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Results for “Surrogate Optimization Algorithms”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Deducing subnanometer cluster size and shape distributions of heterogeneous supported catalysts

Abstract Infrared (IR) spectra of adsorbate vibrational modes are sensitive to adsorbate/metal interactions, accurate, and easily obtainable in-situ or operando. While they are the gold standards for characterizing single-crystals and large nanoparticles, analogous spectra for highly dispersed heterogeneous catalysts consisting of single-atoms and ultra-small clusters are lacking. Here, we combine data-based approaches with physics-driven surrogate models to generate synthetic IR spectra from first-principles. We bypass the vast combinatorial space of clusters by determining viable, low-energy structures using machine-learned Hamiltonians, genetic algorithm optimization, and grand canonical Monte Carlo calculations. We obtain first-principles vibrations on this tractable ensemble and generate single-cluster primary spectra analogous to pure component gas-phase IR spectra. With such spectra as standards, we predict cluster size distributions from computational and experimental data, demonstrated in the case of CO adsorption on Pd/CeO 2 (111) catalysts, and quantify uncertainty using Bayesian Inference. We discuss extensions for characterizing complex materials towards closing the materials gap.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Multifidelity multiobjective optimization for wake-steering strategies

Abstract. Wake steering is an emerging wind power plant control strategy where upstream turbines are intentionally yawed out of perpendicular alignment with the incoming wind, thereby “steering” wakes away from downstream turbines. However, trade-offs between the gains in power production and fatigue loads induced by this control strategy are the subject of continuing investigation. In this study, we present a multifidelity multiobjective optimization approach for exploring the Pareto front of trade-offs between power and loading during wake steering. A large eddy simulation is used as the high-fidelity model, where an actuator line representation is used to model wind turbine blades and a rainflow-counting algorithm is used to compute damage equivalent loads. A coarser simulation with a simpler loads model is employed as a supplementary low-fidelity model. Multifidelity Bayesian optimization is performed to iteratively learn both a surrogate of the low-fidelity model and an additive discrepancy function, which maps the low-fidelity model to the high-fidelity model. Each optimization uses the expected hypervolume improvement acquisition function, weighted by the total cost of a proposed model evaluation in the multifidelity case. The multifidelity approach is able to capture the logit function shape of the Pareto frontier at a computational cost only 30 % that of the single-fidelity approach. Additionally, we provide physical insights into the vortical structures in the wake that contribute to the Pareto front shape.

17 WIND ENERGY↗
DOE OSTI2020

Calibration of hyperelastic constitutive models: the role of boundary conditions, search algorithms, and experimental variability

The calibration of hyperelastic constitutive models of soft tissue and tissue surrogates is often treated as an exercise in curve-fitting to the average experimental response, and many of the complicating factors such as experimental boundary conditions and data variability are ignored. Here, we focus on three questions that arise in this area: the ramifications of ignoring the experimental boundary conditions, the use of local optimizers, and the role of data variability. Using data from a uniaxial extension experiment on a tissue surrogate, we study how these three factors affect the calibration of isotropic hyperelastic constitutive models. Our results show that even with the simplest of constitutive models, it is necessary to look beyond a "good fit" to the average.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Machine Learning-Assisted High-Temperature Reservoir Thermal Energy Storage Optimization: Numerical Modeling and Machine Learning Input and Output Files

This data set includes the numerical modeling input files and output files used to synthesize data, and the reduced-order machine learning models trained from the synthesized data for reservoir thermal energy storage site identification. In this study, a machine-learning-assisted computational framework is presented to identify High-Temperature Reservoir Thermal Energy Storage (HT-RTES) site with optimal performance metrics by combining physics-based simulation with stochastic hydrogeologic formation and thermal energy storage operation parameters, artificial neural network regression of the simulation data, and genetic algorithm-enabled multi-objective optimization. A doublet well configuration with a layered (aquitard-aquifer-aquitard) generic reservoir is simulated for cases of continuous operation and seasonal-cycle operation scenarios. Neural network-based surrogate models are developed for the two scenarios and applied to generate the Pareto fronts of the HT-RTES performance for four potential HT-RTES sites. The developed Pareto optimal solutions indicate the performance of HT-RTES is operation-scenario (i.e., fluid cycle) and reservoir-site dependent, and the performance metrics have competing effects for a given site and a given fluid cycle. The developed neural network models can be applied to identify suitable sites for HT-RTES, and the proposed framework sheds light on the design of resilient HT-RTES systems. All the simulations and the neural network model were done by Idaho National Laboratory. A detailed description of the work was reported in publication linked below.

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

Machine-learning-assisted high-temperature reservoir thermal energy storage optimization

High-temperature reservoir thermal energy storage (HT-RTES) has the potential to become an indispensable component in achieving the goal of the net-zero carbon economy, given its capability to balance the intermittent nature of renewable energy generation. In this study, a machine-learning-assisted computational framework is presented to co-optimize the performance metrics of HT-RTES by combining physics-based simulation with stochastic hydrogeologic formation and thermal energy storage operation parameters, artificial neural network regression of the simulation data, and genetic algorithm-enabled multi-objective optimization. A doublet well configuration with a layered (aquitard-aquifer-aquitard) generic reservoir is simulated for cases of continuous operation and seasonal-cycle operation scenarios. Further, neural network-based surrogate models are developed for the two scenarios and applied to generate the Pareto fronts of the HT-RTES performance for four potential HT-RTES sites. The developed Pareto optimal solutions indicate the performance of HT-RTES is operation-scenario (i.e., fluid cycle) and reservoir-site dependent, and the performance metrics have competing effects for a given site and a given fluid cycle. The developed neural network models can be applied to identify suitable sites for HT-RTES, and the proposed framework sheds light on the design of resilient HT-RTES systems.

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

Development of lean, efficient, and fast physics-framed deep-learning-based proxy models for subsurface carbon storage

In this work, we present deep-learning-based surrogate models for CCUS developed with four different algorithms and a physics-framed two-phase flow problem involving displacement of water by CO 2 . The deep-learning models were trained using 3D datasets describing the pressure plume, CO 2 saturation plume, and water extraction rate generated by numerical simulation. The hyperparameters defining the architecture of the neural networks were optimized to determine the slimmest network size and training parameters that give the most efficient performance at the least training cost. To develop a robust model that closely mimics the governing physical laws, the discretized form of the two-phase fluid transport equation was used to formulate the supervised deep-learning task. The algorithms investigated in this study predicted the data to above 95% accuracy, with the multi-layer perceptron model demonstrating the best performance by balancing training speed, prediction time, and prediction accuracy with lean network capacity. Furthermore, the surrogate models simultaneously predict reservoir pressure and CO 2 saturation in every grid block, including the surface well extraction rate and bottomhole pressure, at all simulation times for a given static model realization in just a few seconds on a standard desktop computer. A key outcome of this study is that limits can be placed on network design parameters to avoid over designing neural networks, with associated efficiencies in training and prediction times. This is very useful because large volumes of data may be generated in CCUS projects and over-design of neural network architectures imposes penalties that are antithetical to the goal of near-real time forecasting.

58 GEOSCIENCES↗
DOE OSTI2024

Non-smooth Bayesian optimization in tuning scientific applications

Tuning algorithmic parameters to optimize the performance of large, complicated computational codes is an important problem involving finding the optima and identifying regimes defined by non-smooth boundaries in black-box functions. Within the Bayesian optimization framework, the Gaussian process surrogate model produces smooth mean functions, but functions in the tuning problem are often non-smooth, which is exacerbated by the fact that we usually have limited sequential samples from the black-box function. Here, motivated by these issues encountered in tuning, we propose a novel Gaussian process model called a clustered Gaussian process (cGP), where the components are dynamically updated by clustering. In our studies, the performance of cGP can be better than stationary GPs in nearly 90% of the experiments and better than non-stationary GPs in nearly 70% of the repeated experiments while requiring less computational cost. cGP provides a novel approach for dynamic GP, computes more efficiently than recursive partitioning, and discovers non-smoothness regimes. We provide extensive experiments including high-performance computing (HPC) and industrial simulation functions to show the effectiveness of our methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Uncertainty propagation and sensitivity analysis for constrained optimization of nuclear waste vitrification

Abstract The vitrification of high‐level waste (HLW) by heating a mixture of glass‐forming chemicals (GFCs) with the waste can be improved using a constrained optimization problem. This study explores how different uncertainty propagation (UP) methods implemented with the optimization process can affect the glass formulation of nuclear waste glasses. UP is the effort of propagating uncertain inputs through a system to understand and quantify output distributions. Uncertainty intervals are crafted from output distributions to inform the optimization algorithm. UP is often implemented with Monte Carlo (MC) sampling for large nonlinear systems, which can be difficult to implement within a constrained optimization algorithm that requires derivative information. Other UP methods often used for optimization under uncertainty (OUU) can be designed to work within an established constrained optimization framework. Methods of UP are evaluated in this study including iterative sampling approaches, first‐order approximations, and surrogate modeling with machine learning (ML). A method of dimensional reduction based on global sensitivity analysis is introduced to support the UP methods for the large dimensionality of the problem. Analytical UP methods able to achieve similar optimums 10 times faster than the baseline MC approach, and produce 93.9% similar output distributions are reported.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2019

High-Dimensional Spectral Sampling

A wide variety of applications in science and engineering depend on effectively and efficiently exploring high- dimensional parameter spaces. Common examples are uncertainty quantification, inverse problems, or various optimization approaches. In such applications, the first step is to create an initial uniform, random sampling of the space to create a baseline of knowledge. The simulations evaluated at these samples are then used for subsequent processing. In its most generic form, the goal of sampling is to produce the maximal amount of information with the minimal number of samples. However, despite being the first step and thus influencing the performance of the entire workflow, the quality of the initial sample designs is rarely analyzed or optimized. This project develops a new spectral sampling theory for analyzing and creating experiment designs in high-dimensional spaces. Further, new algorithms for estimating sample properties and sample synthesis are designed. Finally, applications of the proposed spectral sampling tools in surrogate modeling, scientific machine learning and image analysis are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Harnessing the power of gradient-based simulations for multi-objective optimization in particle accelerators

Abstract Particle accelerator operation requires simultaneous optimization of multiple objectives. Multi-objective optimization (MOO) is particularly challenging due to trade-offs between the objectives. Evolutionary algorithms, such as genetic algorithms (GAs), have been leveraged for many optimization problems, however, they do not apply to complex control problems by design. This paper demonstrates the power of differentiability for solving MOO problems in particle accelerators using a deep differentiable reinforcement learning (DDRL) algorithm. We compare the DDRL algorithm with model-free reinforcement learning (MFRL), GA, and Bayesian optimization (BO) for simultaneous optimization of heat load and trip rates in the continuous electron beam accelerator facility. The underlying problem enforces strict constraints on both individual states and actions as well as cumulative (global) constraints on energy requirements of the beam. Using historical accelerator data, we develop a physics-based surrogate model which is differentiable and allows for back-propagation of gradients. The results are evaluated in the form of a Pareto-front with two objectives. We show that the DDRL outperforms MFRL, BO, and GA on high dimensional problems.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

PyApprox: A software package for sensitivity analysis, Bayesian inference, optimal experimental design, and multi-fidelity uncertainty quantification and surrogate modeling

PyApprox is a Python-based one-stop-shop for probabilistic analysis of numerical models such as those used in the earth, environmental and engineering sciences. Easy to use and extendable tools are provided for constructing surrogates, sensitivity analysis, Bayesian inference, experimental design, and forward uncertainty quantification. The algorithms implemented represent a wide range of methods for model analysis developed over the past two decades, including recent advances in multi-fidelity approaches that use multiple model discretizations and/or simplified physics to significantly reduce the computational cost of various types of analyses. An extensive set of Benchmarks from the literature is also provided to facilitate the easy comparison of new or existing algorithms for a wide range of model analyses. Here, this paper introduces PyApprox and its various features, and presents results demonstrating the utility of PyApprox on a benchmark problem modeling the advection of a tracer in groundwater.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Machine learning models for PDE constrained optimization

Partial differential equation (PDE)-constrained optimization problems arise in a variety of scientific and engineering applications, such as topology optimization, electrodynamics, fluid dynamics, and structural dynamics. However, these problems are often challenging and computationally expensive to solve, due to the need to solve the PDEs within the optimization loop. One approach to reducing the computational cost of these methods while providing convergence guarantees is through inexact trust region methods; this method uses lower fidelity solutions of the PDE at early stages of the optimization and adjusts the required accuracy of inexact PDE solvers as the optimization progresses. In this work, we explore the use of machine learning based surrogate models with these inexact trust region methods. We first demonstrate the potential of this approach by using Gaussian processes as the surrogate model and test this on a simple PDE-constrained optimization problem. We then document explorations into improving the computational costs of evolutional deep neural network / neural Galerkin methods, with the eventual goal of using these methods with the inexact trust region algorithms. We are able to speed up these approaches, albeit at the cost of lower accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Representative Period Selection for Robust Capacity Expansion Planning in Low-carbon Grids

With the increasing urgency to decarbonize power systems, while mitigating extreme events, capacity expansion models can play a vital role in reliably planning the expansion of power systems and facilitating the integration of renewable energy sources. Optimizing capacity expansion generally involves selecting surrogate representative days from forecasts of load and the generation profiles of variable renewable energy resources. To properly select those representative days, we propose a novel input-based approach in combination with the k-means clustering algorithm that utilize three unique operational inputs: load shedding, renewable curtailment, and transmission congestion. The proposed method allows for more robust and cost-effective capacity planning. The method is validated using a capacity expansion model and a production cost model based on California Independent System Operator (CAISO)'s decarbonization goals, and results in reduced costs and drastically lower load shedding.

Anderson, Osten P.↗
DOE OSTI2024

Decomposition and Algorithmic Approaches for Solving Large-Scale Process Family Design Problems

Our most recent work expands the water desalination case study from 76 variants to 10,897 variants using the equation-oriented model built in Pyomo as part of the PARETO project. Using the discretization formulation presented in Stinchfield (2024a), rather than solving for all 10,897 variants simultaneously, we decompose the formulation into subproblems containing subsets of variants from the process family. We solve the overall problem with Progressive Hedging (PH) deployed in parallel on a distributed HPC cluster using the open-source Python package mpi-sppy (Knueven et al., 2023). This approach allowed us to solve this process family design problem to ~1.5% relative optimality gap in about 5 hours; in comparison, Gurobi reached ~50% relative optimality gap in about 6 hours (Stinchfield et al., 2024b). However, this approach still requires discretization of the common unit module design ranges; additionally, PH acts as a heuristic for MILP’s with gap-closing capabilities. Ideally, we would not have to use ML surrogates or discretization to solve this problem, instead solving the process family design problem with the equation-oriented model directly to achieve the most accurate results. However, recall that we did not consider solving the MINLP directly due to complexity and size. In this work, we aim to decompose and solve this large-scale MINLP using a Structured Nonlinear Global Optimization algorithm presented by Cao and Zavala (2019).

Stinchfield, Georgia↗
DOE OSTI2021

Practical algorithms for multivariate rational approximation

We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models for high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process to efficiently and robustly compute the coefficients of the rational approximation. Our second approach is based on an optimization formulation that allows us to include structural constraints on the rational approximation (in particular, constraints demanding the absence of singularities), resulting in a semi-infinite optimization problem that we solve using an outer approximation approach. We present results for synthetic and real-life HEP data, and we compare the approximation quality of our approaches with that of traditional polynomial approximations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Benders Decomposition Using Graph Modeling and Multi-Parametric Programming

Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Adaptive Data-Driven Deep-Learning Surrogate Model for Frontal Polymerization in Dicyclopentadiene

Frontal polymerization (FP) is a self-sustaining curing process that enables rapid and energy-efficient manufacturing of thermoset polymers and composites. Computational methods conventionally used to simulate the FP process are time-consuming, and repeating simulations are required for sensitivity analysis, uncertainty quantification, or optimization of the manufacturing process. Here, in this work, we develop an adaptive surrogate deep-learning model for FP of dicyclopentadiene (DCPD), which predicts the evolution of temperature and degree of cure orders of magnitude faster than the finite-element method (FEM). The adaptive algorithm provides a strategy to select training samples efficiently and save computational costs by reducing the redundancy of FEM-based training samples. The adaptive algorithm calculates the residual error of the FP governing equations using automatic differentiation of the deep neural network. A probability density function expressed in terms of the residual error is used to select training samples from the Sobol sequence space. The temperature and degree of cure evolution of each training sample are obtained by a 2D FEM simulation. The adaptive method is more efficient and has a better prediction accuracy than the random sampling method. With the well-trained surrogate neural network, the FP characteristics (front speed, shape, and temperature) can be extracted quickly from the predicted temperature and degree-of-cure fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Optimization on Manifolds via Graph Gaussian Processes

This paper integrates manifold learning techniques within a Gaussian process upper confidence bound algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.

Bayesian optimization↗