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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Uncertainty Quantification for Data-Driven Machine Learning Models in Nuclear Engineering Applications: Where We Are and What Do We Need?

Machine learning (ML) has been leveraged to tackle a diverse range of tasks in almost all branches of nuclear engineering. Many of the successes in ML applications can be attributed to the recent performance breakthroughs in deep learning, the growing availability of computational power, data, and easy-to-use ML libraries. However, these empirical successes have often outpaced our formal understanding of the ML algorithms. An important but under-rated area is uncertainty quantification (UQ) of ML. ML-based models are subject to approximation uncertainty when they are used to make predictions, due to sources including but not limited to, data noise, data coverage, extrapolation, imperfect model architecture and the stochastic training process. The goal of this paper is to clearly explain and illustrate the importance of UQ of ML. We will elucidate the differences in the basic concepts of UQ of physics-based models and data-driven ML models. Various sources of uncertainties in physical modeling and data-driven modeling will be discussed, demonstrated, and compared. We will also present and demonstrate a few techniques to quantify the ML prediction uncertainties, including Monte Carlo dropout, deep ensemble, Bayesian neural networks, Gaussian Processes and conformal prediction. Lastly, we will discuss the need for building a verification, validation and UQ framework to establish ML credibility.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Nonequilibrium formulation of varying-temperature bit erasure

Landauer's principle states that erasing a bit of information at fixed temperature T costs at least $k$ B $T$ ln 2 units of work. Here we investigate erasure at varying temperature, to which Landauer's result does not apply. Here we formulate bit erasure as a stochastic nonequilibrium process involving a compression of configuration space, with physical and logical states associated in a symmetric way. Erasure starts and ends at temperature T, but temperature can otherwise vary with time in an arbitrary way. Defined in this way, erasure is governed by a set of nonequilibrium fluctuation relations that show that varying-temperature erasure can done with less work than $k$ B $T$ ln 2. As a result, erasure and the complementary process of bit randomization can be combined to form a work-producing engine cycle.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Effective description of ajar systems with a 𝑈⁡(1) symmetry

We introduce the concept of “ajar systems” as an intermediate case between closed and open systems, where the time scale for charge exchange with the environment is parametrically larger than all other characteristic time scales. The Schwinger-Keldysh effective action for such finite-temperature systems exhibits a symmetry group G 1 × G 2 weakly broken to its diagonal subgroup G diag , which we systematically describe using spurion techniques. For G = U(1), we calculate leading-order corrections to correlation functions in both diffusive and spontaneously broken phases. Unlike systems with approximate symmetries where both real and imaginary parts of dispersion relations receive corrections, ajar systems modify only the imaginary part—preserving gapless modes while adding finite damping.

Effective field theory↗
DOE OSTI2024

Modeling stochastic fluctuations in relativistic kinetic theory

Using the information current, we develop a Lorentz-covariant framework for modeling equilibrium fluctuations in relativistic kinetic theory in the grand-canonical ensemble. The resulting stochastic theory is proven to be causal and covariantly stable, and its predictions do not depend on the choice of spacetime foliation used to define the grand-canonical probabilities. As expected, in a box containing N > 5 particles, Boltzmann’s molecular chaos postulate is broken with (almost exact) probability N -1/2 , leading to a breakdown of the Boltzmann equation in small systems. Here, we also verify that, in ultrarelativistic gases, transient hydrodynamics already accounts for at least 80% of the equilibrium fluctuations of the stress-energy tensor at a given time. Finally, we compute the correlators at nonequal times for two selected collision kernels: that of a chemically active diluted solution, and that of ultrarelativistic scalar particles self-interacting via a quartic potential. For the former, we compute the density-density correlators analytically in real space, and dehydrodynamization of the stochastic theory is proven to occur whenever the mean free path diverges at high energy.

Astronomy & Astrophysics↗
DOE OSTI2025

Time-Resolved Stochastic Dynamics of Quantum Thermal Machines

Steady-state quantum thermal machines are typically characterized by a continuous flow of heat between different reservoirs. However, at the level of discrete stochastic realizations, heat flow is unraveled as a series of abrupt quantum jumps, each representing an exchange of finite quanta with the environment. Here, in this work, we present a framework that resolves the dynamics of quantum thermal machines into cycles classified as enginelike, coolinglike, or idle. We analyze the statistics of individual cycle types and their durations, enabling us to determine both the fraction of cycles useful for thermodynamic tasks and the average waiting time between cycles of a given type. Central to our analysis is the notion of intermittency, which captures the operational consistency of the machine by assessing the frequency and distribution of idle cycles. Our framework offers a novel approach to characterizing thermal machines, with significant relevance to experiments involving mesoscopic transport through quantum dots.

full counting statistics↗
DOE OSTI2025

Evaluation of Seismic Artificial Intelligence with Uncertainty

Artificial intelligence has transformed the seismic community with deep learning models (DLMs) that are trained to complete specific tasks within workflows. However, there is still a lack of robust evaluation frameworks for evaluating and comparing DLMs. Here, we address this gap by designing an evaluation framework that jointly incorporates two crucial aspects: performance uncertainty and learning efficiency. To target these aspects, we meticulously construct the training, validation, and test splits using a clustering method tailored to seismic data and enact an expansive training design to segregate performance uncertainty arising from stochastic training processes and random data sampling. The framework’s ability to guard against misleading declarations of model superiority is demonstrated through the evaluation of PhaseNet (Zhu and Beroza, 2018), a popular seismic phase picking DLM, under three training approaches. Our framework helps practitioners choose the best model for their problem and set performance expectations by explicitly analyzing model performance with uncertainty at varying budgets of training data.

58 GEOSCIENCES↗
DOE OSTI2025

Post-hoc reweighting of hadron production in the Lund string model

We present a method for reweighting flavor selection in the Lund string fragmentation model. This is the process of calculating and applying event weights enabling fast and exact variation of hadronization parameters on pre-generated event samples. The procedure is post hoc, requiring only a small amount of additional information stored per event, and allowing for efficient estimation of hadronization uncertainties without repeated simulation. Weight expressions are derived from the hadronization algorithm itself, and validated against direct simulation for a wide range of observables and parameter shifts. The hadronization algorithm can be viewed as a hierarchical Markov process with stochastic rejections, a structure common to many complex simulations outside of high-energy physics. This perspective makes the method modular, extensible, and potentially transferable to other domains. We demonstrate the approach in Pythia, including both coverage considerations and timing benefits. For the purpose of this paper, our goal is to develop and demonstrate the the formalism, and we therefore exclude several model variations for baryon production (popcorn model, junction production) needed for proton collisions. These will be the topic of a future paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Cosmogenic 3 He exposure dating in mafic rocks by “Virtual mineral separation” of pyroxene

We describe a “virtual mineral separation” method for measuring the cosmogenic 3 He concentration in pyroxene in mafic rocks that consist mainly of plagioclase and pyroxene, without physically separating the minerals. This approach is significantly faster and more cost-effective than the conventional method, which requires physical separation and purification of pyroxene grains by time-consuming and labor-intensive crushing, acid cleaning, magnetic separation, HF etching, and handpicking under a microscope. The premise of the method is that helium diffusivity is much higher in plagioclase than in pyroxene, so controlled preheating of a mixed whole-rock sample can degas 3 He from plagioclase while retaining all 3 He in pyroxene. A second heating step releases all 3 He from pyroxene for measurement. To then obtain a 3 He concentration in pyroxene rather than the whole rock, we determine the pyroxene weight fraction in the sample using X-ray computed tomography (CT). A comparison of 3 He concentrations in pyroxene measured using virtual mineral separation with those measured in the same samples by physical mineral separation in previous work shows no evidence of systematic bias between the methods. Virtual mineral separation greatly simplifies the workflow for 3 He exposure-dating of mafic rocks, reduces time, effort, and cost, and permits measurements on very small samples. This enables new emerging applications of exposure dating, such as quantifying stochastic surface processes, ecosystem studies, and potential subglacial bedrock exposure dating.

Geosciences↗
DOE OSTI2026

Conservation laws and effective hadronization models

Hadronization models based on local string-breaking dynamics are typically Markovian by construction, yet the physical ensemble of final states is shaped by global constraints that couple the entire fragmentation trajectory. Recasting hadronization as a conditioned stochastic diffusion process provides a precise mathematical resolution to this tension. In particular, this language reveals explicitly that constraints stemming from conservation laws induce non-Markovian correlations between otherwise independent fragmentation steps, and that these correlations can be absorbed exactly into a renormalization of the local dynamics through a Doob $h$-transform. We develop this formalism for a $q\bar{q}$ string in the chiral limit, where the longitudinal-transverse factorization of the Lund kernel becomes exact, enabling systematic power counting and clean ultraviolet (UV)/infrared (IR) separation. The dynamics organize naturally into a tower of effective theories distinguished by the remaining string mass, spanning a UV fixed point with scale-invariant transport coefficients, an intermediate regime where transverse phase space induces controlled running, and an IR boundary layer where non-local effects enter at leading order. The tower exhibits genuine Wilsonian structure, including $β$-functions, anomalous dimensions, and systematic matching conditions. The resulting framework achieves a clean factorization of universal microscopic fragmentation dynamics from infrared constraint effects, and opens new directions for both the theoretical analysis and practical simulation of hadronization.

Menzo, Tony [Alabama U.; Fermilab] (ORCID:00000002↗
DOE OSTI2026

Multi-Agent Control Planes for Quantum Networks: A Scalable Architecture for Autonomous Quantum Internet Management

Quantum networks are expected to enable distributed quantum computing, secure communication, and global entanglement distribution. However, operating such networks presents significant challenges, including stochastic quantum processes, fragile entanglement resources, dynamic topology, and cross-layer control requirements. Current quantum network control architectures largely rely on centralized or hierarchical controllers inspired by classical software-defined networking (SDN). While effective for small testbeds, these approaches face scalability, latency, and reliability limitations as quantum networks grow. This paper proposes a multi-agent control plane architecture for quantum networks. In this design, intelligent software agents operate at quantum nodes, repeaters, and orchestration layers, collectively managing entanglement generation, routing, purification, and scheduling. The distributed intelligence of the agent system allows the network to adapt dynamically to quantum hardware variability and environmental noise. We argue that multi-agent systems provide significant advantages over centralized control approaches, including scalability, resilience, local autonomy, and real-time adaptation. The paper discusses architectural design principles, agent coordination mechanisms, and research challenges in deploying multi-agent control planes for the emerging quantum Internet.

Alnajjar, Anees [ORNL] (ORCID:0000000237101601)↗
DOE OSTI2025

Energy-momentum-conserving stochastic differential equations and algorithms for the nonlinear Landau-Fokker-Planck equation

Coulomb collision is a fundamental diffusion process in plasmas that can be described by the Landau-Fokker-Planck (LFP) equation or the stochastic differential equation (SDE). While energy and momentum are conserved exactly in the LFP equation, they are conserved only on average by the conventional corresponding SDEs, suggesting that the underlying stochastic process may not be well defined by such SDEs. Here, in this study, we derive new SDEs with exact energy-momentum conservation for the Coulomb collision by factorizing the collective effect of field particles into individual particles and enforcing Newton's third law. These SDEs, when interpreted in the Stratonovich sense, have a particularly simple form that represents pure diffusion between particles without drag. To demonstrate that the new SDEs correspond to the LFP equation, we develop numerical algorithms that converge to the SDEs and preserve discrete conservation laws. Simulation results are presented in a benchmark of various relaxation processes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Computing Nonequilibrium Responses with Score-Shifted Stochastic Differential Equations

Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic dynamics. For nonequilibrium systems, perturbations cannot be interpreted simply by monitoring fluctuations in a conjugate observable and general response results rely on path ensemble averaging. Furthermore, these techniques do not apply to perturbations that affect the diffusion tensor in a stochastic system. Here, we introduce an “effective” physical process that represents the diffusion perturbed dynamics and enables accurate calculations of responses to a change in the diffusion. Interestingly, the effective dynamics contain an additional drift involving the instantaneous “score” of the system, and we leverage score matching algorithms to carry out nonequilibrium response calculations on systems for which the exact stationary distribution is unknown.

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

Solid State Quantum Refrigeration Superconducting, Absorption and Measurement Based (Final Technical Report)

During this DOE grant, DE-SC0017890, in place for the past six years, all proposed research was carried out and published in peer-reviewed papers, as well as other projects that emerged during the research. In that effort the research team accomplished all proposed research, as well as many closely related research projects discovered and conceived of during the grant. These works included “Efficient Quantum Measurement Engines”, a work published in Physical Review Letters, giving a theory of quantum measurement-based engines, which uses quantum measurement as a resource. These engines are designed to efficiently convert energy from the stochastic quantum measurement process into useful work. Further publications include “Experimental Realization of a Quantum Dot Energy Harvester”, a joint theory and experimental work in collaboration with the group of Charles Smith in Cambridge, UK, as well as long time theoretical collaborators, Rafael Sánchez and Björn Sothmann. This work, featured as an Editor’s Suggestion in Physical Review Letters, realized an earlier theoretical proposal of ours, whereby two resonant tunneling quantum dots are connected to a central electronic cavity that is heated by a hot energy source. We also published “Superconducting Quantum Refrigerator: Breaking and Rejoining Cooper Pairs with Magnetic Field Cycles” a work done in collaboration with experimentalist Francesco Giazotto from ENS Pisa, Italy, which also resulted in a patent. This paper, published in Phys. Rev. Applied, advanced the concept of a cyclic fridge based on the normal/superconducting phase transition together with layered materials separated by tunnel junctions. We also completed the proposed research on a heat transistor, publishing “Thermal transistor and thermometer based on Coulomb-coupled conductors”, carried out as a collaboration between my group and theorists Splettstoesser (Lund U., Sweden), Sothmann (U. Duisburg-Essen, Germany), and Sánchez (U. Autónoma de Madrid, Spain). We carried out an analysis of a quantum coupled to a quantum point contact as a sensitive thermometer and heat transistor. We found the optimal statistical estimator for the temperature and compared it with experiments on the same type of devices. We also investigated autonomous quantum absorption refrigerators using quantum dots to cool by using a very hot thermal reservoir to drive heat between two other reservoirs. In the article “Quantifying the quantum heat contribution from a driven superconducting circuit”, we demonstrated that for a driven superconducting circuit, we showed heat flow provided by a hot source to the qubit can be switched on and off by varying external parameters, the frequency and the intensity of the driving. In the work “Stochastic thermodynamic cycles of a mesoscopic thermoelectric engine”, we reconsidered the autonomous thermoelectric heat engine in terms of underlying cycles. Rather than periodic behavior, the cycles were stochastic in nature. Nevertheless, by undertaking a graph theoretical analysis of the elementary transport processed, great quantitative and qualitative insight could be found. We also considered the quantum measurement process and showed that a quantum version of Maxwell’s demon could be related to the work extraction of a quantum system, closely related to arrow-of-time measures for quantum measurement, as described in our article “Thermodynamics of quantum measurement and Maxwell's demon's arrow of time”. This work was selected in Phys. Rev. A as an Editor’s Suggestion. A recent preprint titled “Cyclic Superconducting Quantum Refrigerators Using Guided Fluxon Propagation” accomplished an important piece of this grant: to propose a new kind of quantum refrigerator using the dynamics of fluxons in a type II superconductor. This invention envisioned a race-track type geometry where fluxons are confined. By applying a gradient of magnetic field together with electric current in a Corbino geometry, the circulating fluxons can actively cool a cold reservoir, realizing a new type of cyclic superconducting refrigerator. We also investigated the possibility of thermal control from different points of view. The application of quantum measurement to the system gives a new kind of control on the system of interest – we have pioneered this approach and shown that measurement can boost the thermal power of quantum engines as described in “Continuous measurement boosted adiabatic quantum thermal machines”. The ability to have heat flows on demand is an outstanding challenge, and we have provided new solutions to this problem in Thermal control across a chain of electronic nanocavities” for a chain of electron cavities using gating voltage control. The control methods using qubit/qubit coupling to create absorption fridges at their most fundamental level have also been developed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Simulating Atmospheric Processes in Earth System Models and Quantifying Uncertainties With Deep Learning Multi‐Member and Stochastic Parameterizations

Abstract Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated uncertainty quantification to learn subgrid convective and turbulent processes and surface radiative fluxes of a superparameterization embedded in an Earth System Model (ESM). We explore three methods to construct stochastic parameterizations: (a) a single Deep Neural Network (DNN) with Monte Carlo Dropout; (b) a multi‐member parameterization; and (c) a Variational Encoder Decoder with latent space perturbation. We show that the multi‐member parameterization improves the representation of convective processes, especially in the planetary boundary layer, compared to individual DNNs. The respective uncertainty quantification illustrates that methods (b) and (c) are advantageous compared to a dropout‐based DNN parameterization regarding the spread of convective processes. Hybrid simulations with our best‐performing multi‐member parameterizations remained challenging and crash within the first days. Therefore, we develop a pragmatic partial coupling strategy relying on the superparameterization for condensate emulation. Partial coupling reduces the computational efficiency of hybrid Earth‐like simulations but enables model stability over 5 months with our multi‐member parameterizations. However, our hybrid simulations exhibit biases in thermodynamic fields and differences in precipitation patterns. Despite this, the multi‐member parameterizations enable improvements in reproducing tropical extreme precipitation compared to a traditional convection parameterization. Despite these challenges, our results indicate the potential of a new generation of multi‐member machine learning parameterizations leveraging uncertainty quantification to improve the representation of stochasticity of subgrid effects.

Behrens, Gunnar [Deutsches Zentrum für Luft‐ und R↗
DOE OSTI2024

Characterization of latent image of electron beam resist via critical-dimension resonant soft X-ray scattering

Metrology plays a crucial role in semiconductor manufacturing by providing accurate and precise measurement and characterization of critical parameters. With the development of high-resolution extreme ultraviolet lithography (EUVL) processes, critical dimensions are shrinking to sub-10 nm. Resist materials encounter the challenge of providing heightened sensitivity and a handle on exacerbating stochastic variations. A comprehensive understanding of the chemical profile of the latent image is pivotal for mitigating stochastic effects and optimizing pattern quality. However, the subtle differences in chemistry between the exposed and unexposed regions of the resists make it extremely challenging to characterize the latent images with sub-nanometer precision. Here, we develop the metrology with critical-dimension resonant soft X-ray scattering (CD-RSoXS) to probe the chemical profiles of latent images stored in resist after exposure. The combination of absorption spectroscopy and enhanced scattering contrast makes it possible to characterize the subtle structural and chemical variations in the latent image. Moreover, the results of the measurements are compared with the simulations with a finite element method–based Maxwell solver to extract a detailed profile of the latent and developed images. We demonstrate that the CD-RSoXS technique can provide valuable insights into the high spatial resolution and local chemical sensitivity simultaneously, which is crucial to understanding the resolution limits and stochastic effects in EUVL processes.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Raptor: A Python Library for Porosity Predictions in Additive Manufacturing

Raptor is an efficient Python library for simulating stochastic lack-of-fusion (sLoF) defects in additive manufacturing (AM) processes. These defects arise from stochastic variations in the melt pool boundary leading to undermelting from insufficient overlap between adjacent melt pools or successive layers (Grasso & Colosimo, 2017; Khairallah et al., 2016). Performance variability of AM parts is a pressing challenge in qualification and certification of AM parts; this is in part due to the poorly understood formation rate and statistics of sLoF defects. Raptor is designed to capture the explicit morphologies of sLoF defects and their statistics to accelerate qualification and certification efforts of AM parts in critical applications.

Subraveti, Vamsi [Vanderbilt University]↗
DOE OSTI2026

Stochastic Microgrid Scheduling With Chance‐Constrained Resilience Consideration

Traditionally, it is assumed that microgrids transition seamlessly from grid‐connected operation to islanded mode in the event of sudden main grid outages. In reality, the islanding process, especially unintentional islanding, is rarely seamless. Instead, it is subject to voltage and frequency fluctuations caused by the instantaneous disconnection of the point of common coupling (PCC) switch, variations in loads and renewable generation output and even the protection tripping of distributed energy resources (DERs). To mitigate these fluctuations and facilitate a smooth islanding process, we propose a stochastic microgrid scheduling model that incorporates chance‐constrained resilience measures. Specifically, the resilience measure is defined as the probability of successful islanding (PSI), that is, the probability that a microgrid can mitigate the generation‐demand imbalance caused by the disconnection of the PCC switch, variations in load and renewable generation and DER tripping. This measure is modelled using chance constraints. Unlike existing reliability and resilience indices, which typically neglect the possibility of microgrid/DER failure under extreme events and assume their survival while primarily focussing on reducing impact duration or magnitude, the proposed PSI‐based framework explicitly addresses microgrid and DER survival during the islanding transition. The formulated nonlinear chance constraints are approximated using a multiinterval approach and equivalently represented as a mixed‐integer linear programming (MILP) formulation. Case study results validate the proposed method, showing that the PSI estimation error is reduced to less than 8%, compared to approximately 28% with existing methods. Various sensitivity analyses on the DER tripping rate and PSI settings were performed to validate the robustness of the proposed method. In particular, the necessity of accounting for DER tripping in the PSI calculation was demonstrated.

chance constrained optimization↗