwise estimates to full tensor fields compatible with the physics of the site.

Engineering↗
DOE OSTI2022

Blade planform design optimization to enhance turbine wake control

Abstract This study considers optimizing the planform of wind turbine blades to ultimately enhance wind plant controls, namely, wake steering strategies. Adjoint‐enabled unsteady actuator line simulations are carried out to obtain gradients for optimization of several different performance objectives with respect to blade chord length at 10 locations along blade span. We demonstrate different blade design optimizations that can maximize time‐averaged lateral wake deflection, entrainment of kinetic energy, or total power of multiple turbines. Our optimized designs can produce a 4+% increase in wake deflection, a 4× increase in vertical kinetic energy entrainment, or a 3.6% increase in power when compared with the baseline case. While lateral wake deflection is only modestly sensitive to chord changes, we find that increasing the outboard chord length can dramatically increase kinetic energy entrainment, resulting in faster wake recovery and gains in net power. While this work develops only a few case studies emphasizing relative performance improvements and general trends, these results show the promise of a framework that combines mid‐fidelity computation with adjoint‐based optimization for control and design problems.

WIND ENERGY↗
DOE OSTI2022

Minimum feature size control in level set topology optimization via density fields

A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the solid-void interface and the density field describes the distribution of a fictitious porous material using the solid isotropic material with penalization. These fields are governed by two sets of independent optimization variables which are initially coupled using a penalty for hole nucleation. The strength of the density field penalization and projection is gradually increased during the optimization process to promote a 0-1 density distribution. In addition, a second penalty regulates the evolution of the density field in the void phase. The treatment of the density field combined with the second penalty mitigate the appearance of small design features. The minimum feature size of optimized designs is controlled by the radius of the linear filter applied to the density optimization variables. The structural response is predicted by the extended finite element method, the sensitivities by the adjoint method, and the optimization variables are updated by a gradient-based optimization algorithm. Numerical examples investigate the robustness of this approach with respect to algorithmic parameters and mesh refinement. The results show the applicability of the combined density level set topology optimization approach for both optimal hole nucleation and for minimum feature size control in 2D and 3D. This comes, however, at the cost of a more complex problem formulation and additional computational cost due to an increased number of optimization variables.

42 ENGINEERING↗
DOE OSTI2021

Calibration of elastoplastic constitutive model parameters from full-field data with automatic differentiation-based sensitivities

Here, we present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.

42 ENGINEERING↗
DOE OSTI2023

Bayesian inversion and the Tomita–Takesaki modular group

We show that conditional expectations, optimal hypotheses, disintegrations and adjoints of unital completely positive maps are all instances of Bayesian inverses. We study the existence of the latter by means of the Tomita–Takesaki modular group and we provide extensions of a theorem of Takesaki as well as a theorem of Accardi and Cecchini to the setting of not necessarily faithful states on finite-dimensional C* -algebras.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Randomized Sketching Algorithms for Low-Memory Dynamic Optimization

This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a given control; the goal is to find the value of the control that minimizes an objective. While the control is often low dimensional, the state is typically more expensive to store. This paper suggests using randomized matrix approximation to compress the state as it is generated and shows how to use the compressed state to reliably solve the original dynamic optimization problem. Concretely, the compressed state is used to compute approximate gradients and to apply the Hessian to vectors. The approximation error in these quantities is controlled by the target rank of the sketch. This approximate first- and second-order information can readily be used in any optimization algorithm. As an example, we develop a sketched trust-region method that adaptively chooses the target rank using a posteriori error information and provably converges to a stationary point of the original problem. Numerical experiments with the sketched trust-region method show promising performance on challenging problems such as the optimal control of an advection-reaction-diffusion equation and the optimal control of fluid flow past a cylinder.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Gradient-based optimization of 3D MHD equilibria

Using recently developed adjoint methods for computing the shape derivatives of functions that depend on magnetohydrodynamic (MHD) equilibria (Antonsen et al. , J. Plasma Phys. , vol. 85, issue 2, 2019; Paul et al. , J. Plasma Phys. , vol. 86, issue 1, 2020), we present the first example of analytic gradient-based optimization of fixed-boundary stellarator equilibria. We take advantage of gradient information to optimize figures of merit of relevance for stellarator design, including the rotational transform, magnetic well and quasi-symmetry near the axis. With the application of the adjoint method, we reduce the number of equilibrium evaluations by the dimension of the optimization space ( ${\sim }50\text {--}500$ ) in comparison with a finite-difference gradient-based method. We discuss regularization objectives of relevance for fixed-boundary optimization, including a novel method that prevents self-intersection of the plasma boundary. We present several optimized equilibria, including a vacuum field with very low magnetic shear throughout the volume.

Physics↗
DOE OSTI2020

A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO

In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Wind Turbine Rotor Design Using High-Fidelity Aerostructural Optimization

Large wind turbines yield more energy but demand careful aeroelastic blade design. Coupled multiphysics design strategies can reduce wind energy costs by exploiting fluid-structure interactions. This work presents the first high-fidelity aerostructural optimization study of a large wind turbine rotor. We use blade-resolved fluid dynamics and structural solvers in a monolithic gradient-based optimization framework to explore steady-state torque and blade mass tradeoffs. The coupled-adjoint approach computes gradients efficiently, enabling the optimization of over 100 structural and geometric parameters simultaneously. Our optimization study modifies a DTU 10 MW benchmark with a simplified structure and isotropic material properties. The tightly coupled optimizations increase torque by 14% while reducing rotor mass by 9% or reduce blade mass by 27% while maintaining torque. Blade-resolved models provide greater design freedom, enabling 5% higher mass reductions than conventional parameterizations at equal torque. This framework paves the way for more detailed high-fidelity optimization studies to complement conventional design approaches.

17 WIND ENERGY↗
DOE OSTI2023

Deep learning closure models for large-eddy simulation of flows around bluff bodies

Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$ . Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $t \in [0, \infty )$ , especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications.

Mechanics↗
DOE OSTI2022

Image-domain DAS 3D VSP elastic transmission tomography

SUMMARY Full-wavefield elastic imaging of active-source seismic data acquired by downhole receivers commonly offers higher-resolution subsurface images in the vicinity of a borehole compared to conventional surface seismic data sets, which can lack higher-frequency wavefield components due to longer travel paths and increased attenuation. An increasingly used approach for downhole acquisition is vertical seismic profiling (VSP), which has become more attractive when coupled with distributed acoustic sensing (DAS) using optical fibres installed in wells. The main difficulty for generating high-quality images with full-wavefield imaging tools for DAS VSP data, though, is the need for an accurate velocity model. To build plausible velocity models using active-source DAS VSP data, we adopt a 3-D image-domain elastic transmission tomography technique, originally developed for surface-recorded passive (microseismic) data, by exchanging the source and receiver positions (i.e. reciprocity) to mimic a passive-seismic surface monitoring scenario. The inversion approach exploits various images for each source constructed through time-reverse imaging (TRI) of downgoing P- and S-wave first-arrival waveforms. The TRI process uses the kinetic term of the (extended) PS energy imaging condition that exhibits sufficient sensitivity to velocity model errors. The method automatically updates the P- and S-wave velocity models to optimize image focusing via adjoint-state inversion. We illustrate the efficacy of the adopted elastic inversion technique using an active-source DAS 3-D VSP field data set acquired in the North Slope of Alaska. The numerical experiments demonstrate that the inverted elastic velocity models can be further used in full-wavefield acoustic/elastic imaging algorithms to obtain accurate subsurface images.

Oren, Can (ORCID:000000019534265X)↗