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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A unified ensemble soil moisture dataset across the continental United States

Abstract A unified ensemble soil moisture (SM) package has been developed over the Continental United States (CONUS). The data package includes 19 products from land surface models, remote sensing, reanalysis, and machine learning models. All datasets are unified to a 0.25-degree and monthly spatiotemporal resolution, providing a comprehensive view of surface SM dynamics. The statistical analysis of the datasets leverages the Koppen-Geiger Climate Classification to explore surface SM’s spatiotemporal variabilities. The extracted SM characteristics highlight distinct patterns, with the western CONUS showing larger coefficient of variation values and the eastern CONUS exhibiting higher SM values. Remote sensing datasets tend to be drier, while reanalysis products present wetter conditions. In-situ SM observations serve as the basis for wavelet power spectrum analyses to explain discrepancies in temporal scales across datasets facilitating daily SM records. This study provides a comprehensive soil moisture data package and an analysis framework that can be used for Earth system model evaluations and uncertainty quantification, quantifying drought impacts and land–atmosphere interactions and making recommendations for drought response planning.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Inferring Plant Acclimation and Improving Model Generalizability With Differentiable Physics‐Informed Machine Learning of Photosynthesis

Net photosynthesis (A N ) is a key component of the global carbon cycle influencing climate feedback over decadal scales. Although plant acclimation to environmental changes can modify A N , traditional vegetation models in Earth system models (ESMs) often rely on plant functional type (PFT)-specific parameterizations or simplified acclimation assumptions limiting generalizability across time, space, and PFTs. In this study, we developed a differentiable photosynthesis model to learn the environmental dependencies of V c,max25 (maximum carboxylation rate at 25°C, representing photosynthetic capacity), as this genre of hybrid physics-informed machine learning can seamlessly train neural networks and process-based equations together. Compared to PFT-specific parameterization of V c,max25 , learning the environment dependencies of key photosynthetic parameters improved model spatiotemporal generalizability. Applying environmental acclimation to V c,max25 led to substantial variations in global mean A N indicating the need to address acclimation in ESMs. The model effectively captured multivariate observations (V c,max25 , A N , and stomatal conductance (g s )) simultaneously with multivariate constraints, improving generalization across space and PFTs. It also learned sensible acclimation relationships of V c,max25 to different environmental conditions. The model explained more than 54%, 57%, and 62% of the variance of A N , g s , and V c,max25 , respectively, presenting a first global-scale spatial test benchmark of A N and g s . These results highlight the potential for differentiable modeling to enhance process-based modules in ESMs and effectively leverage information from large, multivariate data sets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Technical Assessment of the Application of Digital Twin and Prognostic Tools for Condition Monitoring

This report was prepared for the U.S. Nuclear Regulatory Commission (NRC) to present use cases of the application of advanced technologies toward meeting the current and future regulatory requirements for maintenance and condition monitoring of structures, systems, and components (SSCs). The advanced technologies considered in this work, collectively referred to as digital twin (DT) technologies, are advanced sensors and instrumentation, data analytics, machine learning and artificial intelligence (ML/AI), and physics-based models. The report presents two use cases of reactor coolant pumps (RCPs) and heat pipes in nuclear power plants (NPPs) with technical and regulatory considerations and opportunities in using advanced technologies for conditional monitoring. Key findings from the exploration of these considerations are as follows: - Uncertainties in sensor data and model predictions must be rigorously addressed through validation and verification processes - Regulatory compliance is paramount, necessitating data driven models to be developed in line with existing codes and standards, as well as considering potential future guidelines for advanced reactors - Explainability and transparency in ML/AI models are essential for developing operator trust and regulatory review, including methods that enhance the interpretability of complex data-driven predictions - Condition monitoring programs must be evaluated for their effectiveness in reducing maintenance-preventable function failures (MPFF) and aligning with plant performance criteria - The deployment of advanced technologies for condition monitoring could lead to a transition from periodic to continuous monitoring, thereby optimizing maintenance schedules - Collaborative efforts between industry stakeholders, regulatory bodies, and technology developers are crucial for the successful adoption of advanced technologies for condition monitoring systems in nuclear facilities In summary, the introduction of advanced technologies into condition monitoring programs represents a significant leap forward in the domain of NPP maintenance. By harnessing the capabilities of advanced sensors, data analytics, and ML/AI, NPP operators can transition from a time-based to a condition-based maintenance approach. This shift can potentially enhance the reliability and safety of critical plant components while optimizing maintenance efforts and minimizing unnecessary outages. The NRC is continuing to explore the regulatory aspects of advanced technologies as part of inservice inspection and inservice testing (ISI and IST) programs by pursuing additional research in this technical area.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Gold–Thiolate Nanocluster Dynamics and Intercluster Reactions Enabled by a Machine Learned Interatomic Potential

Monolayer protected metal clusters comprise a rich class of molecular systems and are promising candidate materials for a variety of applications. While a growing number of protected nanoclusters have been synthesized and characterized in crystalline forms, their dynamical behavior in solution, including prenucleation cluster formation, is not well understood due to limitations both in characterization and first-principles modeling techniques. Recent advancements in machine-learned interatomic potentials are rapidly enabling the study of complex interactions such as dynamical behavior and reactivity on the nanoscale. Here, we develop an Au-S-C-H atomic cluster expansion (ACE) interatomic potential for efficient and accurate molecular dynamics simulations of thiolate-protected gold nanoclusters (Au n (SCH 3 ) m ). Trained on more than 30,000 density functional theory calculations of gold nanoclusters, the interatomic potential exhibits ab initio level accuracy in energies and forces and replicates nanocluster dynamics including thermal vibration and chiral inversion. Long dynamics simulations (up to 0.1 μs time scale) reveal a mechanism explaining the thermal instability of neutral Au 25 (SR) 18 clusters. Specifically, we observe multiple stages of isomerization of the Au 25 (SR) 18 cluster, including a chiral isomer. Additionally, we simulate coalescence of two Au 25 (SR) 18 clusters and observe series of clusters where the formation mechanisms are critically mediated by ligand exchange in the form of [Au-S] n rings.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Biopolymer-Templated Titania Film Formation for Nanostructured Coatings Revealed by Machine Learning-Supported Time-Resolved Analysis

This study presents a machine learning approach to derive the film formation of biopolymer-templated titania nanostructures during spray deposition, in combination with in situ grazing-incidence small-angle X-ray scattering (GISAXS). A neural network trained on synthetic GISAXS data directly predicts domain-size distributions from experimental two-dimensional scattering patterns, capturing the full kinetics of nanostructure evolution with high temporal resolution. The predictions reveal hierarchical size distributions and periodic growth features, consistent with layer-by-layer spray deposition and validated by complementary scanning electron microscopy (SEM) imaging. Quantitative comparison with conventional parametric GISAXS fits shows good qualitative agreement, with systematic differences explained by domain-shape assumptions and resolved by applying a geometric scaling factor. Simulated SEM-like surfaces derived from neural network outputs reproduce the porous, foam-like nanoscale morphology observed experimentally, reinforcing the method’s credibility. This integrated approach enables real-time, nondestructive, statistically averaged monitoring of bulk nanostructure development in functional coatings, offering a scalable methodology to accelerate the characterization and process control of sustainably manufactured nanostructured titania films for energy-related applications such as photocatalysis and photovoltaics.

Heger, JulianEliah↗
DOE OSTI2024

On the compatibility of established methods with emerging artificial intelligence and machine learning methods for disaster risk analysis

Abstract There is growing interest in leveraging advanced analytics, including artificial intelligence (AI) and machine learning (ML), for disaster risk analysis (RA) applications. These emerging methods offer unprecedented abilities to assess risk in settings where threats can emerge and transform quickly by relying on “learning” through datasets. There is a need to understand these emerging methods in comparison to the more established set of risk assessment methods commonly used in practice. These existing methods are generally accepted by the risk community and are grounded in use across various risk application areas. The next frontier in RA with emerging methods is to develop insights for evaluating the compatibility of those risk methods with more recent advancements in AI/ML, particularly with consideration of usefulness, trust, explainability, and other factors. This article leverages inputs from RA and AI experts to investigate the compatibility of various risk assessment methods, including both established methods and an example of a commonly used AI‐based method for disaster RA applications. This article utilizes empirical evidence from expert perspectives to support key insights on those methods and the compatibility of those methods. This article will be of interest to researchers and practitioners in risk‐analytics disciplines who leverage AI/ML methods.

Mathematical Methods In Social Sciences↗
DOE OSTI2025

On the Need to Align Intent and Implementation in Uncertainty Quantification for Machine Learning

Quantifying uncertainties for machine learning (ML) models is a foundational challenge in modern data analysis. This challenge is compounded by at least two key aspects of the field: (a) inconsistent terminology surrounding uncertainty and estimation across disciplines, and (b) the varying technical requirements for establishing trustworthy uncertainties in diverse problem contexts. In this position paper, we aim to clarify the depth of these challenges by identifying these inconsistencies and articulating how different contexts impose distinct epistemic demands. We examine the current landscape of estimation targets (e.g., prediction, inference, simulation-based inference), uncertainty constructs (e.g., frequentist, Bayesian, fiducial), and the approaches used to map between them. Drawing on the literature, we highlight and explain examples of problematic mappings. To help address these issues, we advocate for standards that promote alignment between the \textit{intent} and \textit{implementation} of uncertainty quantification (UQ) approaches. We discuss several axes of trustworthiness that are necessary (if not sufficient) for reliable UQ in ML models, and show how these axes can inform the design and evaluation of uncertainty-aware ML systems. Our practical recommendations focus on scientific ML, offering illustrative cases and use scenarios, particularly in the context of simulation-based inference (SBI).

Trivedi, Shubhendu [MIT] (ORCID:0000000312374301)↗
DOE OSTI2024

Towards verifiable cancer digital twins: tissue level modeling protocol for precision medicine

Cancer exhibits substantial heterogeneity, manifesting as distinct morphological and molecular variations across tumors, which frequently undermines the efficacy of conventional oncological treatments. Developments in multiomics and sequencing technologies have paved the way for unraveling this heterogeneity. Nevertheless, the complexity of the data gathered from these methods cannot be fully interpreted through multimodal data analysis alone. Mathematical modeling plays a crucial role in delineating the underlying mechanisms to explain sources of heterogeneity using patient-specific data. Intra-tumoral diversity necessitates the development of precision oncology therapies utilizing multiphysics, multiscale mathematical models for cancer. This review discusses recent advancements in computational methodologies for precision oncology, highlighting the potential of cancer digital twins to enhance patient-specific decision-making in clinical settings. We review computational efforts in building patient-informed cellular and tissue-level models for cancer and propose a computational framework that utilizes agent-based modeling as an effective conduit to integrate cancer systems models that encode signaling at the cellular scale with digital twin models that predict tissue-level response in a tumor microenvironment customized to patient information. Furthermore, we discuss machine learning approaches to building surrogates for these complex mathematical models. These surrogates can potentially be used to conduct sensitivity analysis, verification, validation, and uncertainty quantification, which is especially important for tumor studies due to their dynamic nature.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Conductivity Spectroscopy for Investigation and Discovery of Photovoltaic Materials

Conductivity spectroscopy is an extremely powerful set of methods for probing the properties of optoelectronic materials, especially photovoltaics, where photoconductivity is one of the best spectroscopic proxies for performance. Despite this power, they are substantially less commonly used than time-resolved photoluminescence (for instance) because they tend to be more expensive to implement (THz) and/or require specialized knowledge (GHz) to construct instruments, which are not widely available. The goal of this review is to illustrate the utility of these experiments in the discovery and study of photovoltaic absorber materials and simultaneously make them more accessible to the community by providing a central tutorial resource. We provide a comprehensive review of how conductivity spectroscopy has developed over the past decade and been applied in the discovery and development of photovoltaic materials, with a primary focus on emerging solution-processable technologies. Along the way we aim to demystify conductivity spectroscopy with focused tutorial sections that explain the physical models used to fit the data and illustrate how to think about “high-frequency conductivity”.

14 SOLAR ENERGY↗
DOE OSTI2025

Uncertainty Quantification for Data-Driven Machine Learning Models in Nuclear Engineering Applications: Where We Are and What Do We Need?

Machine learning (ML) has been leveraged to tackle a diverse range of tasks in almost all branches of nuclear engineering. Many of the successes in ML applications can be attributed to the recent performance breakthroughs in deep learning, the growing availability of computational power, data, and easy-to-use ML libraries. However, these empirical successes have often outpaced our formal understanding of the ML algorithms. An important but under-rated area is uncertainty quantification (UQ) of ML. ML-based models are subject to approximation uncertainty when they are used to make predictions, due to sources including but not limited to, data noise, data coverage, extrapolation, imperfect model architecture and the stochastic training process. The goal of this paper is to clearly explain and illustrate the importance of UQ of ML. We will elucidate the differences in the basic concepts of UQ of physics-based models and data-driven ML models. Various sources of uncertainties in physical modeling and data-driven modeling will be discussed, demonstrated, and compared. We will also present and demonstrate a few techniques to quantify the ML prediction uncertainties, including Monte Carlo dropout, deep ensemble, Bayesian neural networks, Gaussian Processes and conformal prediction. Lastly, we will discuss the need for building a verification, validation and UQ framework to establish ML credibility.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Generative Models for Crystalline Materials

Understanding structure-property relationships in materials is fundamental in condensed matter physics and materials science. Over the past few years, machine learning (ML) has emerged as a powerful tool for advancing this understanding and accelerating materials discovery. Early ML approaches primarily focused on constructing and screening large material spaces to identify promising candidates for various applications. More recently, research efforts have increasingly shifted toward generating crystal structures using end-to-end generative models. This review analyzes the current state of generative modeling for crystal structure prediction and de novo generation. It examines crystal representations, outlines the generative models used to design crystal structures, and evaluates their respective strengths and limitations. Furthermore, the review highlights experimental considerations for evaluating generated structures and provides recommendations for suitable existing software tools. Emerging topics, such as modeling disorder and defects, integration in advanced characterization, incorporating synthetic feasibility constraints, and model explainability are explored. Ultimately, this work aims to inform both experimental scientists looking to adapt suitable ML models to their specific circumstances and ML specialists seeking to understand the unique challenges related to inverse materials design and discovery.

Metni, Houssam [Karlsruhe Inst. of Technology (KIT↗
DOE OSTI2024

Observational benchmarks inform representation of soil organic carbon dynamics in land surface models

Abstract. Representing soil organic carbon (SOC) dynamics in Earth system models (ESMs) is a key source of uncertainty in predicting carbon–climate feedbacks. Machine learning models can help identify dominant environmental controllers and establish their functional relationships with SOC stocks. The resulting knowledge can be integrated into ESMs to reduce uncertainty and improve predictions of SOC dynamics over space and time. In this study, we used a large number of SOC field observations (n=54 000), geospatial datasets of environmental factors (n=46), and two machine learning approaches (namely random forest, RF, and generalized additive modeling, GAM) to (1) identify dominant environmental controllers of global and biome-specific SOC stocks, (2) derive functional relationships between environmental controllers and SOC stocks, and (3) compare the identified environmental controllers and predictive relationships with those in models used in Phase 6 of the Coupled Model Intercomparison Project (CMIP6). Our results showed that the diurnal temperature, drought index, cation exchange capacity, and precipitation were important observed environmental predictors of global SOC stocks. While the RF model identified 14 environmental factors that describe climatic, vegetation, and edaphic conditions as important predictors of global SOC stocks (R2=0.61, RMSE = 0.46 kg m−2), current ESMs oversimplify the relationships between environmental factors and SOC, with precipitation, temperature, and net primary productivity explaining > 96 % of the variability in ESM-modeled SOC stocks. Further, our study revealed notable disparities among the functional relationships between environmental factors and SOC stocks simulated by ESMs compared with observed relationships. To improve SOC representations in ESMs, it is imperative to incorporate additional environmental controls, such as the cation exchange capacity, and refine the functional relationships to align more closely with observations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Chromium-doped uranium dioxide fuels: A review

UO 2 doped with parts per million CR 2 O 3 powder is considered a potential near term accident tolerant fuel candidate. Here, the results of decades of industry and academic research into Cr-doped UO 2 are analyzed and their shortcomings are critiqued. Focusing on the incorporation mechanisms of Cr into the fuel matrix, we explore a mechanistic understanding of the characteristic properties of Cr-doped UO 2 , notably, enhanced fission gas retention attributed to enlarged grain sizes following sintering, along with marginal improvements in the thermophysical properties. The findings of recent X-ray Adsorption Near Edge Spectroscopy studies were compared and put into conversation with historic data regarding the incorporation of Cr in UO 2 . On the basis of defect mechanisms, the case is made for the substitutional incorporation of Cr governing the lattice solubility but not the enhanced U diffusivity. Instead, Cr/CR 2 O 3 redox chemistry in a well-defined oxygen potential explains the differences in the U diffusivity and O/M ratio. The primary mechanism of doping enhanced grain growth is found to be liquid assisted sintering due to a CRO (1) eutectic phase at the grain boundaries. The role of inhomogeneities in Cr concentration in UO 2 at various length scales across the materials microstructure is highlighted and connected to promising experimental and modeling work to fill in the gaps in the current understanding of Cr-doped UO 2 . The review considers both the open scientific questions and engineering applications to illustrate the deep connections between the practice and theory in the design of accident tolerant nuclear fuels. In conclusion, the review ends with an outline of future works that combine meticulous irradiation studies and high resolution experiments with next generation modeling and simulations techniques empowered by machine learning advances to accelerate the fabrication and adoption of Cr-doped UO 2 light water reactors.

Cleveland, Mack Wesley [Massachusetts Inst. of Tec↗
DOE OSTI2025

Descriptors for Cu facets for CO2 reduction reaction activity

Computation screening is crucial for designing efficient electrochemical catalysts for carbon dioxide (CO2R) reduction to valuable hydrocarbons and oxygenates. Herein, leveraging density functional theory calculations of the CO adsorption energy ΔE_CO on seventeen Cu terminations, we discover a strong linear correlation between ΔE_CO and the recently experimentally measured CO2R electrochemical currents (ACS Catal. 2022, 12, 11, 6578–6588). Examining the ab initio thermodynamics of the early critical intermediates CO*, COH*, and CHO*, we find that CO* → CHO* is the thermodynamically preferred step, and notably shows a volcano trend with the experimental currents where the maximum CO2R current corresponds to the moderate CHO* formation energy. Importantly, we show that increasing the step and kink density of the Cu termination not only enhances CO adsorption strength but also modulates the CO* → CHO* pathway, as respectively exemplified in the (941) and (741) facets. We also explain why (741) is exceptional with high CO2R activity as measured experimentally due to its relatively low activity toward the hydrogen evolution reaction compared with the other Cu surfaces. Beyond the general CO adsorption energy that only shows a linear trend with CO2R activity, we show that the reaction CO* → CHO* free energy is a descriptor that displays a volcano relationship with the overall CO2R activity on Cu facets.

machine learning↗
DOE OSTI2025

Machine Learning Analysis of Temperature-Strain Relationships for Structural Health Monitoring of Pipes: Self-powered wireless sensor system for health monitoring of liquid-sodium cooled fast reactors

This report presents machine learning (ML) analysis of temperature-strain relationships for structural health monitoring of nuclear reactor stainless steel (SS) pipes with the strain gauge sensor directly printed on the pipe with a 3D conformal aerosol jet printer. We investigate correlations for two sensor pairs installed on the same SS304 pipe: commercial K-type thermocouple with a printed gold strain gauge (TC3-SG3), and commercial K-type thermocouple with commercial Kyowa strain gauge (TC0-SG0). The temperature ranges for the sensor pairs TC0-SG0 and TC3-SG3 are 20.00°C to 266.37°C and 39.95°C to 219.28°C respectively. ML algorithms in this study include Linear Regression (baseline method), Ridge Regression, Lasso Regression, and Gradient Boosting. Performance evaluation metrics include Root Mean Square Error (RMSE), Mean Square Error (MSE), Mean Absolute Error (MAE), R 2 Score, and Explained Variance. Using advanced feature engineering techniques, we extracted 27 temperature-based features and 30 strategic inclusion features. The best performance was obtained with the Gradient Boosting method, which achieves prediction accuracy of R 2 = 0.9999 and RMSE = 7.69 μStrain for TC0-SG0, and R 2 = 0.9998 and RMSE = 18.03 μStrain for TC3-SG3. While the temperature-strain correlations are weaker for the gauge directly printed on the pipe than for the commercial strain gauge, deployment-ready performance exceeding industry standards is achieved for both sensor pairs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Monitoring of Liquid Metal Reactor Heater Zones with Recurrent Neural Network Learning of Temperature Time Series

Advanced high-temperature fluid reactors (ARs), such as sodium fast reactors (SFRs) and molten salt cooled reactors (MSCRs) utilize high-temperature fluids at ambient pressure. To melt the fluid during reactor startup and prevent fluid freezing during cooldown, the thermal–hydraulic systems of such ARs include heater zones consisting of specific heaters with controllers, temperature sensors, and thermal insulation. The failure of heater zones due to insulation material degradation or improper installation, resulting in parasitic heat losses, can lead to fluid freezing. The detection of faults using a heat-transfer model is difficult because of a lack of knowledge of the experimental details. Data-driven machine learning of heater zone temperature time series offers a viable alternative. In this study, we benchmarked the performance of recurrent neural networks (RNNs) in an analysis of heat-up transient temperature time series of heater zones installed on a liquid sodium vessel. The RNN models include long short-term memory (LSTM) and gated recurrent unit (GRU) networks, as well as their bi-directional variants, BiLSTM and BiGRU. Anomalous temperature points were designated using a percentile-based threshold applied to residual fluctuations in the detrended temperature time series. Additionally, the impact of the exponentially weighted moving average (EWMA) method on detection accuracy was examined. The RNN models’ performance was assessed using precision, recall, and F 1 score metrics. Results demonstrated that RNN models effectively detect anomalies in temperature time series with the best models for each heater zone achieving F 1 scores of over 93%. To explain the variations in RNN model performance across different heater zones, we used Kullback–Leibler (KL) divergence to quantify the relative entropy between training and testing data, and the Detrended Fluctuation Analysis (DFA) to assess long-range temporal correlations. For datasets with strong long-range correlations and minimal relative entropy between training and testing data, GRU is the best-performing model. When the data exhibits weaker long-term correlations and a significant relative entropy between training and testing distributions, BiGRU shows the best performance. For the data sets with intermediate values of both KL divergence and DFA, the best performance is obtained with LSTM and BiLSTM, respectively.

gated recurrent unit↗
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↗