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DOE OSTI2024

MENT-Flow: maximum-entropy phase space tomography using normalizing flows

Generative models can be trained to reproduce low-dimensional projections of high-dimensional phase space distributions. Normalizing flows are generative models that parameterize invertible transformations, allowing exact probability density evaluation and sampling. Consequently, flows are unbiased entropy estimators and could be used to solve the high-dimensional maximum-entropy tomography (MENT) problem. In this work, we evaluate a flow-based MENT solver (MENT-Flow) against exact maximum-entropy solutions and Minerbo's iterative MENT algorithm in two dimensions.

Hoover, Austin↗

DOE OSTI2022

Methodology for assessing the maximum potential impact of separations opportunities in industrial processes

Separation technologies currently used in U.S. manufacturing industries are estimated to account for more than 20% of plant energy consumption. However, accurately determining the impact of new separation technology solutions can sometimes be difficult, especially when evaluating a slate of new candidate separation technologies, each of which has its own separation performance, energy demand, and capital cost. In these cases, a typical approach is to assess each new separation technology by collecting performance and cost information and then using that information to develop a techno-economic analysis to identify overall benefits. While this approach is thorough, it can be time consuming and can hinder reaching a critical understanding of the potential of a given separation challenge, especially when there is no known solution. To address these issues, we developed an assessment methodology, using industrial screening processes, that can be used to better understand the potential impacts of addressing a given separation challenge. This paper presents an overview of our separation challenge stream assessment methodology. The methodology involves defining an “ideal” separator and deriving the associated minimum separation energy. The “ideal” separator represents the most optimistic outlook of a given opportunity so the maximum impact from existing and not-yet-developed solutions can be assessed. Using established biorefinery models, we applied the methodology to 10 different separation challenge streams from two different biomass conversion platforms to identify the type of information that can be obtained. Three of the ten challenge streams assessed had maximum possible cost savings predictions >20%, and associated reductions in process energy carbon intensity ranging from 0 to 54%. Two streams had cost and energy savings potential that were < 5%. Some of the opportunity drivers from the various assessments include higher product yields, reduction or elimination of downstream equipment, new co-products, and cost savings associated with raw materials and energy consumption. The information from these assessments can help guide the selection or development of new separation technology solutions based on the various potential factors that drive the projected benefits.

09 BIOMASS FUELS↗

DOE OSTI2024

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

Physics↗

DOE OSTI2023

Maximum respiration rates in hyporheic zone sediments are primarily constrained by organic carbon concentration and secondarily by organic matter chemistry

Abstract. River corridors are fundamental components of the Earth system, and their biogeochemistry can be heavily influenced by processes in subsurface zones immediately below the riverbed, referred to as the hyporheic zone. Within the hyporheic zone, organic matter (OM) fuels microbial respiration, and OM chemistry heavily influences aerobic and anaerobic biogeochemical processes. The link between OM chemistry and respiration has been hypothesized to be mediated by OM molecular diversity, whereby respiration is predicted to decrease with increasing diversity. Here we test the specific prediction that aerobic respiration rates will decrease with increases in the number of unique organic molecules (i.e., OM molecular richness, as a measure of diversity). We use publicly available data across the United States from crowdsourced samples taken by the Worldwide Hydrobiogeochemical Observation Network for Dynamic River Systems (WHONDRS) consortium. Our continental-scale analyses rejected the hypothesis of a direct limitation of respiration by OM molecular richness. In turn, we found that organic carbon (OC) concentration imposes a primary constraint over hyporheic zone respiration, with additional potential influences of OM richness. We specifically observed respiration rates to decrease nonlinearly with the ratio of OM richness to OC concentration. This relationship took the form of a constraint space with respiration rates in most systems falling below the constraint boundary. A similar, but slightly weaker, constraint boundary was observed when relating respiration rate to the inverse of OC concentration. These results indicate that maximum respiration rates may be governed primarily by OC concentration, with secondary influences from OM richness. Our results also show that other variables often suppress respiration rates below the maximum associated with the richness-to-concentration ratio. An important focus of future research will identify physical (e.g., sediment grain size), chemical (e.g., nutrient concentrations), and/or biological (e.g., microbial biomass) factors that suppress hyporheic zone respiration below the constraint boundaries observed here.

58 GEOSCIENCES↗

DOE OSTI2022

Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated nitrogen atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. Furthermore, these results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

A differentiable approach to the maximum independent set problem using dataless neural networks

The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging datasets of the combinatorial structures of interest drawn from some distribution of problem instances. Reinforcement learning has also been employed to find such structures. Here, in this paper, we propose a different approach in that no data is required for training the neural networks that produce the solution. In this sense, what we present is not a machine learning solution, but rather one that is dependent on neural networks and where backpropagation is applied to a loss function defined by the structure of the neural network architecture as opposed to a training dataset. In particular, we reduce the popular combinatorial optimization problem of finding a maximum independent set to a neural network and employ a dataless training scheme to refine the parameters of the network such that those parameters yield the structure of interest. Additionally, we propose a universal graph reduction procedure to handle large-scale graphs. The reduction exploits community detection for graph partitioning and is applicable to any graph type and/or density. Experimental results on both real and synthetic graphs demonstrate that our proposed method performs on par or outperforms state-of-the-art learning-based methods in terms of the size of the found set without requiring any training data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Uniqueness and global optimality of the maximum likelihood estimator for the generalized extreme value distribution

The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory and is in common use for analysing the far tail of observed phenomena, yet important asymptotic properties of likelihood-based estimation under this standard model have not been established. In this paper, we prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit relations in a tight neighbourhood of the true shape parameter.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Solving larger maximum clique problems using parallel quantum annealing

Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave Systems, which we consider in this work, is sparsely connected and moderately sized (on the order of thousands of qubits), thus necessitating a minor-embedding of a logical problem onto the physical qubit hardware. The combination of relatively small hardware sizes and the necessity of a minor-embedding can mean that solving large optimization problems is not possible on current quantum annealers. In this research, we show that a hybrid approach combining parallel quantum annealing with graph decomposition allows one to solve larger optimization problem accurately. We apply the approach to the Maximum Clique problem on graphs with up to 120 nodes and 6395 edges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

An optical-input Maximum Likelihood Estimation feedback system demonstrated on tokamak horizontal equilibrium control

A readily parallelized Maximum Likelihood Estimation (MLE) algorithm with linear computational complexity is demonstrated in real time using only measurements from an extreme ultraviolet (EUV) diagnostic to control the horizontal position of a tokamak plasma. A set of trial emissivity profiles are parameterized by the control quantity of interest (R m ), and the MLE is identified from the profile which minimizes the signal reconstruction residual. The algorithm depends on an empirically determined likelihood function with exponential form. EUV emission (λ ≈ 15eV-1keV) is captured in a poloidal plane by four 16-channel AXUV diodes mounted at different poloidal angles with radial and angular resolution sufficient to discern plasma equilibrium evolution in HBT-EP. Calculations of the plasma major radius by the system are consistent within diagnostic uncertainty for the majority of the discharge with those of: a weighted average of vertical soft X-ray or EUV chords, magnetic sensors, and an equilibrium reconstruction. The feedback system corrects for a horizontal displacement of the major radius equal to 20% of the plasma minor radius by adjusting the vertical field produced from 40 in-vessel control coils in real time. The MLE calculation is performed on a GPU in a 15 μs cycle, with similar performance in this application to a simple weighted average of vertical chords. Finally, results demonstrate horizontal position control using magnetic actuators and an optical observer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Climatic factors and human population changes in Eurasia between the Last Glacial Maximum and the early Holocene

Archaeological records document a significant expansion of populations from the Last Glacial Maximum (LGM, ~23–19 ka) to the early Holocene (EH, ~9 ka) in Eurasia, which is often attributed to the influence of orbital-scale climate changes. Yet, information remains limited concerning the climatic factor(s) which were responsible for conditioning demographic patterns. Here, in this work, we present results from an improved Minimalist Terrestrial Resource Model (MTRM), forced by a transient climate simulation from the LGM to the EH. Simulated potential hunter-gatherer population densities and spatial distributions across Eurasia are supported by observed archaeological sites in Europe and China. In the low latitudes, potential population size change was predominantly controlled by precipitation and its strong influence on plant and animal resources. In the middle-high latitudes, temperature was the dominant driver in influencing potential population size change and animal resource availability. Different regional responses of potential populations to climate change across Eurasia - owing to variations in available food resources between the LGM and EH - provide a better understanding of human dispersal during the Late Pleistocene.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Re-evaluating probable maximum precipitation estimates: sensitivity to transposition domains and storm rotation using modern datasets

This study examines the sensitivity of Probable Maximum Precipitation (PMP) estimates to key methodological decisions embedded in the legacy approach adopted in the U.S. National Weather Service Hydrometeorological Reports No. 51 and No. 52. Although widely used for infrastructure design and risk regulation, fundamental aspects of PMP estimation—such as storm sample size, transposition domain, maximization procedures, and storm rotation—remain poorly constrained and lack formal guidance. Using the Red Rock watershed in Iowa as a case study, and leveraging the 2002–2023 NOAA Analysis of Record for Calibration (AORC) precipitation dataset, we systematically evaluate how each methodological choice, individually and in combination, influences PMP estimates. Our findings demonstrate that PMP is not a fixed physical upper bound but rather a modeling construct shaped heavily by user-defined assumptions. Notably, PMP values derived from modern gridded rainfall datasets can be substantially higher than the legacy estimate used in the original spillway design for Red Rock Dam. Decisions regarding storm sample size, domain extent, climatological window, and particularly storm rotation all contributed to higher PMP estimates. Storm rotation alone—a loosely constrained element in the current PMP practice—can amplify PMP by more than 25%. These results reveal the lack of standardized bounds in current PMP workflows and the need for systematic sensitivity and uncertainty analysis. As PMP estimation shifts toward probabilistic approaches, incorporating physically meaningful storm attributes will be key to developing more transparent, defensible methods for dam safety and climate-resilient infrastructure.

Probable maximum precipitation↗

DOE OSTI2023

Maximum Supersaturation in the Marine Boundary Layer Clouds Over the North Atlantic

Abstract The maximum supersaturation ( S x ) in clouds is a key parameter affecting the cloud's microphysical and radiative properties. We investigate the S x of the marine boundary layer clouds by combining airborne and surface observations in the Eastern North Atlantic. The cloud droplet number concentration ( N c ) in the least diluted cloud cores agrees well with the number concentration of particles larger than the Hoppel Minimum (HM) ( N >HM ) below clouds, indicating that the HM represents the average size threshold above which particles are activated to form cloud droplets. The S x values derived from surface observations vary from 0.10% to 0.50% from June 2017 to June 2018, with a clear seasonal variation exhibiting higher values during winter. Most of the S x variance (∼60%) can be explained by the cloud condensation nuclei (CCN) concentration and updraft velocity ( w ), with the CCN concentration playing a more important role than w in explaining the variation of S x . The influence of CCN concentration on S x leads to a buffered response of N c to aerosol perturbations. The response of N c to low aerosol concentration during winter is further buffered by the high w . The global Community Earth System Model (CESM) simulated S x values in the Azores have a positive bias compared to measured S x , likely due to overestimated w and underestimated CCN concentration. The CESM simulated S x exhibits higher values further north over the North Atlantic Ocean, which is attributed to stronger w . The suppression of S x by aerosol is also evident in regions with high CCN concentrations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Integrating Maximum Entropy Production Theory and Machine Learning to Improve Global Evapotranspiration Modeling

Accurate estimation of terrestrial evapotranspiration (ET) is vital for understanding global water and energy cycles. However, current global ET estimations are not well constrained. This study introduces an integrated framework combining the Maximum Entropy Production (MEP) theory with Random Forest (RF) model to improve global ET estimation. Specifically, in contrast to direct ET estimation by the RF model, the integrated framework (MEP‐RF) trains to predict error of MEP‐simulated ET. MEP‐RF outperforms RF in spatiotemporal extrapolation. Attribution analysis with in situ observations reveals that the inputs of MEP are the most critical variables for the ET process, including net radiation, vegetated area, soil moisture, and surface temperature. We further drive MEP‐RF with global reanalysis and satellite data sets of these four inputs, yielding a global mean terrestrial ET of 548 mm/year, with 77% attributed to transpiration. The global ET increased at a rate of 0.85 mm/year per year during 2003–2021, primarily due to vegetation greening rather than rising temperature, while decreasing soil moisture led to decreasing regional ET. The integrated framework provides a novel approach for the estimation of global ET without the need for hard‐to‐obtain and thus uncertain inputs, such as wind speed, surface roughness, aerodynamic and canopy stomatal resistance. Therefore, MEP‐RF offers an independent method on existing global ET products. It represents a promising physically based approach that can be incorporated into Earth System Models to enhance water and energy cycle simulations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

The Influence of the Number of Tree Searches on Maximum Likelihood Inference in Phylogenomics

Maximum likelihood (ML) phylogenetic inference is widely used in phylogenomics. As heuristic searches most likely find suboptimal trees, it is recommended to conduct multiple (e.g., 10) tree searches in phylogenetic analyses. However, beyond its positive role, how and to what extent multiple tree searches aid ML phylogenetic inference remains poorly explored. Here, we found that a random starting tree was not as effective as the BioNJ and parsimony starting trees in inferring the ML gene tree and that RAxML-NG and PhyML were less sensitive to different starting trees than IQ-TREE. We then examined the effect of the number of tree searches on ML tree inference with IQ-TREE and RAxML-NG, by running 100 tree searches on 19,414 gene alignments from 15 animal, plant, and fungal phylogenomic datasets. We found that the number of tree searches substantially impacted the recovery of the best-of-100 ML gene tree topology among 100 searches for a given ML program. In addition, all of the concatenation-based trees were topologically identical if the number of tree searches was ≥10. Quartet-based ASTRAL trees inferred from 1 to 80 tree searches differed topologically from those inferred from 100 tree searches for 6/15 phylogenomic datasets. Lastly, our simulations showed that gene alignments with lower difficulty scores had a higher chance of finding the best-of-100 gene tree topology and were more likely to yield the correct trees.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Canopy Structure Exhibits Linear and Nonlinear Links to Biome‐Level Maximum Light Use Efficiency

Maximum light use efficiency (ε max ) represents a plant's capacity to convert light into carbon during photosynthesis. Although prior studies have explored ε max variations between sunlit and shaded leaves or its temporal ties to canopy structure, the spatial relationship between biome-level ε max (ε biome ) and biome structure remains poorly understood. We analysed data from 320 eddy covariance sites (~855 site-years) with satellite-derived near-infrared reflectance of vegetation (NIRv) and leaf area index (LAI). We introduced NIRvN (NIRv/LAI) to isolate architectural effects from leaf quantity. Site-level ε max was calculated and aggregated by biome to derive ε biome . Results show ε biome rises nonlinearly with NIRv and LAI, saturating at high LAI, with crops and tropical evergreen forests deviating from this trend. Conversely, ε biome decreases linearly with increasing NIRvN, indicating that biomes with greater NIR scattering efficiency exhibit lower ε biome . These results enhance understanding of structural influences on carbon uptake across global biomes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Maximum likelihood estimation of difference scaling functions for suprathreshold judgments

Maximum likelihood estimation (MLE) has been used to produce perceptual scales from binary judgments of triads and quadruples. This method relies on Thurstone’s theory of a stochastic perceptual process where the perceived difference of two stimuli is the difference in their perceived strengths. It is possible that the perception of a suprathreshold difference is overestimated when adding smaller differences, a phenomenon referred to as diminishing returns. The current approach to construct a perceptual scale using MLE does not account for this phenomenon. We present a way to model the perception of differences using MLE and Thurstone’s theory, adapted to allow the possibility of diminishing returns. This method is validated using Monte Carlo simulated responses to experimental triads and can correctly model diminishing returns, the absence of diminishing returns, and the opposite of diminishing returns both in the cases when a perceptual scale is known and when the true perceived strengths of the stimuli are unknown. Additionally, this method was applied to empirical data sets to determine its feasibility in investigations of perception. Ultimately, it was found that this analysis allows for more accurate modeling of suprathreshold difference judgments, a more complete understanding of the perceptual processes underlying comparisons, and the evaluation of Thurstone’s theory of difference judgments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

The Principle of Maximum Conformality Correctly Resolves the Renormalization-Scheme-Dependence Problem

In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can serve as a mini-review of PMC. In a recently published article, P. M. Stevenson has claimed that “the PMC is ineffective and does nothing to resolve the renormalization-scheme-dependence problem”, concluding incorrectly that the success of PMC predictions is due to the PMC being a “laborious, ad hoc, and back-door” version of the Principle of Minimal Sensitivity (PMS). We show that such conclusions are incorrect, deriving from a misinterpretation of the PMC and an overestimation of the applicability of the PMS. The purpose of the PMC is to achieve precise fixed-order pQCD predictions, free from conventional renormalization schemes and scale ambiguities. We demonstrate that the PMC predictions satisfy all the self-consistency conditions of the renormalization group and standard renormalization-group invariance; the PMC predictions are thus independent of any initial choice of renormalization scheme and scale. The scheme independence of the PMC is also ensured by commensurate scale relations, which relate different observables to each other. Moreover, in the Abelian limit, the PMC dovetails into the well-known Gell-Mann–Low framework, a method universally revered for its precision in QED calculations. Due to the elimination of factorially divergent renormalon terms, the PMC series not only attains a convergence behavior far superior to that of its conventional counterparts but also deftly curtails any residual scale dependence caused by the unknown higher-order terms. This refined convergence, coupled with its robust suppression of residual uncertainties, furnishes a sound and reliable foundation for estimating the contributions from unknown higher-order terms. Anchored in the bedrock of standard renormalization-group invariance, the PMC simultaneously eradicates the factorial divergences and eliminates superfluous systematic errors, which inversely provides a good foundation for achieving high-precision pQCD predictions. Consequently, owing to its rigorous theoretical underpinnings, the PMC is eminently applicable to virtually all high-energy hadronic processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Miscanthus × giganteus increases soil maximum water holding capacity compared to maize

Soil ecosystem services, like the ability to store water, have been depleted after a century of conventional, annual cropping, and perennial crops offer a solution to this and other agricultural environmental issues. We assessed the impact of Miscanthus × giganteus (miscanthus), a perennial biomass crop, on soil water holding capacity and structure compared to continuous maize (Zea mays L.) at two sites in Iowa. After three growing seasons, we measured the following: (1) maximum water holding capacity (MWHC) with and without soil structure, and (2) total porosity and pore size distribution (PSD) via micro-computed tomography (microCT). Miscanthus increased MWHC by 14.7% across both sites relative to maize (p = 0.002), and we attributed this to structural changes due to the lack of a crop effect when measured on structureless soils. No significant changes were detected in soil organic matter, texture, total porosity, or PSD that could explain the increase in MWHC under miscanthus. Our findings suggest that the increases in MWHC are primarily due to structural changes rather than increases in soil organic matter or porosity (at least porosity detectable by microCT). This study highlights miscanthus' potential to enhance soil water storage and underscores the need for further investigation to clarify the mechanisms through which this biomass crop influences soil structural properties.

60 APPLIED LIFE SCIENCES↗