Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Gaussian process surrogates”

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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Bayesian D‐Optimal Designs for Gaussian Process Surrogate Models

Computer experiments often employ space-filling strategies to create surrogate models with strong predictive performance. The impact of model parameter estimation for Gaussian process surrogates, however, is often overlooked. Obtaining a better initial estimate of the covariance lengthscale parameter, θ, can greatly improve the resulting Gaussian process fit through more effective sequential acquisitions during active learning. In this work, we propose a novel initial design maximizing the Bayesian D-optimality criterion of the Gaussian process lengthscale parameter. Previously published results have shown the emphasis on lengthscale estimation to be promising, but relied on an empirically driven design creation process. Our Bayesian D-optimal designs are rooted in information theory and lead to more informative sequential acquisitions by improving lengthscale estimation. In many cases, these gains eventually result in better surrogates than those seeded with space-filling initial designs. Furthermore, Bayesian D-optimal designs can be tailored to either isotropic or anisotropic covariance structures, and the Bayesian framework enables the inclusion of prior knowledge in the design process, offering greater flexibility and adaptability. Through several simulation studies, we demonstrate the advantages of Bayesian D-optimal designs in terms of both lengthscale estimation accuracy and predictive performance during active learning.

Bayesian experimental design↗
DOE OSTI2025

Enhancing Gaussian Process Surrogates for Optimization and Posterior Approximation via Random Exploration

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical GP-UCB algorithm, but the additional random exploration step accelerates their convergence, nearly achieving the optimal convergence rate. Furthermore, to facilitate Bayesian inference with intractable likelihoods, we propose to utilize optimization iterates for maximum a posteriori estimation to build a Gaussian process surrogate model for the unnormalized log-posterior density. We provide bounds for the Hellinger distance between the true and the approximate posterior distributions in terms of the number of design points. We demonstrate the effectiveness of our Bayesian optimization algorithms in nonconvex benchmark objective functions, in a machine learning hyperparameter tuning problem, and in a black-box engineering design problem. The effectiveness of our posterior approximation approach is demonstrated in two Bayesian inference problems for parameters of dynamical systems.

Bayesian inference↗
DOE OSTI2025

Accurate and uncertainty-aware multi-task prediction of HEA properties using prior-guided deep Gaussian processes

Surrogate modeling techniques have become indispensable in accelerating the discovery and optimization of high-entropy alloys (HEAs), especially when integrating computational predictions with sparse experimental observations. This study systematically evaluates the training and testing performance of four prominent surrogate models—conventional Gaussian processes (cGP), Deep Gaussian processes (DGP), encoder-decoder neural networks for multi-output regression and eXtreme Gradient Boosting (XGBoost)—applied to a hybrid dataset of experimental and computational properties of the 8-component HEA system Al-Co-Cr-Cu-Fe-Mn-Ni-V. We specifically assess their capabilities in predicting correlated material properties, including yield strength, hardness, modulus, ultimate tensile strength, elongation, and average hardness under dynamic/quasi-static conditions, alongside auxiliary computational properties. The comparison highlights the strengths of hierarchical deep modeling approaches in handling heteroscedastic, heterotopic, and incomplete data commonly encountered in materials science. Our findings illustrate that combined surrogate models such as DGPs infused with machine-learned priors outperform other surrogates by effectively capturing inter-property correlations and by assimilating prior knowledge. This enhanced predictive accuracy positions the combined surrogate models as powerful tools for robust and data-efficient materials design.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A Gaussian process based surrogate approach for the optimization of cylindrical targets

Simulating direct-drive inertial confinement experiments presents significant computational challenges, both due to the complexity of the codes required for such simulations and the substantial computational expense associated with target design studies. Machine learning models, and in particular, surrogate models, offer a solution by replacing simulation results with a simplified approximation. In this study, we apply surrogate modeling and optimization techniques that are well established in the existing literature to one-dimensional simulation data of a new cylindrical target design containing deuterium–tritium fuel. These models predict yields without the need for expensive simulations. We find that Bayesian optimization with Gaussian process surrogates enhances sampling efficiency in low-dimensional design spaces but becomes less efficient as dimensionality increases. Nonetheless, optimization routines within two-dimensional and five-dimensional design spaces can identify designs that maximize yield, while also aligning with established physical intuition. Optimization routines, which ignore constraints on hydrodynamic instability growth, are shown to lead to unstable designs in 2D, resulting in yield loss. However, routines that utilize 1D simulations and impose constraints on the in-flight aspect ratio converge on novel cylindrical target designs that are stable against hydrodynamic instability growth in 2D and achieve high yield.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
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 OSTI2024

Targeted Adaptive Design

Modern advanced manufacturing and advanced materials design often require searches of relatively high-dimensional process control parameter spaces for settings that result in optimal structure, property, and performance parameters. The mapping from the former to the latter must be determined from noisy experiments or from expensive simulations. Here, we abstract this problem to a mathematical framework in which an unknown function from a control space to a design space must be ascertained by means of expensive noisy measurements, which locate control settings generating desired design features within specified tolerances, with quantified uncertainty. We describe targeted adaptive design (TAD), a new algorithm that performs this sampling task efficiently. TAD creates a Gaussian process surrogate model of the unknown mapping at each iterative stage, proposing a new batch of control settings to sample experimentally and optimizing the updated expected log-predictive probability density of the target design. TAD either stops upon locating a solution with uncertainties that fit inside the tolerance box or uses a measure of expected future information to determine that the search space has been exhausted with no solution. TAD thus embodies the exploration-exploitation tension in a manner that recalls, but is essentially different from, Bayesian optimization and optimal experimental design.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Multi-Fidelity Modeling and Control for Building Temperature Control

The ability to control energy loads such as a building's heating, ventilation, and air conditioning (HVAC) system can help facilitate increased penetration of variable renewable energy sources into the electric grid. To be able to control these HVAC systems more effectively, detailed simulations of the corresponding building physics is becoming increasingly important. These detailed simulations can be complex, nonlinear, and can require immense computational power when used in an advanced control method such as model predictive control (MPC), prompting the need to explore less computationally intensive strategies. In this work, a multi-fidelity approach is proposed to combine samples from a complex, high-fidelity model with a simple, low-fidelity model within the MPC control loop. More specifically, the parameters of a reduced-order, linear building model are periodically updated with knowledge from its high-fidelity counterpart - an EnergyPlus model - in an online fashion using a Gaussian Process surrogate model. Hence, highly accurate predictions of current and future conditions in a building are maintained with a substantially reduced computational burden compared to using the high-fidelity models alone. In other words, this linear parameter varying model preserves the low computational requirements of a low-order linear model while accurately modeling a building's dynamics. This allows a building controller to take highly informed actions without requiring a large computational budget.

building modeling↗
DOE OSTI2026

Using Flory–Huggins-informed human-in-the-loop Bayesian optimization to map the phase diagram of polymer blends

Mapping the phase diagram of polymer blends is an essential step in controlling the structure–property relationship of polymer-based materials. However, traditional grid-based approaches are inefficient and rely on subjective judgements for terminating the experimental campaign. Artificial intelligence-guided experimentation offers a compelling alternative, especially when data-driven decision-making is interfaced with established polymer thermodynamics to improve efficiency and interpretability. Here, we introduce a physics-informed Bayesian optimization approach to guide the mapping of the phase diagram of a model blend containing poly(methyl methacrylate) and poly(styrene-ran-acrylonitrile). Physical information is derived from a Flory–Huggins representation of the spinodal curve, which is integrated into the Bayesian optimization process as a structured prior mean that acts as a soft constraint. Implemented as a human-in-the-loop workflow, the approach leverages optical imaging of film cloudiness with iterative Gaussian process surrogate modeling and a parameter selection decision policy to identify the composition-temperature conditions for sequential iterations. Convergence of kernel and Flory–Huggins-based hyperparameters provided a stopping criterion, ensuring an objective and interpretable termination of the experimental campaign. The framework recovered the known lower critical solution temperature (∼160 °C), while increasing material efficiency through targeted sampling. This work establishes a proof-of-concept for the application of Bayesian optimization workflows to study polymer blend miscibility.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Selecting Critical Scenarios of DER Adoption in Distribution Grids Using Bayesian Optimization

We develop a new methodology to select scenarios of DER adoption most critical for distribution grids. Anticipating risks of future voltage and line flow violations due to additional PV adopters is central for utility investment planning but continues to rely on deterministic or ad hoc scenario selection. We propose a highly efficient search framework based on multi-objective Bayesian Optimization. We treat underlying grid stress metrics as computationally expensive black-box functions, approximated via Gaussian Process surrogates and design an acquisition function based on probability of scenarios being Pareto-critical across a collection of line- and bus-based violation objectives. Our approach provides a statistical guarantee and offers an order of magnitude speed-up relative to a conservative exhaustive search. Case studies on realistic feeders with 200-400 buses demonstrate the effectiveness and accuracy of our approach.

Mulkin, Olivier↗
DOE OSTI2024

Portable, heterogeneous ensemble workflows at scale using libEnsemble

libEnsemble is a Python-based toolkit for running dynamic ensembles, developed as part of the DOE Exascale Computing Project. The toolkit utilizes a unique generator–simulator–allocator paradigm, where generators produce input for simulators, simulators evaluate those inputs, and allocators decide whether and when a simulator or generator should be called. The generator steers the ensemble based on simulation results. Generators may, for example, apply methods for numerical optimization, machine learning, or statistical calibration. libEnsemble communicates between a manager and workers. Flexibility is provided through multiple manager–worker communication substrates each of which has different benefits. These include Python’s multiprocessing, mpi4py, and TCP. Multisite ensembles are supported using Balsam or Globus Compute. We overview the unique characteristics of libEnsemble as well as current and potential interoperability with other packages in the workflow ecosystem. We highlight libEnsemble’s dynamic resource features: libEnsemble can detect system resources, such as available nodes, cores, and GPUs, and assign these in a portable way. These features allow users to specify the number of processors and GPUs required for each simulation; and resources will be automatically assigned on a wide range of systems, including Frontier, Aurora, and Perlmutter. Such ensembles can include multiple simulation types, some using GPUs and others using only CPUs, sharing nodes for maximum efficiency. We also describe the benefits of libEnsemble’s generator–simulator coupling, which easily exposes to the user the ability to cancel, and portably kill, running simulations based on models that are updated with intermediate simulation output. We demonstrate libEnsemble’s capabilities, scalability, and scientific impact via a Gaussian process surrogate training problem for the longitudinal density profile at the exit of a plasma accelerator stage. In conclusion, the study uses gpCAM for the surrogate model and employs either Wake-T or WarpX simulations, highlighting efficient use of resources that can easily extend to exascale.

Dynamic ensembles↗
NASA NTRS2026

Benchmarking Bayesian Optimization Frameworks and Acquisition Strategies for Materials Discovery and Autonomous Laboratories

Bayesian optimization (BO) can accelerate materials discovery by guiding expensive experiments toward the most promising processing conditions. We systematically compare five BO surrogate and framework combinations (Gaussian processes in Ax, Gaussian processes and Monte-Carlo neural networks in BayBE, random forests in Lolopy, and tree-structured Parzen (TPE) estimators in Hyperopt) on three benchmarks that mimic common materials design tasks (a discrete solid-electrolyte composition space, a hybrid discrete/continuous laminate-composite design problem solved with micromechanics modeling, and the continuous Ishigami analytic function which is a standard optimization benchmark). Each BO surrogate is paired with posterior mean, probability of improvement, and expected improvement acquisition functions and run for 100 trials from randomized initial samples with uniform random search providing a control. Across five random seeds per setting, BayBE’s Gaussian-process surrogate with expected improvement consistently reached ≥95 % of the known optimum in the fewest evaluations, while Lolopy’s random forest matched or exceeded GP performance on purely categorical or mixed spaces at a higher computational cost. Posterior mean alone often stagnated at local optima, underscoring the need for exploration, whereas probability and expected improvement balanced exploration and exploitation leading to better optimization in fewer trials. Execution times ranged from milliseconds for TPE to minutes for neural-network and random-forest surrogates. These results establish baseline expectations for BO in automated materials laboratories and highlight expected improvement with Gaussian processes as a reliable first choice, with random forests offering a strong alternative when categorical variables dominate. The benchmark suite and code are released to facilitate future surrogate, acquisition, and constraint-handling research in data-driven materials optimization.

Bayesian optimization↗
DOE OSTI2026

JetGP: A derivative enhanced Gaussian process library

Derivative enhanced Gaussian Processes (DEGPs) can significantly improve surrogate model accuracy over standard Gaussian Process (GP) formulations by incorporating derivative information. However, standard implementations scale poorly with dimension, limiting their use in high dimensional engineering problems. JetGP is a Python framework that unifies existing derivative enhanced GP methodologies into a single library and extends them to support arbitrary order derivative information. The library implements four complementary formulations: standard derivative enhanced Gaussian Processes (DEGP), directional DEGP (DDEGP), generalized directional DEGP (GDDEGP), and weighted DEGP (WDEGP). By unifying these approaches in a consistent interface with robust numerical implementations, JetGP enables practitioners to balance predictive accuracy and computational efficiency for high dimensional optimization, uncertainty quantification, and sensitivity analysis in engineering design.

Derivative enhanced Gaussian process↗
DOE OSTI2025

Advancements in Constitutive Model Calibration: Leveraging the Power of Full‐Field DIC Measurements and In Situ Load Path Selection for Reliable Parameter Inference

Accurate material characterization and model calibration are essential for computationally supported high-consequence engineering decisions. Historically, characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data are collected for a specific model of interest, (3) use deterministic methods that provide best-fit parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work brings together several recent advancements into an improved workflow called interlaced characterization and calibration (ICC) that advances the state-of-the-art in constitutive model calibration. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) quantifies parameter uncertainty through Bayesian inference and (4) incorporates these advancements into a quasi real-time feedback loop. The ICC framework is demonstrated here on the calibration of a material model using simulated full-field data for an aluminium cruciform specimen being deformed biaxially. The cruciform is actively driven through the myopically preferred load path using Bayesian optimal experimental design, which selects load steps that yield the maximum expected information gain (EIG). Principal component analysis (PCA) is performed on the model predictions of full-field displacements, and fast surrogate models are built to approximate the input-output relationships of the expensive finite element model. Furthermore, the tools developed and demonstrated here show that high-fidelity constitutive models can be efficiently and reliably calibrated with quantified uncertainty, thus supporting credible decision-making and potentially increasing the agility of solid mechanics modelling by enabling utilization of computational simulations at earlier stages of the design cycle.

Bayesian optimal experimental design↗
DOE OSTI2026

Deep Gaussian process-based cost-aware batch Bayesian optimization for complex materials design campaigns

The accelerating pace and expanding scope of materials discovery demand optimization frameworks that efficiently navigate vast design spaces with complex response surfaces while judiciously allocating limited evaluation resources. We present a cost-aware, batch Bayesian optimization scheme powered by deep Gaussian process (DGP) surrogates and a heterotopic querying strategy. Our DGP surrogate, formed by stacking GP layers, models complex hierarchical relationships among high-dimensional compositional features and captures correlations across multiple target properties, propagating uncertainty through successive layers. We integrate evaluation cost into an upper-confidence-bound acquisition extension, which, together with heterotopic querying, proposes small batches of candidates in parallel, balancing exploration of under-characterized regions with exploitation of high-mean, low-variance predictions across correlated properties. Applied to refractory high-entropy alloys for high-temperature applications, our framework converges to optimal formulations in fewer iterations with cost-aware queries than conventional GP-based BO, highlighting the value of deep, uncertainty-aware, cost-sensitive strategies in materials campaigns.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Active Learning‐Driven Inkless Additive Nanomanufacturing for Printed Electronics

Inkless additive nanomanufacturing for printed electronics promises broad material and substrate versatility, yet the high-dimensional print parameter space makes tuning print parameters time-intensive. We present a Bayesian optimization study that constructs a digital twin from printed-silver data to benchmark surrogate models, acquisition functions, and batch sizes head-to-head to achieve user-specified target resistance. Tested surrogate models included Gaussian process, random forest, and Bayesian neural network surrogates with expected improvement and confidence bound acquisition functions. In total, we evaluate 48 unique model configurations alongside a random sampling baseline for comparison. For printed silver, the Bayesian neural network with a batch size of one achieved the lowest average cumulative regret, approximately four times more efficient on average than random sampling. To balance performance and substrate space, a random forest model with expected improvement and a batch size of four was chosen as the model for validation testing. Applying this chosen configuration to copper with an additional print parameter, the model achieved a resistance within 0.15 Ω of a 1 Ω target in fewer than 30 printed lines across five validation sets. Altogether, the workflow yields a tuned and validated model that efficiently guides experiments toward the target while simultaneously learning the parameter space.

Bevel, Colton [Auburn University, AL (United State↗
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↗