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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

EFIT‐AI: Machine Learning and Artificial Intelligence Assisted Equilibrium Reconstruction for Tokamak Experiments and Burning Plasmas (Final Report)

The EFIT-AI project is creating a modern advanced equilibrium reconstruction code suitable for tokamak experiments of burning plasmas. EFIT [1,2] was the first and is the most extensively used equilibrium reconstruction code in the world. This project builds on the production-level experience and adds key elements as follows. 1. A Model Order Reduction (MOR) version of the two-dimensional (2D) Grad-Shafranov equation solver (EFIT-MORNN) using physics-informed neural networks. 2. Improved optimization and data analysis capabilities using a Bayesian framework enhanced with machine learning. 3. A MOR version of the three-dimensional (3D) perturbed equilibrium reconstruction tool.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Stopping criteria for ending autonomous, single detector radiological source searches

While the localization of radiological sources has traditionally been handled with statistical algorithms, such a task can be augmented with advanced machine learning methodologies. The combination of deep and reinforcement learning has provided learning-based navigation to autonomous, single-detector, mobile systems. However, these approaches lacked the capacity to terminate a surveying/search task without outside influence of an operator or perfect knowledge of source location (defeating the purpose of such a system). Two stopping criteria are investigated in this work for a machine learning navigated system: one based upon Bayesian and maximum likelihood estimation (MLE) strategies commonly used in source localization, and a second providing the navigational machine learning network with a “stop search” action. A convolutional neural network was trained via reinforcement learning in a 10 m × 10 m simulated environment to navigate a randomly placed detector-agent to a randomly placed source of varied strength (stopping with perfect knowledge during training). The network agent could move in one of four directions (up, down, left, right) after taking a 1 s count measurement at the current location. During testing, the stopping criteria for this navigational algorithm was based upon a Bayesian likelihood estimation technique of source presence, updating this likelihood after each step, and terminating once the confidence of the source being in a single location exceeded 0.9. A second network was trained and tested with similar architecture as the previous but which contained a fifth action: for self-stopping. The accuracy and speed of localization with set detector and source initializations were compared over 50 trials of MLE-Bayesian approach and 1000 trials of the CNN with self-stopping. The statistical stopping condition yielded a median localization error of ~1.41 m and median localization speed of 12 steps. The machine learning stopping condition yielded a median localization error of 0 m and median localization speed of 17 steps. This work demonstrated two stopping criteria available to a machine learning guided, source localization system.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Uncertainty-aware mixed-variable machine learning for materials design

Abstract Data-driven design shows the promise of accelerating materials discovery but is challenging due to the prohibitive cost of searching the vast design space of chemistry, structure, and synthesis methods. Bayesian optimization (BO) employs uncertainty-aware machine learning models to select promising designs to evaluate, hence reducing the cost. However, BO with mixed numerical and categorical variables, which is of particular interest in materials design, has not been well studied. In this work, we survey frequentist and Bayesian approaches to uncertainty quantification of machine learning with mixed variables. We then conduct a systematic comparative study of their performances in BO using a popular representative model from each group, the random forest-based Lolo model (frequentist) and the latent variable Gaussian process model (Bayesian). We examine the efficacy of the two models in the optimization of mathematical functions, as well as properties of structural and functional materials, where we observe performance differences as related to problem dimensionality and complexity. By investigating the machine learning models’ predictive and uncertainty estimation capabilities, we provide interpretations of the observed performance differences. Our results provide practical guidance on choosing between frequentist and Bayesian uncertainty-aware machine learning models for mixed-variable BO in materials design.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Bayesian Support Vector Machine (BSVM)

A machine learning based approach is developed to detect events that have rarely been seen in the historical data. The data can include building energy consumption, sensor data, environmental data and any data that may affect the building's energy consumption. The algorithm is a modified nonlinear Bayesian support vector machine, which examines daily energy consumption profile, detect the days with abnormal events, and diagnose the cause of the events.

Source record↗
DOE OSTI2025

Investigating Kinetic Mechanisms of Soot Formation in Plasma Pyrolysis of Methane via Active Learning (Final Technical Report)

Plasma pyrolysis of methane is an effective route for zero-carbon hydrogen production. Yet, soot generated from pyrolysis of hydrocarbons is detrimental to the climate and human health. There is ample experimental and theoretical evidence that suggests polycyclic aromatic hydrocarbons (PAHs) are the molecular precursors to soot particles. The reaction pathways of PAH formation are intricately dependent on a multitude of process parameters, whose kinetic mechanisms are not well-understood in plasma pyrolysis. This project aims to leverage advances in the kinetic modeling of soot formation in combustion, as well as in surrogate modeling and active learning, to systematically investigate the effects of process parameter on the kinetics of PAH formation in plasma pyrolysis of methane. To this end, we propose to use the PAH formation kinetics model developed by the PPPL/PU group based on the well-established ABF and HACA mechanisms, coupled with low-temperature plasma models. We will develop an active learning (AL) framework based on Bayesian optimization to systematically and data-efficiently explore the complex and multivariable parameter space of plasma pyrolysis in order to quantify the effects of plasma and feed parameters on the ABF and HACA kinetic pathways. AL is the branch of machine learning concerned with systematically querying samples from a system (experimental or computational) to train a data-driven model that maps design parameters to a performance criterion. We will use the data generated via AL to perform global sensitivity analysis, combined with uncertainty quantification, to elucidate the impact of different reaction pathways on minimizing formation of soot precursors. This study will result in an improved understanding of kinetics of PAH formation in plasma pyrolysis and can pave the way for more advanced mechanistic studies (e.g., soot nucleation mechanisms). Additionally, the findings will be useful for establishing practical strategies for increasing the pyrolysis efficiency and producing high-grade carbon for synthesis of nanomaterials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Machine Learning Algorithms for Matching Theories, Simulations, and Observations in Cosmology (Final Project)

The search for simple and elegant equations to explain and predict observable natural phenomena has been a driving force in scientific theory for several centuries. The great successes of Newton's laws, Maxwell's equations, the Schrodinger equation, and the theory of General Relativity have encouraged this perspective, and perhaps a beautiful equation comprising a “theory of everything” remains to be discovered. But now scientists are grappling with systems of ever-increasing complexity, fraught with nonlinearity, and with the quantities of interest often only indirectly observed. Nature may resist a simple description, and the most important discoveries of the next century may be complex theories with countless variables and parameters. The era of big data opens up a promising new approach to scientific discovery in this setting. The predictions of modern theories, even if complex or nonlinear, can be examined through detailed and computationally-intensive simulations that take days or weeks to run and fill petabytes of disk space. The upcoming generation of scientific instruments will provide petabytes of observations at unprecedented resolution and depth. The challenge is to compare data to simulations so as to test theories and identify those that best match the observations. The data are numerous and rich but are subject to noise and various systematic biases. The simulations are large and detailed but are so costly that the effective sample size is small. Moreover, the mapping from data to simulation to the parameters of interest is typically complicated and ill-conditioned. Although these challenges, and the solutions we propose, apply across the sciences, we will ground our efforts by focusing on cosmology. Here, we are truly entering the era of big data in several senses. Ever larger experiments survey larger and larger cosmological volumes, resulting in enormous amounts of pixel data to process and extract the information of cosmological interest. These include large imaging surveys, which collect all the light in broad wavelength ranges over significant fractions of the sky, and spectroscopic surveys, which measure the light as a function of wavelength to map out 3D distances. These experiments are designed to shed light on the big unanswered questions in cosmology. Distilling the petabytes of data into observed quantities for comparison with theory is a daunting task. But these large experiments do not only result in large amounts of data to analyze: if we wish to compare to theories of physics, then we need increasingly extensive predictions for the observed quantities as well, which requires ever-larger cosmological simulations that take substantial -- and at times prohibitive -- computational resources to produce. Our goal is to develop statistical and machine learning methods for using observed and simulated data to advance machine learning with applications cosmology. In particular, we focus our research efforts on the following tasks: The challenge for automated science is that it is computationally impossible and statistically dangerous to consider every possible model in order to find the best one. We will develop Bayesian Optimization based active-learning methods that accelerate both the execution of the simulations and the search for best-fitting parameters. The key idea is to make the simulations adaptive -- across resolutions, time, and parameters -- using the data to search as the simulation runs; Most ML methods operate on simple finite dimensional feature vectors. However, many cosmology and other science applications require ML methods that can operate on more complex objects as inputs or outputs such as functions, distributions, or sets and point clouds. Our goal is to develop efficient ML methods for this problem and demonstrate their applicability in Cosmology, Astrophysics, and other science problems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Accelerating multilevel Markov Chain Monte Carlo using machine learning models

Here, this work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian inference often substitute computationally expensive high-fidelity models with machine learning models, thereby introducing approximation errors, our approach offers a computationally efficient alternative by augmenting high-fidelity models with low-fidelity ones within a hierarchical framework. The multilevel approach utilizes the low-fidelity machine learning model (MLM) for inexpensive evaluation of proposed samples thereby improving the acceptance of samples by the high-fidelity model. The hierarchy in our multilevel algorithm is derived from geometric multigrid hierarchy. We utilize an MLM to accelerate the coarse level sampling. Training machine learning model for the coarsest level significantly reduces the computational cost associated with generating training data and training the model. We present an MCMC algorithm to accelerate the coarsest level sampling using MLM and account for the approximation error introduced. We provide theoretical proofs of detailed balance and demonstrate that our multilevel approach constitutes a consistent MCMC algorithm. Additionally, we derive the expression for cost reduction due to machine learning model to facilitate cost analysis of the hierarchical sampling algorithm. Our technique is demonstrated on a standard benchmark inference problem in groundwater flow, where we estimate the probability density of a quantity of interest using a four-level MCMC algorithm. Our proposed algorithm accelerates multilevel sampling by a factor of two while achieving similar accuracy compared to sampling using the standard multilevel algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Bayesian Approach for Quantifying Data Scarcity when Modeling Human Behavior via Inverse Reinforcement Learning

Computational models that formalize complex human behaviors enable study and understanding of such behaviors. However, collecting behavior data required to estimate the parameters of such models is often tedious and resource intensive. Thus, estimating dataset size as part of data collection planning (also known as Sample Size Determination) is important to reduce the time and effort of behavior data collection while maintaining an accurate estimate of model parameters. In this paper, we present a sample size determination method based on Uncertainty Quantification (UQ) for a specific Inverse Reinforcement Learning (IRL) model of human behavior, in two cases: 1) pre-hoc experiment design—conducted in the planning stage before any data is collected, to guide the estimation of how many samples to collect; and 2) post-hoc dataset analysis—performed after data is collected, to decide if the existing dataset has sufficient samples and whether more data is needed. Here, we validate our approach in experiments with a realistic model of behaviors of people with Multiple Sclerosis (MS) and illustrate how to pick a reasonable sample size target. Our work enables model designers to perform a deeper, principled investigation of effects of dataset size on IRL.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

BatteryPro: A Python Toolkit for Battery Data Analysis and Machine Learning Predictions

Analyzing battery test data for research & development can be time-consuming since battery tests often run on the order of months to years, generating large volumes of data. BatteryPro is a comprehensive Python package and software designed to facilitate advanced analysis and performance predictions for battery test data. Developed for battery researchers, it supports data types from widely used battery testing instruments, including MACCOR and Biologic cycling systems. The software provides a variety of tools for extracting and plotting key battery parameters such as time, voltage, capacity, current, and pressure. In addition to its extensive data analysis capabilities, BatteryPro features a dedicated machine learning module that employs a Bayesian Gaussian Mixture Model (GMM) to predict battery performance and degradation. Users can generate synthetic capacity fade data, calculate fade metrics, and leverage predictive models to forecast long-term battery behavior. The software's graphical user interface (GUI) enhances usability, allowing researchers to upload, merge, and analyze multiple data files with full customizability. The GUI also supports machine learning predictions, enabling users to fit models and make predictions based on selected data and parameters. BatteryPro is built using QtDesigner, scikit-learn, matplotlib, and pandas, ensuring a high level of customization, flexibility, and accuracy in battery data analysis. This tool aims to empower researchers with the ability to perform detailed battery analysis and make informed predictions, ultimately advancing the field of battery research.

25 - ENERGY STORAGE↗
DOE OSTI2012

A Graphical Approach to Diagnosing the Validity of the Conditional Independence Assumptions of a Bayesian Network Given Data

Bayesian networks have attained widespread use in data analysis and decision making. Well studied topics include: efficient inference, evidence propagation, parameter learning from data for complete and incomplete data scenarios, expert elicitation for calibrating Bayesian network probabilities, and structure learning. It is not uncommon for the researcher to assume the structure of the Bayesian network or to glean the structure from expert elicitation or domain knowledge. In this scenario, the model may be calibrated through learning the parameters from relevant data. There is a lack of work on model diagnostics for fitted Bayesian networks; this is the contribution of this paper. We key on the definition of (conditional) independence to develop a graphical diagnostic method which indicates if the conditional independence assumptions imposed when one assumes the structure of the Bayesian network are supported by the data. We develop the approach theoretically and describe a Monte Carlo method to generate uncertainty measures for the consistency of the data with conditional independence assumptions under the model structure. We describe how this theoretical information and the data are presented in a graphical diagnostic tool. We demonstrate the approach through data simulated from Bayesian networks under different conditional independence assumptions. We also apply the diagnostic to a real world data set. The results indicate that our approach is a reasonable way of visualizing and inspecting the conditional independence assumption of a Bayesian network given data.

Bayesian Networks · Structural Model Diagnostics ·↗
DOE OSTI2023

Coupling multi-fidelity xRAGE with machine learning for graded inner shell design optimization in double shell capsules

Bayesian optimization has shown promise for the design optimization of inertial confinement fusion targets. Specifically, in Vazirani et al. [Phys. Plasmas 28 , 122709 (2021)], optimal designs for double shell capsules with graded inner shells were identified using one-dimensional xRAGE simulation yield calculations. While the machine learning models were able to accurately learn and predict one-dimensional simulation target performance, using simulations with higher fidelity would improve design optimization and better match with the expected experimental performance. However, higher fidelity physics modeling, i.e., two-dimensional xRAGE simulations, requires significantly larger computational time/cost, usually at least an order of magnitude, in comparison with one-dimensional simulations. This study presents a multi-fidelity Bayesian optimization, in which the machine learning model leverages low-fidelity (one-dimensional xRAGE) and high-fidelity (two-dimensional xRAGE) simulations to more accurately predict “pre-shot” target performance with respect to the expected experimental performance. By building a multi-fidelity Bayesian optimization framework coupled with xRAGE, the low-fidelity and high-fidelity simulations are able to inform one another, such that we have: (1) improved physics modeling in comparison with using low-fidelity simulations alone, (2) reduced computational time/cost in comparison with using high-fidelity simulations alone, and (3) more confidence in the expected performance of optimized targets during real-world experiments. In the future, we plan to use this robust multi-fidelity Bayesian optimization methodology to expedite the design of graded inner shells further and eventually full capsules as a part of the current double shell campaign at the National Ignition Facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Accelerating the design of lattice structures using machine learning

Lattices remain an attractive class of structures due to their design versatility; however, rapidly designing lattice structures with tailored or optimal mechanical properties remains a significant challenge. With each added design variable, the design space quickly becomes intractable. To address this challenge, research efforts have sought to combine computational approaches with machine learning (ML)-based approaches to reduce the computational cost of the design process and accelerate mechanical design. While these efforts have made substantial progress, significant challenges remain in (1) building and interpreting the ML-based surrogate models and (2) iteratively and efficiently curating training datasets for optimization tasks. Here, we address the first challenge by combining ML-based surrogate modeling and Shapley additive explanation (SHAP) analysis to interpret the impact of each design variable. We find that our ML-based surrogate models achieve excellent prediction capabilities (R 2 > 0.95) and SHAP values aid in uncovering design variables influencing performance. We address the second challenge by utilizing active learning-based methods, such as Bayesian optimization, to explore the design space and report a 5 × reduction in simulations relative to grid-based search. Collectively, these results underscore the value of building intelligent design systems that leverage ML-based methods for uncovering key design variables and accelerating design.

36 MATERIALS SCIENCE↗
DOE OSTI2026

New approaches to Bayesian uncertainty quantification for Nuclear Science (Final Technical Report)

Inverse problems play a central role in experimentation and theory/data comparisons for many areas of modern Nuclear Physics (NP) and High-Energy Physics (HEP). Bayes’s Theorem is a powerful tool for solving Inverse Problems, providing conceptually transparent and unbiased constraints on theoretical parameters and their uncertainties (“Bayesian Inference”) and enabling the quantification of agreement or tension between models and data. However, analyses based on Bayesian Inference are often challenging for NP and HEP applications, either because of the large number of parameters in the problem, the high computational cost, or both. We propose a multi-institutional collaboration to develop and deploy novel Bayesian analysis tools that advance the scientific scope of a broad range of current and future NP experiments. This project brings together NP domain scientists working on several high-profile NP projects for which new, high-performance Bayesian Uncertainty Quantification (“Bayesian UQ”) methods are essential to carry out the science, and data scientists who are developing state-of-the-art methods applicable to these problems. The NP projects in this proposal comprise measurements of the mass and fundamental nature of the neutrino; study of the Quark-Gluon Plasma that filled the early universe; and mapping of natural and anthropogenic radiation environments. While these NP projects have very different scientific goals, with datasets and analysis approaches that differ significantly, they share common requirements for improving computationally intensive Bayesian analyses using advanced Machine Learning algorithms and will benefit strongly from a coherent effort to develop general solutions. This proposal brings together these projects and forefront ML-based data science algorithms to develop such general solutions. The methods developed in this project will also be more widely applicable, thereby advancing science in the larger Nuclear Physics portfolio.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Optimization and stabilization of Fermilab Booster using hybrid Bayesian/RL framework

PIPII project will raise Fermilab Booster intensity and ramp rate. Beam losses will limit average power and are hard to simulate. Presently, Booster uses operator-guided empirical tuning. This task is challenging due to high dimensionality, multiple objectives, critical safety constraints, and drifts. We developed a synergistic suite of Bayesian optimization (BO) and reinforcement learning (RL) tools to optimize and stabilize beam losses. First, active learning was used to build a rough model. Data was collected parasitically using two novel safety constraint types – nonlinear input space restrictions (based on optics model), and uncertainty constraints (to stop bad steps/beam aborts). We then applied online multi-objective BO with scalarized objectives and fitting to improve/rebalance losses, increasing safety margins by 25%. Using BO model as a safety veto, we tried several on/off-policy RL agents for long term stabilization; SAC had best performance. We found that adding contextual (state) information further improved performance, eventually integrating key knobs like linac phase and temperature into the parameter space. Long term testing is ongoing to enable operational use.

Kuklev, Nikita [Fermilab]↗
DOE OSTI2023

Advanced data analysis in inertial confinement fusion and high energy density physics

Bayesian analysis enables flexible and rigorous definition of statistical model assumptions with well-characterized propagation of uncertainties and resulting inferences for single-shot, repeated, or even cross-platform data. This approach has a strong history of application to a variety of problems in physical sciences ranging from inference of particle mass from multi-source high-energy particle data to analysis of black-hole characteristics from gravitational wave observations. The recent adoption of Bayesian statistics for analysis and design of high-energy density physics (HEDP) and inertial confinement fusion (ICF) experiments has provided invaluable gains in expert understanding and experiment performance. In this Review, we discuss the basic theory and practical application of the Bayesian statistics framework. We highlight a variety of studies from the HEDP and ICF literature, demonstrating the power of this technique. Due to the computational complexity of multi-physics models needed to analyze HEDP and ICF experiments, Bayesian inference is often not computationally tractable. Two sections are devoted to a review of statistical approximations, efficient inference algorithms, and data-driven methods, such as deep-learning and dimensionality reduction, which play a significant role in enabling use of the Bayesian framework. We provide additional discussion of various applications of Bayesian and machine learning methods that appear to be sparse in the HEDP and ICF literature constituting possible next steps for the community. We conclude by highlighting community needs, the resolution of which will improve trust in data-driven methods that have proven critical for accelerating the design and discovery cycle in many application areas.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Machine-learned interatomic potentials by active learning: amorphous and liquid hafnium dioxide

We propose an active learning scheme for automatically sampling a minimum number of uncorrelated configurations for fitting the Gaussian Approximation Potential (GAP). Our active learning scheme consists of an unsupervised machine learning (ML) scheme coupled with a Bayesian optimization technique that evaluates the GAP model. We apply this scheme to a Hafnium dioxide (HfO 2 ) dataset generated from a "melt-quench" ab initio molecular dynamics (AIMD) protocol. Our results show that the active learning scheme, with no prior knowledge of the dataset, is able to extract a configuration that reaches the required energy fit tolerance. Further, molecular dynamics (MD) simulations performed using this active learned GAP model on 6144 atom systems of amorphous and liquid state elucidate the structural properties of HfO 2 with near ab initio precision and quench rates (i.e., 1.0 K/ps) not accessible via AIMD. The melt and amorphous X-ray structural factors generated from our simulation are in good agreement with experiment. In addition, the calculated diffusion constants are in good agreement with previous ab initio studies.

36 MATERIALS SCIENCE↗