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At least 271 records · Page 15

Driving mode analysis—How uncertain functional inputs propagate to an output

Abstract Driving mode analysis elucidates how correlated features of uncertain functional inputs jointly propagate to produce uncertainty in the output of a computation. Uncertain input functions are decomposed into three terms: the mean functions, a zero‐mean driving mode, and zero‐mean residual. The random driving mode varies along a single direction, having fixed functional shape and random scale. It is uncorrelated with the residual, and under linear error propagation, it produces an output variance equal to that of the full input uncertainty. Finally, the driving mode best represents how input uncertainties propagate to the output because it minimizes expected squared Mahalanobis distance amongst competitors. These characteristics recommend interpretation of the driving mode as the single‐degree‐of‐freedom component of input uncertainty that drives output uncertainty. We derive the functional driving mode, show its superiority to other seemingly sensible definitions, and demonstrate the utility of driving mode analysis in an application. The application is the simulation of neutron transport in criticality experiments. The uncertain input functions are nuclear data that describe how Pu reacts to bombardment by neutrons. Visualization of the driving mode helps scientists understand what aspects of correlated functional uncertainty have effects that either reinforce or cancel one another in propagating to the output of the simulation.

97 MATHEMATICS AND COMPUTING↗

A formalism for extracting track functions from jet measurements

The continued success of the jet substructure program will require widespread use of tracking information to enable increasingly precise measurements of a broader class of observables. The recent reformulation of jet substructure in terms of energy correlators has simplified the incorporation of universal non-perturbative matrix elements, so called “track functions”, in jet substructure calculations. These advances make it timely to understand how these universal non-perturbative functions can be extracted from hadron collider data, which is complicated by the use jet algorithms. In this paper we introduce a new class of jet functions, which we call (semi-inclusive) track jet functions, which describe measurements of the track energy fraction in identified jets. These track jet functions can be matched onto the universal track functions, with perturbatively calculable matching coefficients that incorporate the jet algorithm dependence. We perform this matching, and present phenomenological results for the charged energy fraction in jets at the LHC and EIC/HERA at collinear next-to-leading logarithmic accuracy. We show that higher moments of the charged energy fraction directly exhibit non-linear Lorentzian renormalization group flows, allowing the study of these flows with collider data. Our factorization theorem enables the extraction of universal track functions from jet measurements, opening the door to their use for a precision jet substructure program.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

D2NO: Efficient handling of heterogeneous input function spaces with distributed deep neural operators

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions that exhibit heterogeneous properties, requiring multiple sensors to handle functions with minimal regularity. To address this issue, discretization-invariant neural operators have been used, allowing the sampling of diverse input functions with different sensor locations. However, existing frameworks still require an equal number of sensors for all functions. We propose a novel distributed approach to further relax the discretization requirements and solve the heterogeneous dataset challenges. Our method involves partitioning the input function space and processing individual input functions using independent and separate neural networks. A centralized neural network is used to handle shared information across all output functions. This distributed methodology reduces the number of gradient descent back-propagation steps, improving efficiency while maintaining accuracy. Here, we demonstrate that the corresponding neural network is a universal approximator of continuous nonlinear operators and present three numerical examples to validate its performance.

97 MATHEMATICS AND COMPUTING↗

Effect of Linker Structure and Functionalization on Secondary Gas Formation in Metal–Organic Frameworks

Rare-earth terephthalic acid (BDC)-based metal–organic frameworks (MOFs) are promising candidate materials for acid gas separation and adsorption from flue gas streams. However, previous simulations have shown that acid gases (H 2 O, NO 2 , and SO 2 ) react with the hydroxyl on the BDC linkers to form protonated acid gases as a potential degradation mechanism. Herein, gas-phase computational approaches were used to identify the formation energies of these secondary protonated acid gases across multiple BDC linker molecules. Formation energies for secondary protonated acid gases were evaluated using both density functional theory (DFT) and correlated wave function methods for varying BDC–gas reaction mechanisms. Upon validation of DFT to reproduce wave function calculation results, rotated conformational linkers and chemically functionalized BDC linkers with -OH, -NH 2 , and -SH were investigated. Furthermore, the calculations show that the rotational conformation affects the molecule stability. Double-functionalized BDC linkers, where two functional groups are substituted onto BDC, showed varied reaction energies depending on whether the functional groups donate or withdraw electrons from the aromatic system. Based on these results, BDC linker design must balance adsorption performance with degradation via linker dehydrogenation for the design of stable MOFs for acid gas separations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Array-Based Machine Learning for Functional Group Detection in Electron Ionization Mass Spectrometry

Mass spectrometry is a ubiquitous technique capable of complex chemical analysis. The fragmentation patterns that appear in mass spectrometry are an excellent target for artificial intelligence methods to automate and expedite the analysis of data to identify targets such as functional groups. To develop this approach, we trained models on electron ionization (a reproducible hard fragmentation technique) mass spectra so that not only the final model accuracies but also the reasoning behind model assignments could be evaluated. The convolutional neural network (CNN) models were trained on 2D images of the spectra using transfer learning of Inception V3, and the logistic regression models were trained using array-based data and Scikit Learn implementation in Python. Our training dataset consisted of 21,166 mass spectra from the United States’ National Institute of Standards and Technology (NIST) Webbook. The data was used to train models to identify functional groups, both specific (e.g., amines, esters) and generalized classifications (aromatics, oxygen-containing functional groups, and nitrogen-containing functional groups). We found that the highest final accuracies on identifying new data were observed using logistic regression rather than transfer learning on CNN models. It was also determined that the mass range most beneficial for functional group analysis is 0–100 m/z. We also found success in correctly identifying functional groups of example molecules selected from both the NIST database and experimental data. Beyond functional group analysis, we also have developed a methodology to identify impactful fragments for the accurate detection of the models’ targets. The results demonstrate a potential pathway for analyzing and screening substantial amounts of mass spectral data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

FunDiff: diffusion models over function spaces for physics-informed generative modeling

Recent advances in generative modeling-particularly diffusion models and flow matching-have been widely used for synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. To address this, we introduce FunDiff, an efficient and robust framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generates continuous functions that can be evaluated at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, demonstrating that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We further demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results indicate that our method can generate physically consistent samples with high fidelity to the target distribution, and exhibit robustness to noisy and low-resolution data.

Wang, Sifan [Yale University, New Haven, CT (Unite↗

The three major axes of terrestrial ecosystem function

The leaf economics spectrum and the global spectrum of plant forms and functions revealed fundamental axes of variation in plant traits, which represent different ecological strategies that are shaped by the evolutionary development of plant species. Ecosystem functions depend on environmental conditions and the traits of species that comprise the ecological communities. However, the axes of variation of ecosystem functions are largely unknown, which limits our understanding of how ecosystems respond as a whole to anthropogenic drivers, climate and environmental variability. Here we derive a set of ecosystem functions from a dataset of surface gas exchange measurements across major terrestrial biomes. We find that most of the variability within ecosystem functions (71.8%) is captured by three key axes. The first axis reflects maximum ecosystem productivity and is mostly explained by vegetation structure. The second axis reflects ecosystem water-use strategies and is jointly explained by variation in vegetation height and climate. The third axis, which represents ecosystem carbon-use efficiency, features a gradient related to aridity, and is explained primarily by variation in vegetation structure. We show that two state-of-the-art land surface models reproduce the first and most important axis of ecosystem functions. However, the models tend to simulate more strongly correlated functions than those observed, which limits their ability to accurately predict the full range of responses to environmental changes in carbon, water and energy cycling in terrestrial ecosystems.

54 ENVIRONMENTAL SCIENCES↗

Supervised learning of a chemistry functional with damped dispersion

Abstract Kohn–Sham density functional theory is widely used in chemistry, but no functional can accurately predict the whole range of chemical properties, although recent progress by some doubly hybrid functionals comes close. Here, we optimized a singly hybrid functional called CF22D with higher across-the-board accuracy for chemistry than most of the existing non-doubly hybrid functionals by using a flexible functional form that combines a global hybrid meta-nonseparable gradient approximation that depends on density and occupied orbitals with a damped dispersion term that depends on geometry. We optimized this energy functional by using a large database and performance-triggered iterative supervised training. We combined several databases to create a very large, combined database whose use demonstrated the good performance of CF22D on barrier heights, isomerization energies, thermochemistry, noncovalent interactions, radical and nonradical chemistry, small and large systems, simple and complex systems and transition-metal chemistry.

Liu, Yiwei (ORCID:0000000288126163)↗

Challenges for density functional theory: calculation of CO adsorption on electrocatalytically relevant metals

Density Functional Theory (DFT) is currently the most tractable choice of theoretical model used to understand the mechanistic pathways for electrocatalytic processes such as CO 2 or CO reduction. In this work, we assess the performance of two DFT functionals designed specifically to describe surface interactions, RTPSS and RPBE, as well as two popular meta-GGA functionals, SCAN and B97M-rV, that have not been a priori optimized for better interfacial properties. We assess all four functionals against available experimental data for prediction of bulk and bare surface properties on four electrocatalytically relevant metals, Au, Ag, Cu, and Pt, and for binding CO to surfaces of these metals. To partially mitigate issues such as thermal and anharmonic corrections associated with comparing computations with experiments, molecular benchmarks against high level quantum chemistry are reported for CO complexes with Au, Ag, Cu and Pt atoms, as well as the CO–water complex and the water dimer. Overall, we find that the surface modified RPBE functional performs reliably for many of the benchmarks examined here, and the meta-GGA functionals also show promising results. Specifically B97M-rV predicts the correct site preference for CO binding on Ag and Au (the only functional tested here to do so), while RTPSS performs well for surface relaxations and binding of CO on Pt and Cu.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Assessing cathode property prediction via exchange-correlation functionals with and without long-range dispersion corrections

In this work, we benchmark calculated interlayer spacings, average topotactic voltages, thermodynamic stabilities, and band gaps in layered lithium transition-metal oxides (TMOs) and their de-lithiated counterparts, which are used in lithium-ion batteries as positive electrode materials, against available experimental data. Specifically, we examine the accuracy of properties calculated within density functional theory (DFT) using eight different treatments of electron exchange-correlation: the strongly constrained and appropriately normed (SCAN) and Perdew–Burke–Ernzerhof (PBE) density functionals, Hubbard-U-corrected SCAN and PBE (i.e., SCAN+U and PBE+U), and SCAN(+U) and PBE(+U) with added long-range dispersion (D) interactions (i.e., DFT(+U)+D). van der Waals interactions are included respectively via the revised Vydrov-Van Voorhis (rVV10) for SCAN(+U) and the DFT-D3 for PBE(+U). We find that SCAN-based functionals predict larger voltages due to an underestimation of stability of the MO2 systems, while also predicting smaller interlayer spacings compared to their PBE-based counterparts. Furthermore, adding dispersion corrections to PBE has a greater effect on voltage predictions and interlayer spacings than with SCAN, indicating that DFT-SCAN – despite being a ground-state theory – fortuitously captures some short and medium-range dispersion interactions better than PBE. While SCAN-based and PBE-based functionals yield qualitatively similar band gap predictions, there is no significant quantitative improvement of SCAN-based functionals over the corresponding PBE-based versions. Finally, we expect SCAN-based functionals to yield more accurate property predictions than the respective PBE-based functionals for most TMOs, given SCAN's stronger theoretical underpinning and better predictions of systematic trends in interlayer spacings, intercalation voltages, and band gaps obtained in this work.

25 ENERGY STORAGE↗

Investigating the vertical distribution of the disk as a function of radial action

As heating processes can broaden the distributions of radial actions and the vertical distributions of the Galactic disks, we investigate the vertical distribution of the Galactic disks as a function of radial action based on Apache Point Observatory Galactic Evolution Experiment (APOGEE) and Gaia data in order to deepen our understanding of the formation and heating history of the Galactic disks. The vertical distributions of the thin and thick Galactic disks defined in the chemical plane were fitted with a simple exponential function with a free parameter of scale height in different radial action ranges. Therefore, we were able to analyze the scale height as a function of radial action for different disk populations. We find that the distributions of radial action for both the thin and thick disks can be approximately described by pseudo-isothermal distributions, which give a statistical measurement for the temperature of the disk as indicated by the mean radial action of the star sample. Estimations of the scale heights in different radial action ranges for these pseudo-isothermal distributions of the disks seem to show fixed relationships between radial action J R and scale height h. We describe these relationships with a two-parameter function of h = √(J R /a)+b, where a and b are free parameters. When testing with a three-parameter function of h = α √(J R /a)+b, we find that this two-parameter function describes the thin disk well, but we note the function should be used with care for the thick disk. When comparing the best-fit relationships between the inner and outer disk for both of the thin and thick disks, we find that the relationships are nearly the same for the thin disks but are different for the thick disks. The inner thick disk shows a nearly flattened relationship, while the outer thick disk presents a gradually increasing relationship. This work highlights an alternative way to unveil the heating history of the disks by investigating the relationship between scale height and radial action, as these relationships encode the formation and heating history of the Galactic disks.

79 ASTRONOMY AND ASTROPHYSICS↗

Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Exploring the exact limits of the real-time equation-of-motion coupled cluster cumulant Green’s functions

In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green’s function approach [Rehr et al., J. Chem. Phys. 152, 174113 (2020)]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz, ensuring the exactness in the expansion limit. In addition, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green’s function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green’s function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green’s function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green’s function approach and other Green’s function approaches in the numerical exact limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Impulse Approximation Scattering Function and Its Use in Monte Carlo Photon Transport Simulations

The viability of using the impulse approximation scattering function in Monte Carlo photon transport simulations is explored. This scattering function can be constructed from the double differential incoherent scattering cross section developed by Ribberfors and Berggren. A commonly used method for modeling photon Doppler broadening, which is referred to as the hybrid Doppler broadening method, can also be derived from this cross section. A new photon Doppler broadening method, called the consistent Doppler broadening method, is derived and discussed. This method eliminates some of the commonly employed approximations in the hybrid Doppler broadening method, in part, by using the impulse approximation scattering function. Integrated incoherent cross sections generated using the impulse approximation scattering function and the widely used Waller-Hartree scattering function are in good agreement above 20 keV. Below 20 keV, differences as high as 70% are observed, which differs from the roughly 5% differences observed by Ribberfors for some of the materials. Integral and spectral quantities for two problems are also generated using the Monte Carlo photon transport capabilities of the Framework for REsearch in Nuclear ScIence and Engineering (FRENSIE). Due to the small, relative result differences observed when using the impulse approximation scattering function, it is considered a viable alternative to the Waller-Hartree scattering function. In addition, some small, but expected, differences in spectral fluxes at low energies can be avoided by adopting the consistent Doppler broadening method.

42 ENGINEERING↗

Combining protein sequences and structures with transformers and equivariant graph neural networks to predict protein function

Abstract Motivation Millions of protein sequences have been generated by numerous genome and transcriptome sequencing projects. However, experimentally determining the function of the proteins is still a time consuming, low-throughput, and expensive process, leading to a large protein sequence-function gap. Therefore, it is important to develop computational methods to accurately predict protein function to fill the gap. Even though many methods have been developed to use protein sequences as input to predict function, much fewer methods leverage protein structures in protein function prediction because there was lack of accurate protein structures for most proteins until recently. Results We developed TransFun—a method using a transformer-based protein language model and 3D-equivariant graph neural networks to distill information from both protein sequences and structures to predict protein function. It extracts feature embeddings from protein sequences using a pre-trained protein language model (ESM) via transfer learning and combines them with 3D structures of proteins predicted by AlphaFold2 through equivariant graph neural networks. Benchmarked on the CAFA3 test dataset and a new test dataset, TransFun outperforms several state-of-the-art methods, indicating that the language model and 3D-equivariant graph neural networks are effective methods to leverage protein sequences and structures to improve protein function prediction. Combining TransFun predictions and sequence similarity-based predictions can further increase prediction accuracy. Availability and implementation The source code of TransFun is available at https://github.com/jianlin-cheng/TransFun.

59 BASIC BIOLOGICAL SCIENCES↗

Taxonomic and functional restoration of tallgrass prairie soil microbial communities in comparison to remnant and agricultural soils

Abstract Restoring ecosystems requires the re-establishment of diverse soil microbial communities that drive critical ecosystem functions. In grasslands, restoration and management require the application of disturbances like fire and grazing. Disturbances can shape microbial taxonomic composition and potentially functional composition as well. We characterized taxonomic and functional gene composition of soil communities using whole genome shotgun metagenomic sequencing to determine how restored soil communities differed from pre-restoration agricultural soils and original remnant soils, how management affects soil microbes, and whether restoration and management affect the number of microbial genes associated with carbohydrate degradation. We found distinct differences in both taxonomic and functional diversity and composition among restored, remnant, and agricultural soils. Remnant soils had low taxonomic and functional richness and diversity, as well as distinct composition, indicating that restoration of agricultural soils does not re-create soil microbial communities that match remnants. Prescribed fire management increased functional diversity, which also was higher in more recently planted restorations. Finally, restored and post-fire soils included high abundances of genes encoding cellulose-degrading enzymes, so restorations and their ongoing management can potentially support functions important in carbon cycling.

Mason, Cayla N. (ORCID:0000000345983824)↗

Information content of higher order galaxy correlation functions

The shapes of galaxy N-point correlation functions can be used as standard rulers to constrain the distance–redshift relationship. The cosmological density fields traced by late-time galaxy formation are initially nearly Gaussian, and hence, all the cosmological information can be extracted from their two-point correlation function. Subsequent non-linear evolution under gravity, as well as halo and then galaxy formation, generates higher order correlation functions. Since the mapping of the initial to the final density field is, on large scales, invertible, it is often claimed that the information content of the initial field’s power spectrum is equal to that of all the higher order functions of the final, non-linear field. This claim implies that reconstruction of the initial density field from the non-linear field renders analysis of higher order correlation functions of the latter superfluous. We show that this claim is false when the N-point functions are used as standard rulers. Constraints available from joint analysis of the two and three-point correlation functions can, in some cases, exceed those offered by the initial power spectrum. We provide a mathematical justification for this claim and demonstrate it using a large suite of N-body simulations. In particular, we show that for the z = 0 real-space matter field in the limit of vanishing shot-noise, taking modes up to k max = 0.2 h Mpc −1 , using the bispectrum alone offers a factor of 2 reduction in the variance on the cosmic distance scale relative to that available from the linear power spectrum.

79 ASTRONOMY AND ASTROPHYSICS↗

Estradiol associations with brain functional connectivity in postmenopausal women

Abstract Objective Previous studies have found that estrogens play a role in functional connectivity in the brain; however, little research has been done regarding how estradiol is associated with functional connectivity in postmenopausal women. The purpose of this study was to examine the relationship between estradiol and functional connectivity in postmenopausal women. Methods Structural and blood oxygenation level–dependent resting-state magnetic resonance imaging scans of 88 cognitively healthy postmenopausal individuals were obtained along with blood samples collected the same day as the magnetic resonance imaging to assess hormone levels. We generated connectivity values in CONN toolbox version 20.b, an SPM-based software. Results A regression analysis was run using estradiol level and regions of interest (ROI), including the hippocampus, parahippocampus, dorsolateral prefrontal cortex, and precuneus. Estradiol level was found to enhance parahippocampal gyrus anterior division left functional connectivity during ROI-to-ROI regression analysis. Estradiol enhanced functional connectivity between the parahippocampal gyrus anterior division left and the precuneus as well as the parahippocampal gyrus anterior division left and parahippocampal gyrus posterior division right. An exploratory analysis showed that years since the final menstrual period was related to enhanced connectivity between regions within the frontoparietal network. Conclusions These results illustrated the relationship between estradiol level and functional connectivity in postmenopausal women. They have implications for understanding how the functioning of the brain changes for individuals after menopause that may eventually lead to changes in cognition and behavior in older ages.

Obstetrics & Gynecology↗