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DOE OSTI2023

A small-box approach to the local crystal structure of Y 3 NbO 7

The local crystal structure of Y 3 NbO 7 was probed using neutron total scattering. Five different structural models were fit to the experimental pair distribution function of this material up to 15 Å. Fits of defect fluorite (Fm$\overline{3}$m), pyrochlore (Fd$\overline{3}$m), and orthorhombic C weberite models (C222 1 ) were attempted based on prior structural investigations of Y 3 NbO 7 and related fluorite-based materials. Orthorhombic P weberite (P222 1 ) and monoclinic weberite models (P112 1 ) were derived via symmetry reduction of the orthorhombic C weberite structure. All models except monoclinic weberite failed to reproduce the experimental pair distribution function. Misfits were clearly visible for peaks arising from atom pairs within the first coordination shell (defect fluorite and pyrochlore) and beyond (orthorhombic C and P weberite). By contrast, monoclinic weberite (γ ≈ 91.8°) provided an excellent fit, with no major misfits observed. This unit cell features distorted YO 8 dodecahedra, YO 7 monocapped octahedra, and NbO 6 octahedra as building blocks. Comparison between the topologies of the cationic and anionic substructures in monoclinic weberite and its parent orthorhombic C structure revealed displacements of the metal atoms along the [100] direction and a less compact spatial distribution of oxygen atoms along the a axis. In conclusion, the monoclinic weberite model presented herein may serve as a starting point to revisit structural modeling of fluorite-based materials with challenging local structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Fourier-informed knot placement schemes for B-spline approximation

Fitting B-splines to scientific data is especially challenging when the given data contain noise, jumps, or corners. Here, we describe how periodic data sets with these features can be efficiently approximated with B-splines by analyzing the Fourier spectrum of the data. Our method uses a collection of spectral filters to compute high-order derivatives, smoothed versions of noisy data, and the locations of jump discontinuities. Further, these quantities are then combined to choose knots that capture the qualitative features of the data, leading to accurate B-spline approximations with few knots. The method we introduce is direct and does not require any intermediate B-spline fitting before choosing the final knot distribution. Aside from fast Fourier transforms to transfer to and from Fourier space, the method runs in linear time with very little communication. We assess performance on several test cases in one and two dimensions, including data sets with jump discontinuities and noise. These tests show the method fits discontinuous data without spurious oscillations and remains effective in the presence of noise.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A functional form for liquid scintillator pulse shapes

Digitization of detector signals enables analysis of the original waveform to extract timing, particle identification, and energy deposition information. Here we present the use of analytical functions based on sigmoids to model and fit such pulse shapes from liquid organic scintillators, though the method should also be applicable to other detector systems. Neutron and gamma interactions in NE213 detectors were digitized from the phototube anode and fit using a sigmoid-based function. The acuity of the fit in extracting timing information and performing neutron-gamma pulse-shape discrimination are presented and discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Validation of the two-region Rossi-alpha model for reflected assemblies

Nuclear criticality safety, nonproliferation and safeguards, emergency response, and stockpile stewardship utilize estimates of the k eff multiplication factor. The value of k eff cannot be directly measured, but it can be inferred from the prompt neutron period. One modality of measuring the prompt neutron period is the Rossi-alpha method, which is predicated on fitting a histogram of detection time differences due to the nonrandom temporal distribution of same-fission-chain neutrons. Recent works have developed the motivation and theory to expand traditional one-region point kinetic models resulting in one-exponential histogram fits to two-region models that result in two-exponential fits. This paper validates the new two-region model using organic scintillator measurements of copper-reflected weapons-grade plutonium (0:83 ≤ k eff ≤ 0:94) and high-density- polyethylene-reflected highly enriched uranium (0:73 ≤ k eff ≤ 0:95). Furthermore, the results show that more thermal systems have shorter prompt neutron periods in the core region due to increased induced-fission probabilities for moderated neutrons. Here, a new parameter introduced by the two- region model is also shown to be correlated to the amount of reflection, and may be used to infer assembly properties such as type and amount of reflector.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

On the analysis of signal peaks in pulse-height spectra

The estimation of the signal location and intensity of a peak in a pulse height spectrum is important for X- ray and γ-ray spectroscopy, charged-particle spectrometry, liquid chromatography, and many other subfields. However, both the ‘‘centroid’’ and ‘‘signal intensity’’ of a peak in a pulse-height spectrum are ill-defined quantities and different methods of analysis will yield different numerical results. Here, we apply three methods of analysis. Method A is based on simple count summation and is likely the technique most frequently applied in practice. The analysis is straightforward and fast, and does not involve any statistical modeling. We find that it provides reliable results only for high signal-to-noise data, but has severe limitations in all other cases. Method B employs a Bayesian model to extract signal counts and centroid from the measured total and background counts. The resulting values are derived from the respective posteriors and, therefore, have a rigorous statistical meaning. The method makes no assumptions about the peak shape. It yields reliable and relatively small centroid uncertainties. However, it provides relatively large signal count uncertainties. Method C makes a strong assumption regarding the peak shape by fitting a Gaussian function to the data. Furthermore, the fit is based again on a Bayesian model. Although Method C requires careful consideration of the Gaussian width (usually given by the detector resolution) used in the fitting, it provides reliable values and relatively small uncertainties both for the signal counts and the centroid.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

A Denoising Autoencoder for Improved Kikuchi Pattern Quality and Indexing in Electron Backscatter Diffraction

The rapid collection and indexing of electron diffraction patterns as produced via electron backscatter diffraction (EBSD) has enabled crystallographic orientation and structural determination, as well as additional property-determining strain and dislocation density information with increasing speed, resolution, and efficiency. Pattern indexing quality is reliant on the noise of the collected electron diffraction patterns, which is often convoluted by sample preparation and data collection parameters. EBSD acquisition is sensitive to many factors and thus can result in low confidence index (CI), poor image quality (IQ), and improper minimization of fit, which can result in noisy datasets and misrepresent the microstructure. In an attempt to enable both higher speed EBSD data collection and enable greater orientation fit accuracy with noisy datasets, an image denoising autoencoder was implemented to improve pattern quality. Here, we show that EBSD data processed through the autoencoder results in a higher CI, IQ, and a more accurate degree of fit. In addition, using denoised datasets in HR-EBSD cross correlative strain analysis can result in reduced phantom strain from erroneous calculations due to the increased indexing accuracy and improved correspondence between collected and simulated patterns.

36 MATERIALS SCIENCE↗

DOE OSTI2026

OzDES Reverberation Mapping of Active Galactic Nuclei: Final Data Release, Black-Hole Mass Results, & Scaling Relations

Over the last decade, the Australian Dark Energy (OzDES) collaboration has used Reverberation Mapping to measure the masses of high redshift supermassive black holes. Here we present the final review and analysis of this OzDES reverberation mapping campaign. These observations use 6-7 years of photometric and spectroscopic observations of 735 Active Galactic Nuclei (AGN) in the redshift range 0.13-3.85 and bolometric luminosity range 44.3 - 47.5 erg/s. Both photometry and spectra are observed in visible wavelengths, allowing for the physical scale of the AGN broad line region to be estimated from reverberations of the H{̱e̱ṯa̱}̱, MgII and CIV emission lines. We successfully use reverberation mapping to constrain the masses of 62 super-massive black holes, and combine with existing data to fit a power law to the lag-luminosity relation for the H{̱e̱ṯa̱}̱ and MgII lines with a scatter of ~0.25 dex, the tightest yet identified, fit specifically for consistency with high redshift AGN. We fit a similarly constrained relation for CIV, resolving a tension with the low luminosity literature AGN by accounting for selection effects arising from finite survey length. We also examine the impact of emission line width and luminosity (related to accretion rate) in reducing the scatter of these scaling relationships and find no significant improvement over the lag-only approach for any of the three lines. Using these relations, we further estimate the masses and accretion rates of 246 AGN with single epoch methods. We also use these relations to estimate the relative sizes of the H{̱e̱ṯa̱}̱, MgII and CIV emitting regions. In short, we provide a comprehensive benchmark of high redshift AGN reverberation mapping at the close of this most recent generation of surveys, including light curves, time-delays, and a set of significantly improved radius-luminosity relations for use with high-redshift populations.

McDougall, Hugh [Queensland U.]↗

DOE OSTI2021

Ab Initio Direct Dynamics

The reactivity and dynamics of molecular systems can be explored computationally by classical trajectory calculations. The traditional approach involves fitting a functional form of a potential energy surface (PES) to the energies from a large number of electronic structure calculations and then integrating numerous trajectories on this fitted PES to model the molecular dynamics. The ever-decreasing cost of computing and continuing advances in computational chemistry software have made it possible to use electronic structure calculations directly in molecular dynamics simulations without first having to construct a fitted PES. In this “on-the-fly” approach, every time the energy and its derivatives are needed for the integration of the equations of motion, they are obtained directly from quantum chemical calculations. This approach started to become practical in the mid-1990s as a result of increased availability of inexpensive computer resources and improved computational chemistry software. The application of direct dynamics calculations has grown rapidly over the last 25 years and would require a lengthy review article. The present Account is limited to some of our contributions to methods development and various applications. To improve the efficiency of direct dynamics calculations, we developed a Hessian-based predictor-corrector algorithm for integrating classical trajectories. Hessian updating made this even more efficient. Furthermore, this approach was also used to improve algorithms for following the steepest descent reaction paths. For larger molecular systems, we developed an extended Lagrangian approach in which the electronic structure is propagated along with the molecular structure. Strong field chemistry is a rapidly growing area, and to improve the accuracy of molecular dynamics in intense laser fields, we included the time-varying electric field in a novel predictor-corrector trajectory integration algorithm. Since intense laser fields can excite and ionize molecules, we extended our studies to include electron dynamics. Specifically, we developed code for time-dependent configuration interaction electron dynamics to simulate strong field ionization by intense laser pulses. Our initial application of ab initio direct dynamics in 1994 was to CH 2 O → H 2 + CO; the calculated vibrational distributions in the products were in very good agreement with experiment. In the intervening years, we have used direct dynamics to explore energy partitioning in various dissociation reactions, unimolecular dissociations yielding three fragments, reactions with branching after the transition state, nonstatistical dynamics of chemically activated molecules, dynamics of molecular fragmentation by intense infrared laser pulses, selective activation of specific dissociation channels by aligned intense infrared laser fields, angular dependence of strong field ionization, and simulation of sequential double ionization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Oxygen Defect Configurations in Single-Phase UO 2.15

Hyperstoichiometric UO 2.15 was characterized by neutron total scattering at high temperature in the single-phase UO 2+x region of the U/O phase diagram. The diffraction data confirmed a single-phase fluorite structure at high temperature. Analysis of the short-range data showed that the same structural model does not fit the pair distribution functions well. Instead, structural models containing specific configurations of oxygen defect clusters best represent the local atomic arrangement. In conclusion, prevalent defect clusters previously proposed were fit to the experimental data, and moderately distorted oxygen cuboctahedra hypothesized by recent molecular dynamics simulations fit the data most accurately.

neutron pair-distribution function analysis↗

DOE OSTI2023

Single-Point Extrapolation to the Complete Basis Set Limit through Deep Learning

Machine learning (ML) offers an attractive method for making predictions about molecular systems while circumventing the need to run expensive electronic structure calculations. Once trained on ab initio data, the promise of ML is to deliver accurate predictions of molecular properties that were previously computationally infeasible. In this work, we develop and train a graph neural network model to correct the basis set incompleteness error (BSIE) between a small and large basis set at the RHF and B3LYP levels of theory. Our results show that, when compared to fitting to the total potential, an ML model fitted to correct the BSIE is better at generalizing to systems not seen during training. We test this ability by training on single molecules while evaluating on molecular complexes. We also show that ensemble models yield better behaved potentials in situations where the training data is insufficient. However, even when only fitting to the BSIE, acceptable performance is only achieved when the training data sufficiently resemble the systems one wants to make predictions on. As a result, the test error of the final model trained to predict the difference between the cc-pVDZ and cc-pV5Z potential is 0.184 kcal/mol for the B3LYP density functional, and the ensemble model accurately reproduces the large basis set interaction energy curves on the S66x8 dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Accurate calculation of many-body energies in water clusters using a classical geometry-dependent induction model

We incorporate geometry-dependent distributed multipole and polarizability surfaces into an induction model that is used to describe the 3- and 4-body terms of the interaction between water molecules. The expansion is carried out up to hexadecapole with the multipoles distributed on the atom sites. Dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole distributed polarizabilities are used to represent the response of the multipoles to an electric field. We compare the model against two large databases consisting of 43,844 3-body terms and 3,603 4-body terms obtained from high level ab initio calculations previously used to fit the MB-pol and q-AQUA interaction potentials. The classical induction model with no adjustable parameters reproduces the ab-initio 3- and 4-body terms contained in these teo Databases with a Root-Mean-Square-Error (RMSE) of 0.104/0.058 and a Mean-Absolute-Error (MAE) of 0.054/0.026 kcal/mol, respectively, results that are on a par with those obtained 1 by fitting the same data using tens of thousands of Permutationally Invariant Polynomials (PIPs). This demonstrates the accuracy of this physically motivated model in describing the 3- and 4-body terms in the interactions between water molecules with no adjustable parameters. The triple-dipole-dispersion energy was included in the 3-body energy and was found to be small but not quite negligible. The model represents a practical, efficient and transferable approach for obtaining accurate non-additive interactions for multi-component systems without the need of performing tens of thousands of high level electronic structure calculations and fitting them with tens of thousands of PIPs.

molecular analysis water, aqueous↗

DOE OSTI2021

The Low-Lying Electronic States of NO 2 : Potential Energy and Dipole Surfaces, Bound States, and Electronic Absorption Spectrum

Nitrogen dioxide, NO 2 , is a free radical composed of the two most abundant elements in Earth’s atmosphere, nitrogen and oxygen, and is relevant to atmospheric and combustion chemistry. The electronic structure of even its lowest-lying states is remarkably complex, with various conical intersections and Renner–Teller pairings, giving rise to complex and perturbed vibronic states. Here we report some analysis of the 18 molecular states of doublet spin-multiplicity formed by combining ground-state N( 4 S u ) and O( 3 P g ) atoms. In this work, three-dimensional potential energy surfaces were fit at the MRCI(Q)-F12/VTZ-F12 level, describing the lowest four ($\tilde X$, $\tilde A$, $\tilde B$, and $\tilde C$) electronic states. A properties-based diabatization procedure was applied to accommodate the intersections, producing energies in a quasidiabatic representation and yielding couplings that were also fit into surfaces. The low-lying vibrational levels on the ground $\tilde X$ state were computed and compared with experimental measurements. Compared to experiment, the lowest 125 calculated vibrational levels (up to 8500 cm –1 above the zero-point energy) have a root-mean-squared error of 16.5 cm –1 . In addition, dipole moments for each of the lowest four electronic states—and the transition dipoles between them—were also computed and fit. With the coupled energy and dipole surfaces, the electronic spectrum was calculated in absolute intensity and compared with experimental measurements. Detailed structure in the experimental spectrum was successfully reproduced, and the total integrated intensity matches experiment to an accuracy of ~1.5% with no empirical adjustments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

OmicsMLMentor: A Web Application for Guided Machine Learning Analysis of Omics Data

Expression-based omics technologies (e.g. proteomics, metabolomics, transcriptomics, etc.) increasingly rely on supervised and unsupervised machine learning (ML) models to find key biomolecules distinguishing conditions, identify natural groupings in biological data, or generate predictions for outcomes of interest. Fitting ML models to omics data presents several challenges, including handling missing data, selecting a normalization method, choosing a valid model, and optimizing hyperparameters, all requiring statistical programming skills to address these challenges. Thus, the open-source web application SLOPE was designed to lower the barrier to ML modeling for omics data. SLOPE supports the fitting of 15 ML models (10 supervised and 5 unsupervised) tailored to omics datasets, such as proteomics, metabolomics, lipidomics, and transcriptomics. SLOPE offers several omics-specific features, including methods for handling missingness (imputation, conversion, removal), normalization tests, ranking of models based on the structure of a user’s data and user input, and optimal hyperparameter selections using cross-validation splits. By streamlining ML workflows for omics analysis, SLOPE address critical gaps in existing online web tools, facilitating a broader adoption of these models for omics research. Here, SLOPE is applied to data from a lignin exposure study to highlight the workflow for fitting both supervised and unsupervised models to data.

lipidomics↗

DOE OSTI2023

Mechanisms Controlling the Energy Barrier for Ion Hopping in Polymer Electrolytes

Here, the present work studies the mechanisms controlling the energy barrier for ion hopping in conducting polymers. Polymer electrolytes usually show Arrhenius-like temperature dependence of the conductivity relaxation time (characteristic time of local ion rearrangements) at temperatures below their glass transition T g . However, our analysis reveals that the Arrhenius fit of this regime leads to unphysically small prefactors, τ 0 $\ll$ 10 –13 s. Imposing a value of 10 –13 s for this parameter renders the fairly unexpected result that the energy barrier for charge transport in these polymers has strong temperature dependence even below T g . Our study also reveals significant temperature variations of the dielectric permittivity and the instantaneous shear modulus in the glassy state of these polymers. Using the Anderson and Stuart model, we demonstrate that these variations provide strong justifications for the temperature variation of energy barrier for ion hopping. Most importantly, the proposed approach reveals that the energy barrier controlling ion hopping in polymer electrolytes is significantly (~30–40%) lower than that estimated using traditional Arrhenius fit. These new insights call for revisions of many earlier results based on apparent Arrhenius fits, and the newly proposed approach can provide more accurate guidance for the design of solid-state electrolytes with enhanced ionic conductivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Evolution of the Cellulose Microfibril through Gamma-Valerolactone-Assisted Co-Solvent and Enzymatic Hydrolysis

Biomass recalcitrance during deconstruction remains a key bottleneck to affordable biomass processing technologies. A clear connection between the cell wall structure and biomass deconstruction is necessary to understand how lignocellulosic material is broken down to valuable monomeric components. Here, we monitor changes in the cellulose microfibril domains of poplar, sorghum, and switchgrass throughout gamma-valerolactone (GVL)–water co-solvent pretreatment and enzymatic hydrolysis using solid-state 13 C cross-polarization magic angle spinning nuclear magnetic resonance spectroscopy (CP/MAS 13 C-NMR) and wide-angle X-ray scattering (WAXS). Spectral fitting of NMR peaks corresponding to different cellulose microenvironments at the C 4 carbon center suggests that a mildly acidic GVL–water co-solvent pretreatment of poplar leads to nearly full removal of xylan–cellulose linkages, which primes the cellulose for enzymatic attack. The spectral fitting also suggests that the pretreatment causes significant depletion of the inaccessible fibril surface domains with an increase in more thermally stable crystalline resonances (I β ). WAXS confirmed a decrease in the lattice spacing between (200) crystalline planes with increasing co-solvent pretreatment severity. These results are interpreted as an opening of bound microfibril surfaces previously inaccessible to the co-solvent system, which leaves behind a more thermally stable, crystalline domain that is potentially prone to relaxation and recrystallization. Full conversion of residual GVL-pretreated biomass was achieved after the GVL co-solvent pretreatment at 140 °C using a commercial enzyme cocktail, CTec2, which contains different cellulases and other enzymes. Spectral fitting of enzymatically hydrolyzed samples by a single engineered cellulase, CelR, suggests that the residual cellulose recalcitrance is mainly due to the inability of CelR to digest the I β crystalline domain present in pretreated samples. This work helps to provide new information regarding the structure of the cell wall and recalcitrance throughout GVL–water mild acidolysis and CelR enzymatic biomass deconstruction by tracking the evolution of structural domains within the cellulose microfibril. This work further directs recommendations for improving the conversion and sugar yields in future studies. Finally, our findings inform inquiry into larger questions of cellulose recalcitrance through GVL pretreatment and CelR enzymatic hydrolysis and give insight into subsequent required steps for full cellulose conversion with attention to the most recalcitrant cellulose structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Source Characterization of the Declared North Korean Nuclear Tests From Regional Distance Coda Wave Spectral Ratios

Abstract Seismic observations of underground nuclear explosions provide crucial data on source yield and depth that cannot easily be estimated from other geophysical methods. However, it is difficult to obtain reliable yield estimates for test sites for which we do not have direct seismic calibration experiments. To obtain source information from uncalibrated sites and paths, local and regional seismic records of six, proximal, declared underground nuclear explosions in North Korea are used to compute spectral ratios of narrow‐band waveform envelopes of body‐wave coda that remove path and site effects to reveal precise, relative source moment. The yields of these explosions are obtained from the observed source ratios by simultaneously fitting the classical source model of Mueller and Murphy (1971), https://doi.org/10.1785/bssa0610061675 to all event pairs. The source model provides an impressive fit to the observations considering that the P phase coda derived source spectral ratios did not require a prior knowledge of the source or regionally calibrated corrections to be applied to the data. However, the observed corner frequencies from S wave coda spectral ratios are lower than the source model predictions, but are well fit by models calculated using the corner frequency consistent with the Fisk conjecture. The results presented here provide novel constraints on the spectral distributions of the energy radiated by the sources of the DPRK test series, and allows for an independent evaluation of existing estimated source model parameters.

58 GEOSCIENCES↗

DOE OSTI2025

Estimating Electron Temperature and Density Using Van Allen Probe Data: Typical Behavior of Energetic Electrons in the Inner Magnetosphere

Abstract The Earth's inner magnetosphere contains multiple electron populations influenced by different factors. The cold electrons of the plasmasphere, warm plasma that contributes to the ring current, and the relativistic plasma of the radiation belts often seem to behave independently. Using omni‐directional flux and energy measurements from the HOPE and Magnetic Electron Ion Spectrometer instruments aboard the Van Allen Probes, we provide a detailed density and temperature description of the inner magnetosphere, offering a comprehensive statistical analysis of the entire Van Allen Probe era. While number density and temperature data at geosynchronous orbit are available, this study focuses on the warm plasma in the inner magnetosphere . Values of density and temperature are extracted by fitting energy and phase space density to obtain the distribution function. The fitted distributions are related to the zeroth and second moments to estimate the number density and temperature. Analysis has indicated that a two Maxwellian fit is sufficient over a wide range of and that there are two independent plasma populations. The more energetic population has a median number density of approximately and a temperature of around 130 keV, with a temperature peak observed between L * = 4 and L * = 4.5. This population is relatively uniform in magnetic local time (MLT). In contrast, the less energetic warm electron population has a median number density of about and a temperature of 7.4 keV. Strong statistical trends in density and temperature across both L * and MLT are presented, along with potential sources driving these variations.

58 GEOSCIENCES↗

DOE OSTI2025

Baseflow Identification via Explainable AI With Kolmogorov‐Arnold Networks

Abstract Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov‐Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN‐derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts; they demonstrate that water availability, rather than potential evapotranspiration, drives baseflow by constraining actual evapotranspiration under arid conditions. On a test set, they increase the Nash‐Sutcliffe efficiency (NSE) by 65%, decrease the root mean squared error by 29%, and increase the Kling‐Gupta efficiency by 34%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water‐balance equation at the mean‐annual scale. The KAN‐derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN‐derived equations based on the original water balance. While the performance of our model and tree‐based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes. Plain Language Summary Equations used in hydrologic model are often suboptimal, resulting in reduced prediction accuracy and efficiency. We implemented Kolmogorov‐Arnold networks (KAN), a machine learning algorithm for deriving symbolic formulations, to estimate groundwater recharge and showed that it outperforms an existing state‐of‐the‐art semi‐empirical formulation. In hydrology, Nash‐Sutcliffe efficiency (NSE), root mean squared error (RMSE), and Kling‐Gupta efficiency (KGE) are commonly used to evaluate model performance. Higher NSE and KGE values indicate better performance, while lower RMSE values are preferable. Our results show that NSE increased by 71%, RMSE decreased by 32%, and KGE improved by 25%. In addition, KAN identifies an optimal functional form and can be used to derive new analytical formulas using the prior knowledge. The KAN‐inspired equation outperformed the original formulation and reduced the fitting parameters. Furthermore, we refined the water‐balance equation at the mean‐annual scale and showed that, based on the new water‐balance equation, KAN can derive new formulations that are superior to the original aridity index formulations (up to 105% increase in NSE) and KAN‐derived equations based on the original water balance. These findings highlight the significant potential of KAN to advance the scientific understanding of a wide range of hydrologic processes. Key Points Kolmogorov‐Arnold networks (KANs) enhance interpretability of machine‐learned hydrological models KAN‐derived symbolic formulations outperform state‐of‐the‐art semi‐empirical aridity indices KAN‐identified functional form yields an analytical index with fewer fitting parameters and improved performance

baseflow↗