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Phenomena Identification and Ranking Table (PIRT) for heat pipes

Heat pipes are advanced passive thermal management devices that utilize phase change and capillary action to achieve efficient heat transfer. However, due to the complexity of the phenomena coupled in heat pipes, including capillary, phase change, turbulence, and compressibility effects, there are high uncertainties in the predictability of their operational regimes and performance. This PIRT exercise, conducted as a collaborative effort involving the Department of Energy (DOE) Microreactor Program (MRP), the Nuclear Regulatory Commission (NRC), and university partners systematically identifies, reviews, and prioritizes critical phenomena affecting the operation of heat pipes based on their importance and knowledge levels. Additional analyses and discussion are provided for phenomena with high importance and low knowledge, such as wick de-wetting, critical heat flux, contact angles, and pressure dynamics. The discussions included the recognizing challenges and proposing future research directions for both modeling and simulation and experimental efforts. Additionally, the report addresses phenomena with medium importance and low knowledge that could impact heat pipe operation during non-normal or transient operation, including frozen startup, laminar to turbulent transition, geyser boiling, wick priming, underfilling conditions, surface roughness of the wick, NCGs trapped in the wick, and the timescales of startup and shutdown. In conclusion, this comprehensive evaluation serves as a valuable resource for guiding future research and development efforts, supporting the successful integration of heat pipes into critical applications such as nuclear reactors, and contributing to the advancement of heat pipe technologies in safety-critical industries.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN

QProR: An Efficient Framework for Quantity-of-Interest Based Progressive Retrieval with Guaranteed Error Control

Scientific applications generate an unprecedented volume of data, overwhelming the network and file systems’ bandwidth and posing challenges for efficient and scalable data retrieval and analysis. Progressive data compression offers a promising solution by enabling on-demand retrieval at reduced size. However, existing progressive methods either fail to bound the errors in essential quantities of interest (QoIs) derived from raw data or suffer from suboptimal retrieval efficiency. In this work, we propose QProR, an efficient QoI-based progressive framework that optimizes progressive retrieval for target QoIs. Our key contributions include: (1) a systematic framework that integrates error-controlled lossy compressors with bitplane encoding while decoupling the two processes for high flexibility and adaptability; (2) a novel weighted bitplane encoding method which incorperates QoI knowledge into data refactoring to enhance retrieval efficiency; (3) an optimized retrieval strategy that accounts for the varying impacts of different variables on multivariate QoIs; (4) comprehensive evaluations using six real-world datasets from multiple scientific applications and thorough comparisons against state of the arts. Experimental results demonstrate that QProR achieves up to 80.38% reduction in the retrieval size under the same requested QoI error tolerance, when compared with the best-performing existing methods. When transferring 384 GB of scientific data to remote sites, QProR delivers up to 1.68 × speedup in the end-to-end data transfer performance.

Li, Wenbo [University of Kentucky]

Unidirectional amplification in the frozen mode regime enabled by a nonlinear defect

A stationary inflection point (SIP) is a spectral singularity of the Bloch dispersion relation ω(k) of a periodic structure where the first and the second derivatives of ω with respect to k vanish. An SIP is associated with a third-order exceptional point degeneracy in the spectrum of the unit-cell transfer matrix, where there is a collapse of one propagating and two evanescent Bloch modes. At the SIP frequency, the incident wave can be efficiently converted into the frozen mode with greatly enhanced amplitude and vanishing group velocity. This can be very attractive for applications, including light amplification. Due to its non-resonant nature, the frozen mode regime (FMR) has fundamental advantages over common cavity resonances. Furthermore, we propose, a novel, to the best of our knowledge, scheme for FMR-based unidirectional amplifiers by leveraging a tailored amplification/attenuation mechanism and a single nonlinear defect. The defect breaks the directional symmetry of the periodic structure and enables nonlinearity-related unidirectional amplification/attenuation in the vicinity of the SIP frequency. We demonstrate the robustness of the amplification mechanism to local impurities and parasitic nonlinearity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Oxidation Chemistry of Bicarbonate and Peroxybicarbonate: Implications for Carbonate Management in Energy Storage

Carbonate formation presents a major challenge to energy storage applications based on low-temperature CO 2 electrolysis and recyclable metal–air batteries. While direct electrochemical oxidation of (bi)carbonate represents a straightforward route for carbonate management, knowledge of the feasibility and mechanisms of direct oxidation is presently lacking. Herein, we report the isolation and characterization of the bis(triphenylphosphine)iminium salts of bicarbonate and peroxybicarbonate, thus enabling the examination of their oxidation chemistry. Infrared spectroelectrochemistry combined with time-resolved infrared spectroscopy reveals that the photoinduced oxidation of HCO 3 – by an Ir(III) photoreagent results in the generation of the short-lived bicarbonate radical in less than 50 ns. The highly acidic bicarbonate radical undergoes proton transfer with HCO 3 – to furnish the carbonate radical anion and H 2 CO 3 , leading to the eventual release of CO 2 and H 2 O, thus accounting for the appearance of H 2 O and CO 2 in both electrochemical and photochemical oxidation experiments. Here, the back reaction of the carbonate radical subsequently oxidizes the Ir(II) photoreagent, leading to carbonate. In the absence of this back reaction, dimerization of the carbonate radical provides entry into peroxybicarbonate, which we show undergoes facile oxidation to O 2 and CO 2 . Together, the results reported identify tangible pathways for the design of catalysts for the management of carbonate in energy storage applications.

25 ENERGY STORAGE

Artificial-intelligence-driven shot reduction in quantum measurement

Variational Quantum Eigensolver (VQE) provides a powerful solution for approximating molecular ground state energies by combining quantum circuits and classical computers. However, estimating probabilistic outcomes on quantum hardware requires repeated measurements (shots), incurring significant costs as accuracy increases. Optimizing shot allocation is thus critical for improving the efficiency of VQE. Current strategies rely heavily on hand-crafted heuristics requiring extensive expert knowledge. This paper proposes a reinforcement learning (RL)-based approach that automatically learns shot assignment policies to minimize total measurement shots while achieving convergence to the minimum of the energy expectation in VQE. The RL agent assigns measurement shots across VQE optimization iterations based on the progress of the optimization. This approach reduces VQE's dependence on static heuristics and human expertise. When the RL-enabled VQE is applied to a small molecule, a shot reduction policy is learned. The policy demonstrates transferability across systems and compatibility with other wavefunction Ansätze. In addition to these specific findings, this work highlights the potential of RL for automatically discovering efficient and scalable quantum optimization strategies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

The influence of kinematics of deformation on polycrystalline halite dynamic recrystallization: Full-field simulation of simple shear versus pure shear

Rock salt, composed mainly of halite, flows viscoplastically over a wide range of geological conditions, strongly impacting the dynamic evolution of sedimentary basins and orogens. Understanding how dislocation creep, which involves dislocation glide, intracrystalline recovery and dynamic recrystallization, influences the microstructure and rheology of halite under various deformation kinematics and temperatures is crucial for enhancing knowledge of salt flow dynamics. Here, this study employs a full-field numerical simulation method to compare the viscoplastic deformation of polycrystalline halite under simple shear and pure shear conditions up to a natural strain of ε = 1.5 at temperatures ranging from 100 °C to 300 °C. The results are presented in terms of crystallographic preferred orientation (CPO), grain shape preferred orientation (SPO), subgrain boundary direction, grain size and strain rate distribution. The results indicate that the crystallographic anisotropy of individual halite crystals is transferred to the polycrystalline scale, resulting in strain localization, particularly in simple shear simulations. The kinematics of deformation affect the evolution and distribution of high strain-rate bands, determining the direction of intragranular substructures and the morphology of strain-induced grain boundaries, with minimal impact on grain size. The intensity of grain boundary migration increases with temperature, significantly influencing grain morphology and size, thereby obscuring strain localization, while having little effect on CPOs. At low strain (ε < 1.0), CPOs relative to both the maximum shortening direction and the grain SPO are similar regardless of the deformation kinematics. At high strain (ε > 1.0), simple shear CPOs exhibit three stronger {100} maxima with a monoclinic symmetry relative to the grain SPO compared to the six {100} maxima with an orthotropic symmetry relative to the grain SPO generated under pure shear. Therefore, microstructures and CPOs can serve as indicators of the strain path in polycrystalline halite under various conditions, aiding in determining the shear sense and elucidating the deformation kinematics of salt structures.

58 GEOSCIENCES

Estimating Soil Thermal Inertia Profiles From the Passive Equilibration of a Temperature Probe

Knowledge of the distribution of soil thermal properties is important for understanding subsurface hydrological and biogeochemical processes. This study describes and evaluates quick thermal profiling (QTP), a new measurement technique aimed at providing rapid, depth-resolved measurements of soil thermal inertia at numerous locations across the landscape. A cylindrical probe with temperature sensors at multiple depths is quickly inserted into the ground, and soil thermal inertia is estimated from how quickly the probe temperature equilibrates with the soil. To this end, a finite volume heat transfer model is used to generate temperature equilibration time series across combinations of controlling factors, and a gridded search inversion approach is applied to infer soil thermal inertia. Field tests in the Arctic indicate that QTP measurements have a minimum uncertainty of 0.14 J m −2 K −1 s −1/2 and covary with dual-probe heat pulse thermal analyzer measurements (concordance correlation coefficient = 0.56) with a root-mean-square error of 0.40 J m −2 K −1 s −1/2 . Besides demonstrating the value of QTP for estimating thermal inertia, this study identifies various sources of measurement uncertainty, particularly probe-soil contact resistance and frictional heating. Further, analysis of soil samples indicates that thermal inertia can be used to estimate thermal conductivity and dry bulk density in the studied area, although such inferences are highly site-specific. Overall, the QTP method holds promise to generate thermal inertia data products and to complement other characterization approaches for advancing understanding of soil properties across far more locations than is currently possible.

Lamb, J. R. [Lawrence Berkeley National Laboratory

Tuning the Lifetimes of Photoinduced Deligation in a Metal–Organic Framework via Linker Functionalization

Recently photoinduced dynamic ligation in a metal–organic frameworks (MOFs) was reported, where a long-lived charge-transfer excited state (ca. 30 μs) featuring partial dissociation between the carboxylate linker and metal-based node was probed by time-resolved infrared (TRIR) spectroscopy. The study offers a new mechanistic perspective to evaluate the potential contribution from the excited state molecular configuration to the performance of MOF photocatalysts. In this work, by employing MIL-101(Fe) as the study platform, we have further explored the influence of intramolecular interactions on the stability of relevant excited states and demonstrated the effective tuning of their lifetimes through the incorporation of different functional groups into the system. The correlations between the varied excited state lifetimes and coordination configurations with specific functional groups (−NH 2 or −NO 2 ) was inferred from the analyses of infrared spectroscopic data and theoretical calculations, revealing the essential role of the intramolecular interactions (i.e., between the added functional groups and the carboxylate group) in the modulation of system energetics. Overall, the work presents a pathway to tune the excited state dynamics and expands the knowledge regarding the photoinduced dynamic ligation in carboxylate-based MOFs.

excited states

A machine learning pipeline for identifying infiltration managed aquifer recharge locations from satellite imagery in the San Joaquin Valley, California

This study focuses on an agricultural region in California’s Central Valley, USA, where Managed Aquifer Recharge (MAR) is widely implemented to mitigate groundwater depletion under increasing water demand and climate variability. A deep learning and machine learning framework was developed to identify infiltration-MAR locations using satellite imagery and environmental data. The framework integrates surface water detection from Sentinel-2 imagery, geospatial delineation of water bodies, spatiotemporal tracking of water body dynamics, and supervised classification using meteorological, environmental, and topographic variables. The framework was applied to a 2379 km² study area southwest of Fresno, where 765 water bodies were detected, including 139 identified MAR sites based on publicly available datasets and expert knowledge. The classification model achieved an accuracy of 0.94 and an F1 score of 0.85. Feature importance analysis indicates that cropland, normalized difference vegetation index (NDVI), and evaporation are among the most influential predictors for infiltration-MAR. Notably, the framework suggests that engineered water management in infiltration-MAR systems can disrupt or even reverse the expected positive correlation between surface water extent and precipitation. These findings provide physically interpretable insights into the characteristics of existing infiltration-MAR facilities and demonstrate the potential of the proposed framework as a reproducible, interpretable, and potentially transferable tool for data-driven infiltration-MAR identification and inventory development under growing climatic and hydrological uncertainty.

Classification

ARM Lead Mentor Selection Process

The Atmospheric Radiation Measurement (ARM) Program was created in 1989 with funding from the U.S. Department of Energy (DOE) to develop several highly instrumented ground stations to study cloud-formation processes and their influence on radiative transfer. This scientific infrastructure provides for fixed sites, mobile facilities, an aerial facility, and a data archive available for use by scientists worldwide through the ARM Climate Research Facility—a scientific user facility. The ARM Climate Research Facility currently operates more than 300 instrument systems that provide ground-based observations of the atmospheric column. To keep ARM at the forefront of climate observations, the ARM infrastructure depends heavily on instrument scientists and engineers, known as Mentors. Mentors must have an excellent understanding of instrumentation theory and operation for their instrument areas and have comprehensive knowledge of critical scale-dependent atmospheric processes. They must also possess the technical and analytical skills to develop new data retrievals that provide innovative approaches for creating research-quality data sets. The ARM Facility seeks the best overall qualified candidate, or team when appropriate, that can fulfill Mentor requirements in a timely manner. The roles and responsibilities of the ARM Instrument Operations Manager are provided in Appendix A. The key role and responsibilities and detailed responsibilities of ARM Lead Mentors are provided in Appendix B and Appendix C, respectively.

47 OTHER INSTRUMENTATION

A Copper-Binding Peptide with Therapeutic Potential against Alzheimer′s Disease: From the Blood–Brain Barrier to Metal Competition

Alzheimer’s disease (AD) is the most common form of dementia worldwide. AD brains are characterized by the accumulation of amyloid-β peptides (Aβ) that bind Cu 2+ and have been associated with several neurotoxic mechanisms. Although the use of copper chelators to prevent the formation of Cu 2+ -Aβ complexes has been proposed as a therapeutic strategy, recent studies show that copper is an important neuromodulator that is essential for a neuroprotective mechanism mediated by Cu 2+ binding to the cellular prion protein (PrPC). Therefore, in addition to metal selectivity and blood–brain barrier (BBB) permeability, an emerging challenge for copper chelators is to prevent the formation of neurotoxic Cu 2+ -Aβ species without perturbing the neuroprotective Cu 2+ -PrPC interaction. Previously, we reported the design of a tetrapeptide (TP) that withdraws Cu 2+ from Aβ(1–16) and impacts the Cu 2+ -induced aggregation of Aβ(1–40). In this study, we improved the drug-like properties of TP in a BBB model, evaluated the metal selectivity of the optimized peptide (TP*), and tested its effect on Cu 2+ coordination to PrPC and proteins involved in copper trafficking, such as copper transporter 1 and albumin. Our results show that changing the stereochemistry of the first residue prevents TP degradation in the BBB model and coadministration of TP with a peptide that increases BBB permeability allows its passage through the BBB model. TP* is highly selective toward Cu 2+ in the presence of Zn 2+ ions, transfers Cu 2+ to copper-trafficking proteins, and forms a ternary TP*-Cu 2+ -PrP species that does not perturb the physiological conformation of PrP and displays only a minor impact in the neuroprotective Cu 2+ -dependent interaction of PrPC with the N-methyl-d-aspartate receptor. Overall, these results show that TP* displays desirable features for a copper chelator with therapeutic potential against AD. Moreover, this is the first study that explores the effect of a Cu 2+ chelator with therapeutic potential for AD on Cu 2+ coordination to PrPC (an emerging key player in AD pathology), integrating recent knowledge about metalloproteins involved in AD with the design of copper chelators against AD.

60 APPLIED LIFE SCIENCES

On Stability and Electrochemical Performance of 316 Stainless Steel in Wastewater: Implications for Resource Recovery

Electrochemical nutrient recovery systems rely on stable electrode materials capable of operating in chemically complex wastewater environments. We investigated corrosion resistance and interfacial electrochemical behavior of 316 stainless steel (SS316) in a synthetic wastewater matrix representative of centrate streams, a key knowledge gap in electrochemical phosphorus recovery. A comprehensive suite of electrochemical techniques (chronoamperometry, cyclic voltammetry, potentiodynamic polarization, and electrochemical impedance spectroscopy (EIS)) and surface characterization methods (scanning electron microscopy, X-ray diffraction) were employed. Results revealed that wastewater containing typical ionic constituents (such as PO 4 3- , NH 4 + , and divalent cations) exhibited enhanced cathodic activity and the formation of a more stable, protective surface film on SS316 that mitigated chloride-induced corrosion. In contrast, SS316 in the NaCl solution showed significant susceptibility to passive layer breakdown and localized corrosion. Time-resolved EIS further confirmed improved interfacial stability and restricted charge transfer in WW over time, in stark contrast to the progressive passive layer degradation in NaCl. Surface analyses corroborated these findings, showing limited surface attack in WW compared to distinct localized corrosion features in NaCl. These findings indicate that competing ionic species in WW effectively mitigate chloride aggressiveness, enhance SS316 stability, and demonstrate improved electrode longevity and reliability for sustainable wastewater-based electrochemical phosphorus recovery applications.

36 MATERIALS SCIENCE

Reaction mechanisms for electrical doping of organic semiconductors using complex dopants

Electrical doping of organic semiconductors (OSCs) can be achieved using simple one-electron reductants and oxidants as n- and p-dopants, respectively, but for such dopants, increased doping strength is accompanied by increased sensitivity to ambient moisture and/or oxygen. “Indirect” or “complex” dopants—defined here as those that generate OSC radical cations or anions via pathways more complex than a single simple electron transfer, i.e., by multistep reactions—represent a means of circumventing this problem. Further, this review highlights the importance of understanding the reaction mechanisms by which such dopants operate for: (i) ensuring a researcher knows the composition of a doped material; (ii) predicting the thermodynamic feasibility of achieving doping with related dopant:OSC combinations; and (iii) predicting whether thermodynamically feasible doping reactions are likely to be rapid or slow, or to require subsequent activation. The mechanistic information available to date for some of the wide variety of complex n- and p-dopants that have been reported is then reviewed, emphasizing that in many cases our knowledge is far from complete.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Unifying Combinatorial and Graphical Methods in Artificial Intelligence

Recently, a new graph Laplacian, called the inner product Laplacian, was introduced which generalizes many existing Laplacians, including the normalized and combinatorial Laplacian and their weighted variants. The key observation behind the inner product Laplacian is that by defining appropriate inner product spaces on the vertices and edges, the standard Laplacians can be recovered as Hodge Laplacians over the simplicial complex formed by the edges and vertices. These inner product spaces form a natural way to incorporate non-combinatorial information into the definition of a domain-specific Laplacian. In particular, in contrast to current domain-specific weighting schemes which rely solely on edge weights, information regarding the similarity of non-adjacent vertices and arbitrary pairs of edges can be effectively incorporated into the Laplacian. In order to illustrate this approach we consider the problem of calculating the potential energy of an atomistic configuration using Graph Neural Networks. In comparison with start-of-the-art approaches, such as SchNet, our approach replaces a learned (via auto-encoder) representation of the atom types with an inner product space on atoms based on scientific knowledge (e.g., electronegativity). We will illustrate how this approach captures key chemical properties of the molecules and compare the energy calculations with state-of-the-art neural network approaches. However, to compute the resulting Laplacian involves a mixture of sparse and dense matrix computation and yields a dense matrix as the basis for the graph convolution. This dense convolutional kernel necessitates moving away from the standard message passing framework for graph neural networks and increases the computational cost of applying the kernel. In order to mitigate these costs we investigate means of leveraging the mixed sparse and dense computations to reduce the overall computational cost and how these approaches can be automatically transferred to energy efficient hardware (e.g., field programmable gate arrays (FPGAs)).

97 MATHEMATICS AND COMPUTING

Bimodal Visualization of Industrial X-Ray and Neutron Computed Tomography Data

Advanced manufacturing creates increasingly complex objects with material compositions that are often difficult to characterize by a single modality. Our collaborating domain scientists are going beyond traditional methods by employing both X-ray and neutron computed tomography to obtain complementary representations expected to better resolve material boundaries. However, the use of two modalities creates its own challenges for visualization, requiring either complex adjustments of bimodal transfer functions or the need for multiple views. Together with experts in nondestructive evaluation, we designed a novel interactive bimodal visualization approach to create a combined view of the co-registered X-ray and neutron acquisitions of industrial objects. Using an automatic topological segmentation of the bivariate histogram of X-ray and neutron values as a starting point, the system provides a simple yet effective interface to easily create, explore, and adjust a bimodal visualization. Here, we propose a widget with simple brushing interactions that enables the user to quickly correct the segmented histogram results. Our semiautomated system enables domain experts to intuitively explore large bimodal datasets without the need for either advanced segmentation algorithms or knowledge of visualization techniques. We demonstrate our approach using synthetic examples, industrial phantom objects created to stress bimodal scanning techniques, and real-world objects, and we discuss expert feedback.

image segmentation

Advances in the photon avalanche luminescence of inorganic lanthanide-doped nanomaterials

Photon avalanche (PA)—where the absorption of a single photon initiates a ‘chain reaction’ of additional absorption and energy transfer events within a material—is a highly nonlinear optical process that results in upconverted light emission with an exceptionally steep dependence on the illumination intensity. Over 40 years following the first demonstration of photon avalanche emission in lanthanide-doped bulk crystals, PA emission has been achieved in nanometer-scale colloidal particles. The scaling of PA to nanomaterials has resulted in significant and rapid advances, such as luminescence imaging beyond the diffraction limit of light, optical thermometry and force sensing with (sub)micron spatial resolution, and all-optical data storage and processing. In this review, we discuss the fundamental principles underpinning PA and survey the studies leading to the development of nanoscale PA. Finally, we offer a perspective on how this knowledge can be used for the development of next-generation PA nanomaterials optimized for a broad range of applications, including mid-IR imaging, luminescence thermometry, (bio)sensing, optical data processing and nanophotonics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Evaluation of the Potential for Precipitation of Solids during Storage of Non-Aluminum SNF Solutions

Non-aluminum clad spent nuclear fuels (NASNF) stored in the L-Area basin will be dissolved in H-Canyon using the 6.3D electrolytic dissolver. The solutions will be stored in either the hot or warm canyon until the preparation of a sludge batch for the Defense Waste Processing Facility. Spent nuclear fuel solutions could be stored for 1-2 years before transfer to the H-Area Tank Farm depending on the interval between sludge batches. The solution level in the storage tanks will be maintained; therefore, precipitation of solids due to evaporation is not an issue. However, the precipitation of solids from completely dissolved SNF due to solution instabilities has been observed during intermediate storage of solutions generating hydrated oxides.The presence of fissile material in these solids is generally associated with zirconium molybdate, which is known to act as a host lattice for Pu and can carry the actinides upon precipitation. The formation of zirconium molybdate solids which carry fissile material is a potential concern for the storage of NASNF solutions. To address this concern, the Savannah River National Laboratory performed a literature review to identify knowledge gaps which may require experimental work to determine if the formation of solids is a concern during storage of these solutions. Based on the literature review, the precipitation of zirconium molybdate solids from the Campaign 1 NASNF solutions during intermediatestorage is expected. This conclusion is supported by the identification of zirconium molybdate solids found on the H-Canyon 6.1D Dissolver MK-12 insert spacer. The formation of the zirconium molybdate solids is attributed to hydrolysis and radiolytic processes in the nitric acid solution. As the molybdate solids form, U and Pu can substitute for Zr in the crystal lattice resulting in co-precipitation. Generally, the Pu substitutes directly into the crystal lattice during precipitation while the U associated with the molybdate solids more likely absorbs from the solution. The U in the NASNF solutions is present as uranyl nitrate, a 2+ cation which will not substitute as easily into the molybdate crystal lattice for the Zr 4+ ion.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W

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