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Spatial Correlations of the Poisson Model for Radiation Transport

Characterizing the relationship between bulk physical properties and mixing in randomly heterogeneous media is a central challenge across many areas of science and engineering. A benchmark model for such studies is the Poisson model, a random tessellation of space by a Poisson process of hyperplanes. In radiation transport studies, the lack of exact expressions for the Poisson model’s spatial multipoint functions has led to approximate methods being used, introducing unquantified sources of error. Here, we recently introduced an exact solution for the Poisson model’s multipoint functions and closely related conditional probability functions (CPFs), providing a new opportunity to understand and reduce these sources of error. In this paper, we enable a more rigorous investigation of radiation transport in stochastic media by applying the recently introduced exact solution for the Poisson model’s CPFs. This paper consists of three main contributions. First, we introduce a unified framework for CPFs of the Poisson model, encompassing the recently introduced exact CPFs as well as the previously introduced atomic mix, nearest-neighbor, and combination CPFs. This framework also includes existing pruning techniques for the approximate CPFs, such as angular exclusion, as well as a novel form of angular exclusion suitable for the exact CPFs. Second, we use the exact CPFs to characterize the spatial regions where each approximate three-point CPF is most accurate, thereby explaining the observed hierarchy of accuracy among the approximate models. Finally, we evaluate material transmittance, reflectance, and flux in a three-dimensional test problem using conditional point sampling, demonstrating the relationship between CPF accuracy and transport simulation accuracy.

Poisson model↗

Kernel learning backward SDE filter for data assimilation

In this paper, we develop a kernel learning backward SDE filter method to estimate the state of a stochastic dynamical system based on its partial noisy observations. A system of forward backward stochastic differential equations is used to propagate the state of the target dynamical model, and Bayesian inference is applied to incorporate the observational information. Further, to characterize the dynamical model in the entire state space, we introduce a kernel learning method to learn a continuous global approximation for the conditional probability density function of the target state by using discrete approximated density values as training data. Numerical experiments demonstrate that the kernel learning backward SDE is highly effective.

97 MATHEMATICS AND COMPUTING↗

A Bayesian model for multivariate discrete data using spatial and expert information with application to inferring building attributes

When modeling sparsely observed multivariate data, strong prior information elicited from experts can be used to bolster predictive accuracy and counteract sampling bias. Similarly, modeling autocorrelation in space can help make use of co-occurrence patterns present in many types of spatial data. To make use of both expert prior information and spatial structure, we propose a novel graphical model for a spatial Bayesian network developed specifically to address challenges in inferring the attributes of buildings from geographically sparse observational data. This model is implemented as the sum of a spatial multivariate Gaussian random field and a tabular conditional probability function in real-valued space prior to projection onto the probability simplex. This modeling form is especially suitable for the usage of prior information in the form of sets of atomic rules obtained from experts. To perform inference with missing data, we implement a Markov chain Monte Carlo scheme composed of alternating steps of Gibbs sampling of missing entries and Hamiltonian Monte Carlo for model parameters. A case study in building attribution is presented to highlight the advantages and limitations of this approach.

97 MATHEMATICS AND COMPUTING↗

Database-wide hazard modelling of the onset of DIII-D tearing modes with field features

The rate of onset (hazard) of tearing modes is modelled probabilistically using statistical learning algorithms. Axisymmetric energy-density equilibrium fields are taken as raw high-dimensional input features which are reduced with principal component analysis. Signal processing of non-axisymmetric magnetics fluctuation array data provides the target information from which to learn. Model selection, visualization and calibration assessment procedures are detailed. Here, the analysis is deployed at large scale across the DIII-D tokamak database. Standard model selection criteria suggest that the energy-density post-processed feature is a better choice for modelling the onset rate compared to the non-processed equilibrium reconstruction solution. Two example applications of the learned rate function are demonstrated: (i) proximity-to-onset discharge monitoring and (ii) database analysis showing an (expected) observational global trend that the general hazard increases as a plasma performance metric increases. An important connection between the hazard function and its use as a conditional probability generator is reviewed in the Appendix.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Inferring adversarial behaviour in cyber‐physical power systems using a Bayesian attack graph approach

Abstract Highly connected smart power systems are subject to increasing vulnerabilities and adversarial threats. Defenders need to proactively identify and defend new high‐risk access paths of cyber intruders that target grid resilience. However, cyber‐physical risk analysis and defense in power systems often requires making assumptions on adversary behaviour, and these assumptions can be wrong. Thus, this work examines the problem of inferring adversary behaviour in power systems to improve risk‐based defense and detection. To achieve this, a Bayesian approach for inference of the Cyber‐Adversarial Power System (Bayes‐CAPS) is proposed that uses Bayesian networks (BNs) to define and solve the inference problem of adversarial movement in the grid infrastructure towards targets of physical impact. Specifically, BNs are used to compute conditional probabilities to queries, such as the probability of observing an event given a set of alerts. Bayes‐CAPS builds initial Bayesian attack graphs for realistic power system cyber‐physical models. These models are adaptable using collected data from the system under study. Then, Bayes‐CAPS computes the posterior probabilities of the occurrence of a security breach event in power systems. Experiments are conducted that evaluate algorithms based on time complexity, accuracy and impact of evidence for different scales and densities of network. The performance is evaluated and compared for five realistic cyber‐physical power system models of increasing size and complexities ranging from 8 to 300 substations based on computation and accuracy impacts.

Sahu, Abhijeet↗

SeqMask: Behavior Extraction Over Cyber Threat Intelligence Via Multi-Instance Learning

Abstract Identification and extraction of Tactics, Techniques and Procedures (TTPs) for Cyber Threat Intelligence (CTI) restore the full picture of cyber attacks and guide the analysts to assess the system risk. Existing frameworks can hardly provide uniform and complete processing mechanisms for TTPs information extraction without adequate knowledge background. A multi-instance learning approach named SeqMask is proposed in this paper as a solution. SeqMask extracts behavior keywords from CTI evaluated by the semantic impact, and predicts TTPs labels by conditional probabilities. Still, the framework has two mechanisms to determine the validity of keywords. One using expert experience verification. The other verifies the distortion of the classification effect by blocking existing keywords. In the experiments, SeqMask reached 86.07% and 73.99% in F1 scores for TTPs classifications. For the top 20% of keywords, the expert approval rating is 92.20%, where the average repetition of keywords whose scores between 100% and 90% is 60.02%. Particularly, when the top 65% of the keywords were blocked, the F1 decreased to about 50%; when removing the top 50%, the F1 was under 31%. Further, we also validate the possibility of extracting TTPs from full-size CTI and malware whose F1 are improved by 2.16% and 0.81%.

Ge, Wenhan↗

Maximally entangled gluons for any x

Individual quarks and gluons at small x inside an unpolarized hadron can be regarded as Bell states in which qubits in the spin and orbital angular momentum spaces are maximally entangled. Using the machinery of quantum information science, we generalize this observation to all values 0 < x <1 and describe gluons (but not quarks) as maximally entangled states between a qubit and a qudit. We introduce the conditional probability distribution P⁡(l z |s z ) of a gluon’s orbital angular momentum l z given its helicity s z . Restricting to the three states l z =0,±1, which constitute a qutrit, we explicitly compute P as a function of x.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

ResStock™ v3.2.0 [SWR-19-15 and SWR-20-07]

The ResStock™ analysis tool was built on NREL's OpenStudio® platform, and is a project geared at modeling existing residential building stocks at national, regional, or local scales with a high-degree of granularity (e.g., one physics-based simulation model for every 200 dwelling units), using the EnergyPlus® simulation engine. Information about ComStock™, a sister tool for modeling the commercial building stock, can be found here: https://www.nrel.gov/buildings/comstock.html This repository contains: Housing characteristics of the U.S. residential building stock, in the form of conditional probability distributions stored as tab-separated value (.tsv) files. Comments at the bottom of each file document data sources and assumptions for each. A library of housing characteristic "options" that translate high-level characteristic parameters into arguments for OpenStudio measures, and which are referenced by the housing characteristic .tsv files and building energy upgrades defined in project definition files Project definition files: v2.3.0 and later: buildstockbatch YML files openable in any text editor v2.2.5 and prior: Project folder openable in PAT Unit-level OpenStudio Measures for automatically constructing OpenStudio Models of each representative dwelling unit model: v3.0.0 and later: OpenStudio-HPXML Measures v2.5.0 and prior: OpenStudio Measures Higher-level OpenStudio Measures for controlling simulation inputs and outputs This repository does not contain software for running ResStock simulations, which can be found as follows: Versions 2.3.0 and later only support the use of buildstockbatch for deploying simulations on high-performance or cloud computing. Version 2.3.0 also removed separate projects for single-family detached and multifamily buildings, in lieu of a combined project_national representing the U.S. residential building stock. See the changelog for more details. Versions 2.2.5 and prior support the use of the publicly available OpenStudio-PAT software as an interface for deploying simulations on cloud computing. Read the documentation for v2.2.5.

Horowitz, Scott↗

Stochastic Price Generation for Evaluating Wholesale Electricity Market Bidding Strategies

This work presents a novel method for generating electricity price scenarios from statistical properties of past electricity prices using a hybrid statistical and reduced-form stochastic model. Previous work in applying stochastic differential equations (SDE) to model electricity prices has focused on daily average prices. To extend stochastic price generation methods to hourly or sub-hourly pricing, we address several weaknesses in the state-of-the-art: (1) we replace the mean-reversion component of the SDE with an ARIMA process that is better able to characterize the daily and weekly trends; (2) we extend the price-spike, or jump process to account for conditional probabilities of price spikes occurring in consecutive time steps by replacing the traditional Poisson process for modeling jumps with a generalized point process model inspired by brain neuron models; and (3) we replace the traditional method of estimating spike intensity with empirical variance with a Markov process based on observed price spike intensity transitions. The method is demonstrated with electricity prices from the US ERCOT market and a use-case example is provided for bidding an energy storage unit into the day-ahead and real-time energy markets of ERCOT using stochastic optimization methods. Results show that the the synthetic price model out performs a (naive) persistence forecast model by resulting in 24% to 47% more in profits over 168 simulated days.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Further development of finite-temperature density functional theory (Technical Report on FG02-08ER46496)

The final year of funding was spent supporting research into extending conditional probability theory to generate the thermal dependence of PBE. The necessary background work led to a paper being published on the uniform electron gas (Dennis Perchak, Ryan J. McCarty, and Kieron Burke, Phys. Rev. B 105, 165143 (2022).). The graduate student John Kozlowski also contributed to a mathematical paper about DFT (Steven Crisostomo, Ryan Pederson, John Kozlowski, Bhupalee Kalita, Antonio C. Cancio, Kiril Datchev, Adam Wasserman, Suhwan Song, and Kieron Burke, Letters in Mathematical Physics 113, 42 (2023).).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

FY24 Progress Report: Disposition of Cracks & Features Observed in the Inner Can Closure Weld Region (ICCWR) of the 3013 Package

The long-term integrity of the 3013 containers is of interest for the safe storage of Pu materials. Although the 3013 standard embodies multiple barrier concept, the integrity of the inner container is considered to be crucial since it protects the Safety Class outer container from its contents. The container is designed to withstand high pressures that could result from the complete radiolysis of the maximum water content permissible by the 3013 standard. Shelf-life studies and destructive examination have not found high gas pressures but have found that corrosive gases are generated. Pitting and stress corrosion cracking (SCC) are considered to be critical corrosion modes for the performance of the inner container and have been observed during destructive examinations. Considerable research has been conducted on the possibility of aqueous electrolytes condensing on the inner container that can promote SCC. These studies indicate the uncertainties surrounding the formation of corrosive environments and the corrosion behavior of container materials. In this initial report, a Bayesian network (BN) model is described that can consider the uncertainties and the causal connections between various factors influencing the corrosion modes of the inner container. The BN model is preliminary and provides an initial framework to identify the necessary information. The report also provides initial experimental results on the electrochemical behavior of stainless steels in anticipated condensed environments from gas phase migration of acidic gases. The experimental results are consistent with the corrosion model. Recommendation for further work on the BN model include assembling an expert group to provide input to the BN structure and quantification of the conditional probability matrix, experimental studies to characterize the microstructure of the container, electrochemical studies to identify critical potentials for localized corrosion and SCC, and crack growth rate studies

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Strong Correlation DMRG and DFT

This project developed new ways to improve computer simulations of materials where electrons interact strongly with each other, a challenge for today’s most widely used method, density functional theory (DFT). We used an exact numerical method, the density matrix renormalization group (DMRG), to create highly accurate reference results for simple model systems, and used these to test DFT, prove when it will converge, and even train machine-learned functionals. We also invented new kinds of localized basis functions (“gausslets” and “multi-sliced gausslets”) and a “sliced-basis” approach that make high-accuracy simulations faster and more practical. These methods were applied to extended hydrogen systems, enabling the direct derivation of accurate low-energy models from first-principles calculations. We also introduced a new formalism, Conditional-Probability DFT, which could bypass traditional approximations. The tools and results from this work, including open-source software releases, will help scientists design and understand complex quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Simulation-based inference for parameter estimation of complex watershed simulators

High-resolution, spatially distributed process-based (PB) simulators are widely employed in the study of complex catchment processes and their responses to a changing climate. However, calibrating these PB simulators using observed data remains a significant challenge due to several persistent issues, including the following: (1) intractability stemming from the computational demands and complex responses of simulators, which renders infeasible calculation of the conditional probability of parameters and data, and (2) uncertainty stemming from the choice of simplified representations of complex natural hydrologic processes. Here, we demonstrate how simulation-based inference (SBI) can help address both of these challenges with respect to parameter estimation. SBI uses a learned mapping between the parameter space and observed data to estimate parameters for the generation of calibrated simulations. To demonstrate the potential of SBI in hydrologic modeling, we conduct a set of synthetic experiments to infer two common physical parameters – Manning's coefficient and hydraulic conductivity – using a representation of a snowmelt-dominated catchment in Colorado, USA. We introduce novel deep-learning (DL) components to the SBI approach, including an “emulator” as a surrogate for the PB simulator to rapidly explore parameter responses. We also employ a density-based neural network to represent the joint probability of parameters and data without strong assumptions about its functional form. While addressing intractability, we also show that, if the simulator does not represent the system under study well enough, SBI can yield unreliable parameter estimates. Approaches to adopting the SBI framework for cases in which multiple simulator(s) may be adequate are introduced using a performance-weighting approach. The synthetic experiments presented here test the performance of SBI, using the relationship between the surrogate and PB simulators as a proxy for the real case.

54 ENVIRONMENTAL SCIENCES↗

Operation Optimization Using Reinforcement Learning with Integrated Artificial Reasoning Framework

In large and complex systems, operational decision-making requires a systematic analysis with a vast amount of data from both process parameters and component status monitoring. In this paper, we present an integrated artificial reasoning approach for system state transition models that can help operational decision-making with explainable and traceable reasoning. The integrated artificial reasoning framework is a physics-based approach of defining the system structure in a Bayesian network, so we leveraged it in a Markov decision process (MDP) for finding optimal operational solutions. In our proposed framework, the MDP is implemented on a dynamic Bayesian network (DBN), which represents causalities in a system. The multilevel flow modeling was utilized in order to extract these causalities in a more efficient and objective manner. Since multilevel flow modeling is based on the fundamental energy and mass conservation laws, the target system is decomposed into several mass, energy, and information structures, which serve as the basis for a DBN. The MDP consists of the processes of finding a solution for the Bellman equation, which can be derived from the conditional probability equations of the constructed DBN. System operators can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from the component degradation process or random failures. We analyzed a simplified example system to illustrate finding an optimal operational policy with this approach.

Kim, Junyung↗

Extrapair offspring of the blue-footed booby show no sign of higher fitness in the first 10 years of life

According to the good genes and genetic compatibility hypotheses, females of socially monogamous species obtain genetic benefits for their offspring by performing extrapair copulations with males of higher quality than their social mates or males with whom they are more genetically compatible. If extrapair offspring do receive genetic benefits in the form of advantageous alleles or more compatible allele combinations, they should outperform their within-pair half-siblings' survival and/or reproductive output. Here, in this study, we followed 52 extrapair and 737 within-pair blue-footed booby, Sula nebouxii, offspring during their first 10 years of life (excluding the embryonic period and the first 10 days after hatching) to assess whether they differed in fledging probability, fledgling body condition, recruitment probability, age at first reproduction, number of breeding events or accumulated breeding success. Extrapair and within-pair offspring did not differ in any of these proxies of fitness. Furthermore, we found that extrapair offspring were equally likely to occur in any hatching position. However, differences in fledgling production over the lifetime could not be ruled out, and because only within-pair production of eggs and fledglings was tallied, the possibility remains that extrapair offspring could produce more extrapair offspring later in life than do within-pair offspring. Furthermore, the possibility of context-dependent genetic benefits occurring only under stressful conditions cannot be discounted because our sample of offspring was obtained in a single exceptionally favourable reproductive season.

59 BASIC BIOLOGICAL SCIENCES↗

Reply to “Comment on ‘The Reduced Detection Rate of Signals That Are Hidden by Earthquakes: Case Studies with Spotlight Detectors That Operate at Seismic Arrays,’ by Joshua D. Carmichael, Brent G. Delbridge, and Richard Alfaro-Diaz” by Paul G. Richards

We reply to a comment that Paul G. Richards (Richards, 2026) directed to an article by Carmichael et al. (2025). Richards expressed concern over two issues. The first issue relates to the size of the explosions discussed in the article. The second relates to the probability that earthquakes and explosions sourced near the same location coincide in time, by chance. We do not address the first issue because the original article does not assign significance to the size of the explosions from the point of view of an experimental party. We do respond to Richards’ comment on the second issue and claim that it can be explained through a clarification about conditional versus joint probabilities. Our present discussion, therefore, describes the difference between the conditional probability that a correlator fails, given that an explosion and earthquake coincidently occur in the same place, and the joint probability that a correlator fails while an earthquake and explosion also coincidentally occur in the same place. This latter, joint probability appears to be rare. We clarify that our original article did not treat the joint probability, only the conditional probability.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Exceedance Probabilities and Recurrence Intervals for Extended Power Outages in the United States

This report provides estimates of recurrence intervals and conditional exceedance probabilities for major power outages by U.S. region between 2015 and 2021. Additionally, we provide estimates for grid management, particularly outages caused by California’s public safety power shutoffs (PSPS), and for natural outages caused by major hurricanes. Outage recurrence intervals are the average number of years between outage events, and conditional exceedance probabilities are the likelihoods that a customer who experiences a major power outage will experience an outage exceeding a given duration. Major outage events are those that affect 10,000 or more customers, as defined by the U.S. Department of Energy’s (DOE’s) Electric Emergency Incident and Disturbance Report, called OE-417 (DOE 2020). These results can be applied to determine the likelihood of experiencing long-duration outages, which can be integrated into cost-benefit analyses of resilience solutions and broader energy resilience studies.

Ericson, Sean↗

Exceedance Probabilities and Recurrence Intervals for Extended Power Outages in the United States

Power outages cause significant economic and societal impacts. An increasing likelihood of extreme weather coupled with aging grid infrastructure is leading to a higher prevalence of extended power outages, which can leave customers without power for multiple days or even weeks. Planners at the facility, local, state, and federal levels are interested in resilience solutions to reduce the impacts of extended power outages. Resilience solutions—such as installing backup systems, integrating microgrid solutions, weatherizing buildings, and hardening distribution and transmission components—can reduce the consequences of extended power outages, but these solutions come with increased capital costs. Conducting cost-benefit analyses is important for determining which steps to take to mitigate the impact of power outages without investing in ineffective and cost-prohibitive resilience solutions. The expected benefits of resilience investments depend on the frequency of power outages of various durations, particularly extended outages lasting several hours, days, or weeks. A significant barrier to resilience planning is the lack of publicly available data on the frequency and duration of extended power outages. The absence of outage duration information severely limits the ability to conduct quantitative cost-benefit analyses of resilience investments. This report provides estimates of recurrence intervals and conditional exceedance probabilities for major power outages by U.S. region between 2015 and 2021. Additionally, we provide estimates for grid management, particularly outages caused by California’s public safety power shutoffs (PSPS), and for natural outages caused by major hurricanes. Outage recurrence intervals are the average number of years between outage events, and conditional exceedance probabilities are the likelihoods that a customer who experiences a major power outage will experience an outage exceeding a given duration. Major outage events are those that affect 10,000 or more customers, as defined by the U.S. Department of Energy’s (DOE’s) Electric Emergency Incident and Disturbance Report, called OE-417 (DOE 2020). These results can be applied to determine the likelihood of experiencing long-duration outages, which can be integrated into cost-benefit analyses of resilience solutions and broader energy resilience studies. We developed a methodology to estimate customer outage durations for extended outage events using publicly available data on customer outages. Shorter-duration power outages are relatively common, with customers experiencing on average more than one power outage each year lasting fewer than 12 hours. An outage event lasting between 1 day and 1 week is expected to occur between once every 16 years and once every 42 years, depending on the region, with an average recurrence rate of once every 32 years across the contiguous United States.

24 POWER TRANSMISSION AND DISTRIBUTION↗