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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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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 OSTI2025

Impact and mitigation of polarized extragalactic foregrounds on Bayesian cosmic microwave background lensing

Future low-noise cosmic microwave background (CMB) lensing measurements from e.g., CMB-S4 will be polarization dominated, rather than temperature dominated. In this new regime, statistically optimal lensing reconstructions outperform the standard quadratic estimator, but their sensitivity to extragalactic polarized foregrounds has not been quantified. Using realistic simulations of polarized radio and infrared point sources, we show for the first time that optimal Bayesian lensing from a CMB-S4-like experiment is insensitive to the expected level of polarized extragalactic foregrounds after masking, as long as an accurate foreground power spectrum is included in the analysis. For more futuristic experiments where these foregrounds could cause a detectable bias, we propose a new method to jointly fit for lensing and the Poisson foregrounds, generalizing the bias hardening from the standard quadratic estimator to Bayesian lensing.

cosmic microwave background↗
DOE OSTI2026

Bayesian discovery of optimal reduced order models from mechanistic and experimental data: A case study of Pd penetration in TRISO fuels using BISON

TRistructural ISOtropic (TRISO) particles rely on a silicon carbide (SiC) layer as the primary structural material and barrier to metallic fission products (FPs) release. Accurate prediction of palladium (Pd) transport and penetration is therefore critical for qualifying TRISO fuels for advanced reactors. The empirical correlation for Pd penetration in BISON is derived from historical particle-fuel data, but cannot explain the large scatter in the experimental data that arises from varying experimental conditions. To aid fuel qualification, we previously developed a mechanistic reduced order model (ROM) using BISON that resolves these dependencies. Here, in this work we build on that mechanistic ROM and perform validation and quantify its uncertainty using Bayesian uncertainty quantification (UQ). calibration against a suite of in-pile and out-of-pile experiments spanning particle compositions, geometries, and operating conditions, and we benchmark it against the empirical correlation. Bayesian UQ identifies influential parameters, calibrates them to data, and yields predictive intervals. Results show that while the empirical correlation can be tuned to fit a single experiment type, it transfers poorly; the mechanistic ROM sustains accuracy with credible uncertainty across disparate conditions. This demonstrates a practical path—via Bayesian UQ applied to mechanistic ROMs—to leverage single-effect experiments for inferring in-reactor behavior and supporting TRISO fuel qualification.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Measurement of $\nu_\mu$ CC Interactions With Two-Proton Final State in MINERvA

This dissertation presents a measurement of charged–current (CC) muon–neutrino interactions with exactly two protons and no pions in the final state (CC~$2p\,0\pi$), using data collected by the MINERvA detector in the NuMI medium–energy beam at Fermilab. Such two–proton topologies are a sensitive probe of nuclear dynamics in the few–GeV regime, including multi–nucleon correlations (npnh, notably $2p2h$) and intranuclear final–state interactions (FSI) such as pion absorption and nucleon rescattering. A precise experimental characterization of these processes is essential both for neutrino–interaction theory and for reducing systematic uncertainties in oscillation experiments that rely on accurate modeling of neutrino–nucleus interactions. Events are selected by requiring a $\nu_\mu$ CC interaction with a reconstructed $\mu^-$ and two proton tracks originating from a common vertex in MINERvA’s finely segmented scintillator tracker, with no reconstructed mesons. Muon charge and momentum are constrained by matching to the MINOS Near Detector, while proton identification exploits energy–loss profiles and stopping–proton features. Backgrounds from pion–producing channels that enter the signal region through FSI or reconstruction effects are constrained with data–driven sidebands (Michel–electron and isolated–cluster “blob” samples) and tuned via a simultaneous fit across signal and sideband regions. To correct detector resolution and acceptance effects, the analysis employs iterative Bayesian unfolding with extensive validation: statistical pseudo–experiments, and robustness checks against generator systematic “universes” and additional strong shape warps. Single–differential cross sections are reported for three observables tailored to the two–proton final state: the opening–angle cosine $\cos\!\left(\theta_{pp}\right)$, the leading–proton momentum, and the subleading–proton momentum. Systematic uncertainties include contributions from neutrino flux, interaction modeling (e.g., npnh and resonance parameters, pion FSI), and detector response (calibration, reconstruction efficiencies). The resulting distributions provide targeted constraints on the interplay of multi–nucleon dynamics and FSI that shape CC~$2p\,0\pi$ final states on hydrocarbon. Comparisons to modern GENIE–based simulations highlight kinematic regions where model components require refinement. These measurements thus inform generator tuning and improve the reliability of neutrino–energy reconstruction strategies for current and future long–baseline oscillation programs.

Syrotenko, Vladyslav S. [Tufts U.]↗
DOE OSTI2021

Bayesian Spatially Varying Multi-Regularization Image Deblurring

Many scientific experiments such as those found in astronomy, geology, microbiology, and X-ray radiography require the use of high-energy instruments to capture images. Since blur and noise are inevitably present in any imaging system, the images must be \deblurred" to extract the full information content. Mathematically, image deblurring is an ill-posed inverse problem that requires regularization. The regularization, in turn, has a large effect on the deblurred image: different regularization strengths, and types, lead to drastically different reconstructions. Moreover, many images contain a mixture of smooth and sharp features which suggests the use of multi-regularization, i.e., varying the type of regularization (e.g. Tikhonov or total variation) across the image. We address these issues by formulating the image deblurring problem within a hierarchical Bayesian framework in which we spatially adapt the strength of the regularization and also vary the regularization type across the image. In this way, the image itself, along with corresponding regularization strength at each pixel, are described jointly by a posterior distribution which we can sample by Markov chain Monte Carlo (MCMC) methods. We illustrate our techniques on simplified test problems and apply them to high-energy X-ray images taken at the Nevada National Security Site. Numerical tests show that our new method is robustly applicable and increases the quality of the image reconstruction when compared to other (Bayesian) methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Optimal experimental design: Formulations and computations

Questions of ‘how best to acquire data’ are essential to modelling and prediction in the natural and social sciences, engineering applications, and beyond. Optimal experimental design (OED) formalizes these questions and creates computational methods to answer them. This article presents a systematic survey of modern OED, from its foundations in classical design theory to current research involving OED for complex models. We begin by reviewing criteria used to formulate an OED problem and thus to encode the goal of performing an experiment. We emphasize the flexibility of the Bayesian and decision-theoretic approach, which encompasses information-based criteria that are well-suited to nonlinear and non-Gaussian statistical models. We then discuss methods for estimating or bounding the values of these design criteria; this endeavour can be quite challenging due to strong nonlinearities, high parameter dimension, large per-sample costs, or settings where the model is implicit. A complementary set of computational issues involves optimization methods used to find a design; we discuss such methods in the discrete (combinatorial) setting of observation selection and in settings where an exact design can be continuously parametrized. Finally we present emerging methods for sequential OED that build non-myopic design policies, rather than explicit designs; these methods naturally adapt to the outcomes of past experiments in proposing new experiments, while seeking coordination among all experiments to be performed. Throughout, we highlight important open questions and challenges.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Performance Evaluation of an Offshore Wave Measurement Buoy in Monochromatic Waves

The accurate measurement of waves underpins marine energy resource characterization, device design, and project development. Datawell wave buoys are widely deployed and have long served as a trusted standard for wave measurements. We quantify the measurement performance, including wave elevation and energy flux estimation, of a Datawell DWR-MkIII buoy using prescribed monochromatic heave motions on a large-amplitude six-degree-of-freedom motion platform at the National Laboratory of the Rockies, assuming the buoy behaves as an ideal wave follower. Commanded motions were validated with an optical motion tracking system while buoy elevation and raw acceleration were recorded. Wave elevations were propagated to wave energy flux estimation using four methods, including one frequency-domain method and three time-domain methods. The Bayesian optimization was applied for design of experiments, and records from three test sites were also applied and evaluated in the present study. Results show two error regions within the nominal period range of 1.6 s to 30 s. For wave periods between 5 s and 25 s, the buoy provides accurate wave height measurements. For short periods less than 5 s, the 1.28 Hz sampling frequency induces sub-Nyquist artifacts that bias elevation and can drive maximum energy flux estimation errors above 100%. For long periods exceeding 25 s, the buoy reported elevation is underpredicted with error depending on period but relatively independent of wave height, with maximum wave height and wave energy flux errors reaching 64% and 87%, respectively. Furthermore, analysis of three field-derived cases shows that frequency-domain estimates at 1.28 Hz agree within 2% of the corresponding 100 Hz estimates, while larger method-dependent differences are observed for the Hilbert method.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Automated experimental design of safe rampdowns via probabilistic machine learning

Abstract Typically the rampdown phase of a shot consists of a decrease in current and injected power and optionally a change in shape, but there is considerable flexibility in the rate, sequencing, and duration of these changes. On the next generation of tokamaks it is essential that this is done safely as the device could be damaged by the stored thermal and electromagnetic energy present in the plasma. This works presents a procedure for automatically choosing experimental rampdown designs to rapidly converge to an effective rampdown trajectory. This procedure uses probabilistic machine learning methods paired with acquisition functions taken from Bayesian optimization. In a set of 2022 experiments at DIII-D, the rampdown designs produced by our method maintained plasma control down to substantially lower current and energy levels than are typically observed. The actions predicted by the model significantly improved as the model was able to explore over the course of the experimental campaign.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Interlaced Characterization and Calibration (ICC) for Improved Computational Simulation Credibility

Accurate material characterization and model calibration are pivotal for simulations used for high-consequence engineering decisions. Current characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data is collected for a specific model of interest, (3) provide only mean parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work developed a new paradigm—coined Interlaced Characterization and Calibration (ICC)—which drives forward the state-of-the-art in model calibration by bringing together recent advancements into one improved workflow. 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) provides uncertainty metrics on the calibrated model parameters, and (4) incorporates these advances into a quasi real-time feedback loop. The ICC framework was validated synthetically with both low-fidelity and high-fidelity simulations paired with several different elastoplastic material models, and was also demonstrated experimentally with an aluminum 6061 cruciform exemplar specimen. Results showed that the ICC framework—in which Bayesian optimal experimental design actively guided the experiment— resulted in calibrations with similar or better accuracy than predetermined experiments based on subject matter expertise. Moreover, the ICC framework produced a complete model calibration— with quantified uncertainties on model parameters—in 1 week, a 5 - 10× increase in efficiency over traditional approaches. Thus, the ICC paradigm improves both the calibration process and quality, by (1) improving efficiency, which increases agility of solid mechanics modeling and enables utilization of computational simulation (CompSim) at earlier stages of the design cycle and (2) providing quantified, and in some cases reduced, parameter uncertainties, which increases confidence in model predictions and supports credible decision making.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Fast Bayesian optimization of Needle-in-a-Haystack problems using zooming memory-based initialization (ZoMBI)

Abstract Needle-in-a-Haystack problems exist across a wide range of applications including rare disease prediction, ecological resource management, fraud detection, and material property optimization. A Needle-in-a-Haystack problem arises when there is an extreme imbalance of optimum conditions relative to the size of the dataset. However, current state-of-the-art optimization algorithms are not designed with the capabilities to find solutions to these challenging multidimensional Needle-in-a-Haystack problems, resulting in slow convergence or pigeonholing into a local minimum. In this paper, we present a Zooming Memory-Based Initialization algorithm, entitled ZoMBI, that builds on conventional Bayesian optimization principles to quickly and efficiently optimize Needle-in-a-Haystack problems in both less time and fewer experiments. The ZoMBI algorithm demonstrates compute time speed-ups of 400× compared to traditional Bayesian optimization as well as efficiently discovering optima in under 100 experiments that are up to 3× more highly optimized than those discovered by similar methods.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Machine learning assisted bayesian inference of mix and hot-spot conditions in NIF implosions

Experiments on the National Ignition Facility (NIF) have provided clear evidence of ablator material mixing into the Hot-Spot, leading to degraded performance. However, inferring the amount of mix and Hot-Spot conditions from typical experimental observations (e.g. x-ray spectra and images) is highly challenging. Here, we have developed an analysis method that utilizes machine learning assisted Bayesian inference to find the probability distributions of the Hot-Spot and mix conditions. This approach uses a neural network, trained on an idealized 2-dimensional representation of the Hot-Spot and mix distribution, and Bayesian inference to find the statistical distributions of Hot-Spot conditions that provide a match with observations. We have tested this method with synthetic data from simulations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Applying Bayesian inference and deterministic anisotropy to retrieve the molecular structure ∣Ψ(R)∣2 distribution from gas-phase diffraction experiments

Abstract Currently, our general approach to retrieving molecular structures from ultrafast gas-phase diffraction heavily relies on complex ab initio electronic or vibrational excited state simulations to make conclusive interpretations. Without such simulations, inverting this measurement for the structural probability distribution is typically intractable. This creates a so-called inverse problem. Here we address this inverse problem by developing a broadly applicable method that approximates the molecular frame structure ∣Ψ( R , t )∣ 2 distribution independent of these complex simulations. We retrieve the vibronic ground state ∣Ψ( R )∣ 2 for both simulated stretched NO 2 and measured N 2 O. From measured N 2 O, we observe 40 mÅ coordinate-space resolution from 3.75 Å −1 reciprocal space range and poor signal-to-noise, a 50X improvement over traditional Fourier transform methods. In simulated NO 2 diffraction experiments, typical to high signal-to-noise levels predict 100–1000X resolution improvements, down to 0.1 mÅ. By directly measuring the width of ∣Ψ( R )∣ 2 , we open ultrafast gas-phase diffraction capabilities to measurements beyond current analysis approaches. This method has the potential to effectively turn gas-phase ultrafast diffraction into a discovery-oriented technique to probe systems that are prohibitively difficult to simulate.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

A multifidelity Bayesian optimization method for inertial confinement fusion design

Due to their cost, experiments for inertial confinement fusion (ICF) heavily rely on numerical simulations to guide design. As simulation technology progresses, so too can the fidelity of models used to plan for new experiments. However, these high-fidelity models are by themselves insufficient for optimal experimental design, because their computational cost remains too high to efficiently and effectively explore the numerous parameters required to describe a typical experiment. Therefore, traditionally, ICF design has relied on low-fidelity modeling to initially identify potentially interesting design regions, which are then subsequently explored via selected high-fidelity modeling. In this paper, we demonstrate that this two-step approach can be insufficient: even for simple design problems, a two-step optimization strategy can lead high-fidelity searching toward incorrect regions and consequently waste computational resources on parameter regimes far away from the true optimal solution. We reveal that a primary cause of this behavior in ICF design problems is the presence of low-fidelity optima in different regions of the parameter space far away from high-fidelity optima. To address this issue, we propose an iterative multifidelity Bayesian optimization method based on Gaussian Process Regression that leverages both low- and high-fidelity models simultaneously. We demonstrate, using both two- and eight-dimensional ICF test problems, that our algorithm can effectively utilize both low-fidelity and high-fidelity models to refine the designs. This approach proves to be more efficient than relying solely on high-fidelity modeling for optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Comparing traditional and Bayesian approaches to ecological meta‐analysis

Abstract Despite the wide application of meta‐analysis in ecology, some of the traditional methods used for meta‐analysis may not perform well given the type of data characteristic of ecological meta‐analyses. We reviewed published meta‐analyses on the ecological impacts of global climate change, evaluating the number of replicates used in the primary studies ( n i ) and the number of studies or records ( k ) that were aggregated to calculate a mean effect size. We used the results of the review in a simulation experiment to assess the performance of conventional frequentist and Bayesian meta‐analysis methods for estimating a mean effect size and its uncertainty interval. Our literature review showed that n i and k were highly variable, distributions were right‐skewed and were generally small (median n i = 5, median k = 44). Our simulations show that the choice of method for calculating uncertainty intervals was critical for obtaining appropriate coverage (close to the nominal value of 0.95). When k was low (<40), 95% coverage was achieved by a confidence interval (CI) based on the t distribution that uses an adjusted standard error (the Hartung–Knapp–Sidik–Jonkman, HKSJ), or by a Bayesian credible interval, whereas bootstrap or z distribution CIs had lower coverage. Despite the importance of the method to calculate the uncertainty interval, 39% of the meta‐analyses reviewed did not report the method used, and of the 61% that did, 94% used a potentially problematic method, which may be a consequence of software defaults. In general, for a simple random‐effects meta‐analysis, the performance of the best frequentist and Bayesian methods was similar for the same combinations of factors ( k and mean replication), though the Bayesian approach had higher than nominal (>95%) coverage for the mean effect when k was very low ( k < 15). Our literature review suggests that many meta‐analyses that used z distribution or bootstrapping CIs may have overestimated the statistical significance of their results when the number of studies was low; more appropriate methods need to be adopted in ecological meta‐analyses.

Pappalardo, Paula↗
DOE OSTI2020

Data from: Comparing traditional and Bayesian approaches to ecological meta-analysis

Despite the wide application of meta-analysis in ecology, some of the traditional methods used for meta-analysis may not perform well given the type of data characteristic of ecological meta-analyses. We reviewed published meta-analyses on the ecological impacts of global climate change, evaluating the number of replicates used in the primary studies (ni) and the number of studies or records (k) that were aggregated to calculate a mean effect size. We used the results of the review in a simulation experiment to assess the performance of conventional frequentist and Bayesian meta-analysis methods for estimating a mean effect size and its uncertainty interval. Our literature review showed that ni and k were highly variable, distributions were right-skewed, and were generally small (median ni =5, median k=44). Our simulations show that the choice of method for calculating uncertainty intervals was critical for obtaining appropriate coverage (close to the nominal value of 0.95). When k was low (<40), 95% coverage was achieved by a confidence interval based on the t-distribution that uses an adjusted standard error (the Hartung-Knapp-Sidik-Jonkman, HKSJ), or by a Bayesian credible interval, whereas bootstrap or z-distribution confidence intervals had lower coverage. Despite the importance of the method to calculate the uncertainty interval, 39% of the meta-analyses reviewed did not report the method used, and of the 61% that did, 94% used a potentially problematic method, which may be a consequence of software defaults. In general, for a simple random-effects meta-analysis, the performance of the best frequentist and Bayesian methods were similar for the same combinations of factors (k and mean replication), though the Bayesian approaches had higher than nominal (>95%) coverage for the mean effect when k was very low (k<15). Our literature review suggests that many meta-analyses that used z-distribution or bootstrapping confidence intervals may have over-estimated the statistical significance of their results when the number of studies was low; more appropriate methods need to be adopted in ecological meta-analyses.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

A Tutorial on Bayesian analysis of linear shock compression data

Gas gun and other shock compression experiments often produce shock wave velocity measurements that are linearly associated with particle velocity. Traditionally, this empirical relationship is quantified with a single Hugoniot curve that is estimated using least squares regression. However, for downstream modeling and simulation tasks, it is often more useful to have multiple Hugoniot curves in the pressure–volume plane that are consistent with the data. We employ Bayesian uncertainty quantification methods as a framework for propagating measurement uncertainty through to model parameters and predictions. Specifically, this Tutorial shows how to sample multiple Hugoniot curves in the pressure–volume plane that are consistent with the shock wave-particle velocity measurements in a two-step Bayesian approach. First, we obtain an analytical expression for the posterior distribution of the linear model parameters using Bayesian linear regression. Second, we propagate samples from the posterior distribution through the Rankine–Hugoniot equations to yield Hugoniot curves in the pressure–volume plane. The procedure is demonstrated with publicly available data on argon, copper, and nickel, and compared against bootstrapping and linear regression. The Bayesian procedure is shown to be interpretable, computationally inexpensive, and less sensitive than an alternative bootstrapping approach to the removal of the point in the copper dataset that has the largest particle velocity. As a Tutorial on Bayesian methodology for the shock compression community, we provide several derivations and explanations that make this paper self-contained, and make all code and data available at github.com/llnl/BALSCD.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2023

Bayesian projection pursuit regression

In projection pursuit regression (PPR), a univariate response variable is approximated by the sum of $M$ “ridge functions,” which are flexible functions of one-dimensional projections of a multivariate input variable. Traditionally, optimization routines are used to choose the projection directions and ridge functions via a sequential algorithm, and $M$ is typically chosen via cross-validation. Here, we introduce a novel Bayesian version of PPR, which has the benefit of accurate uncertainty quantification. To infer appropriate projection directions and ridge functions, we apply novel adaptations of methods used for the single ridge function case ($M$=1), called the Bayesian Single Index Model; and use a Reversible Jump Markov chain Monte Carlo algorithm to infer the number of ridge functions $M$. We evaluate the predictive ability of our model in 20 simulated scenarios and for 23 real datasets, in a bake-off against an array of state-of-the-art regression methods. Finally, we generalize this methodology and demonstrate the ability to accurately model multivariate response variables. Its effective performance indicates that Bayesian Projection Pursuit Regression is a valuable addition to the existing regression toolbox.

97 MATHEMATICS AND COMPUTING↗