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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗
DOE OSTI2024

Practical and Optimal Sequential Bayesian Experimental Design for Complex Systems Incorporating Human Experimenter Preferences (Final Scientific/Technical Report)

Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Supercharging simulation-based inference for Bayesian optimal experimental design

Abstract Bayesian optimal experimental design (BOED) seeks to maximize the expected information gain (EIG) of experiments. This requires a likelihood estimate, which in many settings is intractable. Simulation-based inference (SBI) provides powerful tools for this regime. However, existing work explicitly connecting SBI and BOED is restricted to a single contrastive EIG bound. We show that the EIG admits multiple formulations which can directly leverage modern SBI density estimators, encompassing neural posterior, likelihood, and ratio estimation. Building on this perspective, we define a novel EIG estimator using neural likelihood estimation. Further, we identify optimization as a key bottleneck of gradient based EIG maximization and show that a simple multi-start parallel gradient ascent procedure can substantially improve reliability and performance. With these innovations, our SBI-based BOED methods are able to match or outperform by up to 22% existing state-of-the-art approaches across standard BOED benchmarks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Analysis and Optimization of Seismo-Acoustic Monitoring Networks with Bayesian Optimal Experimental Design

The Bayesian optimal experimental design (OED) problem seeks to identify data, sensor configurations, or experiments which can optimally reduce uncertainty. The goal of OED is to find an experiment that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge about expected data. Therefore, within the context of seismic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types, and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize the ability to locate seismic events from arrival time data of detected seismic phases. In order to do utilize Bayesian OED we must develop four elements:1. A likelihood function that describes the uncertainty of detection and travel times; 2. A Bayesian solver that takes a prior and likelihood to identify the posterior; 3. An algorithm to compute EIG; and, 4. An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we can explore many relevant questions to monitoring such as: how and what multiphenomenology data can be used to optimally reduce uncertainty, how to trade off sensor fidelity and earth model uncertainty, and how sensor types, number, and locations influence uncertainty

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Optimal experimental design using eigenvalue-based criteria with Pyomo.DoE

New developments in automated optimal experimental design within the PSE+ software ecosystem. Advancements in user experience (to reduce the time taken to perform optimal experiment design) and computational capabilities (allowing more diverse experimental design) are shown with an example relevant to critical minerals and materials. Also, a small tutorial on science-based optimal experimental design and novel contributions therein are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations

Optimal experimental design (OED) is the general formalism of sensor placement and decisions on the data collection strategy for engineered or natural experiments. This problem is prevalent in many critical fields such as battery design, numerical weather prediction, geosciences, environmental and urban studies. State-of-the-art computational methods for experimental design do not accommodate correlation structure in observational errors produced by many expensive-to-operate devices such as X-ray machines, radars, and satellites. Discarding evident data correlations leads to biased results, higher expenses, and waste of valuable resources. We present a general formulation of the OED formalism for model-constrained large-scale Bayesian linear inverse problems, where measurement errors are generally correlated. The proposed approach utilizes the Hadamard product of matrices to formulate the weighted-likelihood, and is valid for both finite as well as infinite-dimensional Bayesian inverse problems. Extensive numerical experiments are carried out for empirical verification of the proposed approach using an advection-diffusion model, where the objective is to optimally place a small set of sensors, under a limited budget, to predict the concentration of a contaminant in a closed and bounded domain.

Correlated observations↗
DOE OSTI2021

A Scalable Gradient Free Method for Bayesian Experimental Design with Implicit Models

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.

Zhang, Jiaxin↗
DOE OSTI2024

The Effect of the Prior and the Experimental Design on the Inference of the Precision Matrix in Gaussian Chain Graph Models

Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing (i) the KL divergence between prior and posterior and (ii) the Stein’s loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems

Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Chemometrics and Experimental Design for the Quantification of Nitrate Salts in Nitric Acid: Near-Infrared Spectroscopy Absorption Analysis

Implementing remote, real-time spectroscopic monitoring of radiochemical processing streams in hot cell environments requires efficiency and simplicity. The success of optical spectroscopy for the quantification of species in chemical systems highly depends on representative training sets and suitable validation sets. Selecting a training set (i.e., calibration standards) to build multivariate regression models is both time- and resource-consuming using standard one-factor-at-a-time approaches. This study describes the use of experimental design to generate spectral training sets and a validation set for the quantification of sodium nitrate (0–1 M) and nitric acid (0.1–10 M) using the near-infrared water band centered at 1440 nm. Partial least squares regression models were built from training sets generated by both D- and I-optimal experimental designs and a one-factor-at-a-time approach. The prediction performance of each model was evaluated by comparing the bias and standard error of prediction for statistical significance. D- and I-optimal designs reduced the number of samples required to build regression models compared with one-factor-at-a-time while also improving performance. Models must be confirmed against a validation sample set when minimizing the number of samples in the training set. The D-optimal design performed the best when considering both performance and efficiency by improving predictive capability and reducing number of samples in the training set by 64% compared with the one-factor-at-a-time approach. The experimental design approach objectively selects calibration and validation spectral data sets based on statistical criterion to optimize performance and minimize resources.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2023

Bayesian sequential optimal experimental design for nonlinear models using policy gradient reinforcement learning

We present a mathematical framework and computational methods for optimally designing a finite sequence of experiments. This sequential optimal experimental design (sOED) problem is formulated as a finite-horizon partially observable Markov decision process (POMDP) under a Bayesian setting and with information-theoretic utilities. The formulation is general and may accommodate continuous random variables, non-Gaussian posteriors, and nonlinear forward models. The sOED design policy incorporates elements of feedback and lookahead simultaneously, and we show it to generalize the commonly-used batch and greedy design strategies. We solve for the sOED policy using the policy gradient (PG) method from reinforcement learning, and provide a derivation for the PG expression in the sOED context. Adopting an actor-critic approach, the policy and value functions are parameterized using deep neural networks and improved via PG estimates produced from simulated episodes of designs and observations. The new PG-sOED algorithm is first validated on a linear-Gaussian benchmark, and then compared against other design baselines on a sensor movement problem for contaminant source inversion in a convection-diffusion field. As a result, we provide explanation for the policy behaviors using knowledge of the underlying physical process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Bayesian experimental design and parameter estimation for ultrafast spin dynamics

Abstract Advanced experimental measurements are crucial for driving theoretical developments and unveiling novel phenomena in condensed matter and materials physics, which often suffer from the scarcity of large-scale facility resources, such as x-ray or neutron scattering centers. To address these limitations, we introduce a methodology that leverages the Bayesian optimal experimental design paradigm to efficiently uncover key quantum spin fluctuation parameters from x-ray photon fluctuation spectroscopy (XPFS) data. Our method is compatible with existing theoretical simulation pipelines and can also be used in combination with fast machine learning surrogate models in the event that real-time simulations are unfeasible. Our numerical benchmarks demonstrate the superior performance in predicting model parameters and in delivering more informative measurements within limited experimental time. Our method can be adapted to many different types of experiments beyond XPFS and spin fluctuation studies, facilitating more efficient data collection and accelerating scientific discoveries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

MINE: maximally informative next experiment—toward a new GWAS experimental design and methodology

Abstract The computational methodology of Genome Wide Association Studies (GWAS) currently has several limitations: (i) the number of observations (rows) on a quantitative trait tends to be smaller than the number of single nucleotide polymorphisms (SNPs) (columns) in the design matrix; (ii) each SNP is usually modeled separately, failing to acknowledge interaction between each other (ie epistasis); (iii) there is implicit linkage disequilibrium (LD) between neighboring SNPs due to their linkage. To overcome these issues, we developed a tool that uses ensemble methods to fit mixed linear models to GWAS data, and these ensemble methods include the development of a new experimental design approach in GWAS, which uses the resultant models and data to select the next informative experiment over time. This new adaptive and staged approach for GWAS experimental design was developed and tested in a 3 yr adaptive model-guided discovery experiment against a fixed classical design. In Sorghum bicolor a total of 79, 86, and 78 accessions were tested in years 1, 2, and 3, respectively out of 343 accessions available in the Bioenergy Association Panel (BAP) each identified for 232,303 SNPs, 1 every 2–3 kb in the genomes. We demonstrated the feasibility of MINE enacted with 8 people in the field per year over 3 yr vs in 1 large classical design enacted with 20 people in 1 yr. The MINE results for chromosomal regions identified controlling dry weight were confirmed against results from previous sorghum GWAS experiments and 1 large classical design for the BAP panel.

Genetics & Heredity↗
DOE OSTI2026

ROADRUNNER uranium nitride MiniFuel: Experimental design, fabrication and pre-irradiation baseline characterization for accelerated burnup testing

Uranium nitride (UN) is a promising fuel candidate for advanced reactor systems owing to its high uranium density and thermal conductivity; however, its qualification remains constrained by the scarcity of well-controlled irradiation performance data. Here, to address this limitation, the ROADRUNNER (Research On ADvancing the peRformance of UraNium Nitrides in Extreme enviRonments) campaign employs the MiniFuel platform in the High Flux Isotope Reactor (HFIR) to enable accelerated burnup irradiation testing under tightly controlled and largely isothermal conditions. This paper presents the experimental design, fuel fabrication, and pre-irradiation baseline characterization of the ROADRUNNER UN MiniFuel campaign. Thirty-six UN minidisc specimens were fabricated with systematically varied as-fabricated density (86–96% of theoretical density), carbon impurity content (961–5240 ppm), oxygen content (≤ ∼2000 ppm), and grain size (2.5–24 μm). The irradiation matrix spans nominal fuel temperatures of 873 K, 1173 K, and 1473 K and target burnups of 3.75%, 6.0%, and 7.5% fissions per initial metal atom (FIMA). Neutronic and thermal analyses were performed to define specimen-specific burnup accumulation and temperature histories, establishing the boundary conditions for subsequent in-pile behavior. Comprehensive pre-irradiation characterization—including dimensional metrology, density verification, impurity analysis, X-ray diffraction, Raman spectroscopy, scanning electron microscopy, X-ray computed tomography, and confocal profilometry—provides a detailed baseline for post-irradiation examination. Pre-irradiation data were further used to generate predictive estimates of fission gas release and swelling using existing empirical correlations. This quantitative comparison reveals substantial inter-model divergence at intermediate and elevated temperatures that exceeds propagated input uncertainties, highlighting structural gaps in the historical irradiation database. The ROADRUNNER irradiation campaign is currently underway in HFIR, with initial firs cycle completed in late 2025 and remaining targets scheduled through 2027. The experimental design and baseline dataset presented here establish the framework needed to interpret forthcoming post-irradiation measurements and to provide discriminating data for the validation and refinement of physics-based UN fuel performance models.

Lopes, Denise Adorno [Oak Ridge National Laborator↗
DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗