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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

QCD Theory Meets Information Theory

We present a novel technique to incorporate precision calculations from quantum chromodynamics into fully differential particle-level Monte Carlo simulations. By minimizing an information-theoretic quantity subject to constraints, our reweighted Monte Carlo incorporates systematic uncertainties absent in individual Monte Carlo predictions, achieving consistency with the theory input in precision and its estimated systematic uncertainties. Our method can be applied to arbitrary observables known from precision calculations, including multiple observables simultaneously. It generates strictly positive weights, thus offering a clear path to statistically powerful and theoretically precise computations for current and future collider experiments. As a proof of concept, we apply our technique to event-shape observables at electron-positron colliders, leveraging existing precision calculations of thrust. Our analysis highlights the importance of logarithmic moments of event shapes, which have not been previously studied in the collider physics literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Environmental Controls on Water Vapor Deuterium Excess in the Coastal Boundary Layer: An Information Theory Perspective

We use information theory to quantify the environmental controls on water vapor deuterium excess (D-excess) in coastal Southern California from June 2023 through February 2024. Using Shannon entropy, mutual information (MI), and joint mutual information, metrics that capture both linear and nonlinear relationships, we identify the most informative variables and variable combinations governing D-excess across contrasting marine and continental regimes. Relative humidity with respect to sea surface temperature (RHS) is consistently the strongest individual predictor, explaining up to 27% of D-excess variability during marine conditions but only 10% in continental air masses. The Relative humidity(RHS) + sea surface temperature (SST) combination demonstrates synergistic effects, where their joint influence (explaining up to 36% of D-excess variability) exceeds what either variable achieves individually, confirming their coupled influence on deuterium excess. Wind direction complements RHS most effectively during continental conditions. The best three-variable combination (RHS + SST + Planetary Boundary Layer height) explains 38% of D-excess variability in marine air, while no combination exceeds 20% explanatory power during continental periods. Information theory shows that heteroscedasticity in D-excess relationships indicates regime shifts in controlling processes and quantifies fundamental constraints on predictor variables: some environmental factors like surface pressure or water vapor flux contain insufficient information content to explain D-excess variability regardless of their physical relevance. These results highlight the different predictability limits between marine and continental regimes, challenging the adequacy of linear models and providing a rigorous framework for quantifying the information content of isotope-climate relationships with implications for both modern and paleoclimate applications.

information theory↗
DOE OSTI2015

Symmetric polynomials in information theory: Entropy and subentropy

Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore, we see that H and the intrinsically quantum informational quantity Q become surprisingly closely related in functional form, suggesting a special significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials, we also derive a series of further properties of H and Q.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Information theory optimization of signals from small-angle scattering measurements

Small-angle X-ray scattering (SAXS) of particles in solution informs on the conformational states and assemblies of biological macromolecules (bioSAXS) outside of cryo- and solid-state conditions. In bioSAXS, the SAXS measurement under dilute conditions is resolution limited, and through an inverse Fourier transform, the measured SAXS intensities directly relate to the physical space occupied by the particles via the P (r)-distribution. Yet, this inverse transform of SAXS data has been historically cast as an ill-posed, ill-conditioned problem requiring an indirect approach. Here, we show that through the applications of matrix and information theories, the inverse transform of SAXS intensity data is a well-conditioned problem. The so-called ill-conditioning of the inverse problem is directly related to the Shannon number. By exploiting the oversampling enabled by modern detectors, a direct inverse Fourier transform of the SAXS data is possible, provided the recovered information does not exceed the Shannon number. The Shannon limit corresponds to the maximum number of significant singular values that can be recovered in a SAXS experiment, suggesting this relationship is a fundamental property of band-limited inverse integral transform problems. This correspondence reduces the complexity of the inverse problem to the Shannon limit and maximum dimension. We propose a hybrid scoring function using an information theory framework that assesses both the quality of the model-data fit as well as the quality of the recovered P (r)-distribution. The hybrid score utilizes the Akaike information criteria and Durbin-Watson statistic that considers parameter-model complexity, i.e., degrees of freedom, and the randomness of the model-data residuals. The described tests and findings extend the boundaries for bioSAXS by completing the information theory formalism initiated by Peter B. Moore to enable a quantitative measure of resolution in SAXS, robustly determine maximum dimension, and more precisely define the best parameter model appropriately representing the observed scattering data.

Rambo, Robert P. [Science and Technology Facilitie↗
DOE OSTI2020

Applying Information Theory to Design Optimal Filters for Photometric Redshifts

In this paper we apply ideas from information theory to create a method for the design of optimal filters for photometric redshift estimation. We show the method applied to a series of simple example filters in order to motivate an intuition for how photometric redshift estimators respond to the properties of photometric passbands. We then design a realistic set of six filters covering optical wavelengths that optimize photometric redshifts for z <= 2.3 and i < 25.3. We create a simulated catalog for these optimal filters and use our filters with a photometric redshift estimation code to show that we can improve the standard deviation of the photometric redshift error by 7.1% overall and improve outliers 9.9% over the standard filters proposed for the Large Synoptic Survey Telescope (LSST). We compare features of our optimal filters to the LSST and find that the LSST filters incorporate key features for optimal photometric redshift estimation. Finally, we describe how information theory can be applied to a range of optimization problems in astronomy.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Comparing cosmic web classifiers using information theory

We introduce a decision scheme for optimally choosing a classifier, which segments the cosmic web into different structure types (voids, sheets, filaments, and clusters). Our framework, based on information theory, accounts for the design aims of different classes of possible applications: (i) parameter inference, (ii) model selection, and (iii) prediction of new observations. As an illustration, we use cosmographic maps of web-types in the Sloan Digital Sky Survey to assess the relative performance of the classifiers T-WEB, DIVA and ORIGAMI for: (i) analyzing the morphology of the cosmic web, (ii) discriminating dark energy models, and (iii) predicting galaxy colors. Our study substantiates a data-supported connection between cosmic web analysis and information theory, and paves the path towards principled design of analysis procedures for the next generation of galaxy surveys. We have made the cosmic web maps, galaxy catalog, and analysis scripts used in this work publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

INSURE: An Information Theory iNspired diSentanglement and pURification modEl for Domain Generalization

Domain Generalization (DG) aims to learn a generalizable model on the unseen target domain by only training on the multiple observed source domains. Although a variety of DG methods have focused on extracting domain-invariant features, the domain-specific class-relevant features have attracted attention and been argued to benefit generalization to the unseen target domain. To take into account the class-relevant domain-specific information, in this paper we propose an Information theory iNspired diSentanglement and pURification modEl (INSURE) to explicitly disentangle the latent features to obtain sufficient and compact (necessary) class-relevant feature for generalization to the unseen domain. Specifically, we first propose an information theory inspired loss function to ensure the disentangled class-relevant features contain sufficient class label information and the other disentangled auxiliary feature has sufficient domain information. Additionally, we further propose a paired purification loss function to let the auxiliary feature discard all the class-relevant information and thus the class-relevant feature will contain sufficient and compact (necessary) class-relevant information. Moreover, instead of using multiple encoders, we propose to use a learnable binary mask as our disentangler to make the disentanglement more efficient and make the disentangled features complementary to each other. We conduct extensive experiments on five widely used DG benchmark datasets including PACS, VLCS, OfficeHome, TerraIncognita, and DomainNet. The proposed INSURE achieves state-of-the-art performance. We also empirically show that domain-specific class-relevant features are beneficial for domain generalization. The code is available at https://github.com/yuxi120407/INSURE .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A Suggestion of Converting Protein Intrinsic Disorder to Structural Entropy Using Shannon’s Information Theory

We propose a framework to convert the protein intrinsic disorder content to structural entropy (H) using Shannon’s information theory (IT). The structural capacity (C), which is the sum of H and structural information (I), is equal to the amino acid sequence length of the protein. The structural entropy of the residues expands a continuous spectrum, ranging from 0 (fully ordered) to 1 (fully disordered), consistent with Shannon’s IT, which scores the fully-determined state 0 and the fully-uncertain state 1. The intrinsically disordered proteins (IDPs) in a living cell may participate in maintaining the high-energy-low-entropy state. In addition, under this framework, the biological functions performed by proteins and associated with the order or disorder of their 3D structures could be explained in terms of information-gains or entropy-losses, or the reverse processes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Intensity measure adequacy assessment for nonlinear site response using Information Theory

Nonlinear site response modeling is a crucial aspect of Probabilistic Seismic Hazard Analysis. Site amplification models routinely rely on a rock intensity measure to characterize the strength of the bedrock motion. However, the adequacy of such intensity measures towards predicting amplifications across the oscillator period range has not been investigated in the literature. This paper analyzes the adequacy of rock intensity measures using state of the art criterion established in Performance-Based Earthquake Engineering and techniques from Information Theory. The efficiency and the sufficiency of several rock intensity measure are assessed. It was found that spectral accelerations at low periods usually are adequate for predicting amplifications across the period range. This supports the current practice of using Peak Ground Acceleration in Ground Motion Models. However, for extremely soft sites, which demonstrate nonlinear effects well into the period range, it is better practice to ensure that amplification and spectral acceleration share the same oscillator period. Lastly, for predicting the peak shear strain (an important parameter that controls nonlinearity of site response), Peak Ground Velocity is generally adequate, and this conclusion is in line with the definition of proxy shear strain.

42 ENGINEERING↗
DOE OSTI2016

Random matrix techniques in quantum information theory

The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Exploring Hydrologic Model Process Connectivity at the Continental Scale Through an Information Theory Approach

Exploring water fluxes between hydrological model (HM) components is essential to assess and improve model realism. Many classical metrics for HM diagnosis rely solely on streamflow and hence provide limited insights into model performance across processes. This study applies an information theory measure known as “transfer entropy” (TE) to systematically quantify the transfer of information among major HM components. To test and demonstrate the benefits of TE, we use the Framework for Understanding Structural Errors (FUSE) model to mimic and compare four commonly used HM structures, VIC, PRMS, SACRAMENTO, and TOPMODEL, across 671 catchments spanning a variety of hydrologic regimes in the conterminous United States. We explore connections between HM components and catchment landscape characteristics (e.g., climate, topography, soil, and vegetation) and characterize their nonlinear associations using distance correlation and Spearman correlation coefficients. Our results indicate that while the information transferred from precipitation to runoff is similar across model structures (likely as a result of calibration), the information transferred among other components can vary significantly from a FUSE structure to another. We find that aridity, precipitation duration and frequency, snow fraction, mean elevation, forest area, and leaf area index are often significantly associated with TE between the main HM components. Here, we propose that the presence of meaningful nonlinear associations can be used to diagnose process representation in HMs. Our results highlight the necessity to enhance the conventional streamflow-only calibration approach for a more realistic representation of water dynamics in the models.

large-sample hydrology↗
DOE OSTI2016

Diagnosing the Dynamics of Observed and Simulated Ecosystem Gross Primary Productivity with Time Causal Information Theory Quantifiers

Data analysis and model-data comparisons in the environmental sciences require diagnostic measures that quantify time series dynamics and structure, and are robust to noise in observational data. This paper investigates the temporal dynamics of environmental time series using measures quantifying their information content and complexity. The measures are used to classify natural processes on one hand, and to compare models with observations on the other. The present analysis focuses on the global carbon cycle as an area of research in which model-data integration and comparisons are key to improving our understanding of natural phenomena. We investigate the dynamics of observed and simulated time series of Gross Primary Productivity (GPP), a key variable in terrestrial ecosystems that quantifies ecosystem carbon uptake. However, the dynamics, patterns and magnitudes of GPP time series, both observed and simulated, vary substantially on different temporal and spatial scales. Here we demonstrate that information content and complexity, or Information Theory Quantifiers (ITQ) for short, serve as robust and efficient data-analytical and model benchmarking tools for evaluating the temporal structure and dynamical properties of simulated or observed time series at various spatial scales. At continental scale, we compare GPP time series simulated with two models and an observations-based product. This analysis reveals qualitative differences between model evaluation based on ITQ compared to traditional model performance metrics, indicating that good model performance in terms of absolute or relative error does not imply that the dynamics of the observations is captured well. Furthermore, we show, using an ensemble of site-scale measurements obtained from the FLUXNET archive in the Mediterranean, that model-data or model-model mismatches as indicated by ITQ can be attributed to and interpreted as differences in the temporal structure of the respective ecological time series. At global scale, our understanding of C fluxes relies on the use of consistently applied land models. Here, we use ITQ to evaluate model structure: The measures are largely insensitive to climatic scenarios, land use and atmospheric gas concentrations used to drive them, but clearly separate the structure of 13 different land models taken from the CMIP5 archive and an observations-based product. In conclusion, diagnostic measures of this kind provide data-analytical tools that distinguish different types of natural processes based solely on their dynamics, and are thus highly suitable for environmental science applications such as model structural diagnostics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Maximizing efficiency of dataset compression for machine learning potentials with information theory

Machine learning interatomic potentials (MLIPs) balance high accuracy and lower costs compared to density functional theory calculations, but their performance often depends on the size and diversity of training datasets. Large datasets improve model accuracy and generalization but are computationally expensive to produce and train on, while smaller datasets risk discarding rare but important atomic environments and compromising MLIP accuracy/reliability. Here, we develop an information-theoretical framework to quantify the efficiency of dataset compression methods and propose an algorithm that maximizes this efficiency. By framing atomistic dataset compression as an instance of the minimum set cover (MSC) problem over atom-centered environments, our method identifies the smallest subset of structures that contains as much information as possible from the original dataset while pruning redundant information. The approach is extensively demonstrated on the GAP-20 and TM23 datasets and validated on 64 varied datasets from the ColabFit repository. Across all cases, MSC consistently retains outliers, preserves dataset diversity, and reproduces the long-tail distributions of forces even at high compression rates, outperforming other subsampling methods. Furthermore, MLIPs trained on MSC-compressed datasets exhibit reduced error for out-of-distribution data even in low-data regimes. We explain these results using an outlier analysis and show that such quantitative conclusions could not be achieved with conventional dimensionality reduction methods. The algorithm is implemented in the open-source QUESTS package and can be used for several tasks in atomistic modeling, from data subsampling, outlier detection, and training improved MLIPs at a lower cost.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Model-free estimation of completeness, uncertainties, and outliers in atomistic machine learning using information theory

Abstract An accurate description of information is relevant for a range of problems in atomistic machine learning (ML), such as crafting training sets, performing uncertainty quantification (UQ), or extracting physical insights from large datasets. However, atomistic ML often relies on unsupervised learning or model predictions to analyze information contents from simulation or training data. Here, we introduce a theoretical framework that provides a rigorous, model-free tool to quantify information contents in atomistic simulations. We demonstrate that the information entropy of a distribution of atom-centered environments explains known heuristics in ML potential developments, from training set sizes to dataset optimality. Using this tool, we propose a model-free UQ method that reliably predicts epistemic uncertainty and detects out-of-distribution samples, including rare events in systems such as nucleation. This method provides a general tool for data-driven atomistic modeling and combines efforts in ML, simulations, and physical explainability.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Applying Shannon's information theory to bacterial and phage genomes and metagenomes

All sequence data contain inherent information that can be measured by Shannon’s uncertainty theory. Such measurement is valuable in evaluating large data sets, such as metagenomic libraries, to prioritize their analysis and annotation, thus saving computational resources. Here, Shannon’s index of complete phage and bacterial genomes was examined. The information content of a genome was found to be highly dependent on the genome length, GC content, and sequence word size. In metagenomic sequences, the amount of information correlated with the number of matches found by comparison to sequence databases. A sequence with more information (higher uncertainty) has a higher probability of being significantly similar to other sequences in the database. Measuring uncertainty may be used for rapid screening for sequences with matches in available database, prioritizing computational resources, and indicating which sequences with no known similarities are likely to be important for more detailed analysis.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Using Information Theory to Evaluate Directional Precipitation Interactions Over the West Sahel Region in Observations and Models

Water availability has historically been one of the most significant threats to African regional social and economic well-being. Over the Sahel region, a megadrought during the 1960s and 1970s induced by an abrupt and substantial rainfall reduction caused widespread famine and death. The postdrought recovery, which is still ongoing, has been characterized by gradual increases in rainfall, but with dramatic fluctuations. The large negative human impacts, slow recovery, and variability raise important questions of why and how rainfall dynamics evolve and interact with other components of the regional climate system. Here we provide an observational assessment of rainfall interactions mechanisms (informed by directional transfer of information entropy) that regulate Sahel rainfall. We quantitatively demonstrate that (1) sea surface temperature over the Gulf of Guinea controls moisture advection and transport to the West Sahel region and (2) strong bidirectional interactions exist between local vegetation dynamics and rainfall patterns. Then we assess the directional interaction patterns from nine state-of-the-art Earth System Models (ESMs). We find that most ESMs are able to represent either the unidirectional control of sea surface temperature on precipitation or the bidirectional interaction between vegetation and precipitation. However, none of the ESMs represents both interactive patterns. The GFDL and IPSL-CM5A-LR models successfully reproduced observed patterns over ~50% of the West Sahel region but were not accurate in reproducing observed precipitation regional trends or interannual variation. We propose that the directional information transfer is a powerful mechanistic benchmark to assess model fidelity at the process level.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

An Information Theory Approach on Deciding Spectroscopic Follow-ups

Classification and characterization of variable phenomena and transient phenomena are critical for astrophysics and cosmology. These objects are commonly studied using photometric time series or spectroscopic data. Given that many ongoing and future surveys are conducted in a time domain, and given that adding spectra provides further insights but requires more observational resources, it would be valuable to know which objects we should prioritize to have a spectrum in addition to a time series. We propose a methodology in a probabilistic setting that determines a priori which objects are worth taking a spectrum of to obtain better insights, where we focus on the insight of the type of the object (classification). Objects for which we query their spectrum are reclassified using their full spectral information. We first train two classifiers, one that uses photometric data and another that uses photometric and spectroscopic data together. Then for each photometric object we estimate the probability of each possible spectrum outcome. We combine these models in various probabilistic frameworks (strategies), which are used to guide the selection of follow-up observations. The best strategy depends on the intended use, whether it is obtaining more confidence or accuracy. For a given number of candidate objects (127, equal to 5% of the data set) for taking spectra, we improve the class prediction accuracy by 37% as opposed to 20% of a non-naive (non-random) best-baseline strategy. Our approach provides a general framework for follow-up strategies and can be extended beyond classification to include other forms of follow-ups beyond spectroscopy.

79 ASTRONOMY AND ASTROPHYSICS↗