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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning

This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov–Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure of UQ, enhancing interpretability and robustness in modeling complex functions. Building on this, we introduce Conformalized-KANs, which integrate conformal prediction, a distribution-free UQ technique, with KAN ensembles to generate calibrated prediction intervals with guaranteed coverage.} Extensive numerical experiments are conducted to evaluate the effectiveness of these methods, focusing particularly on the robustness and accuracy of the prediction intervals under various hyperparameter settings. We show that the conformal KAN predictions can be applied to recent extensions of KANs, including Finite Basis KANs (FBKANs) and multifideilty KANs (MFKANs). The results demonstrate the potential of our approaches to significantly improve the reliability and applicability of KANs in scientific machine learning.

• Artificial intelligence (AI) / machine learning ↗
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↗
DOE OSTI2025

SPIKANs: separable physics-informed Kolmogorov–Arnold networks

Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture, recent advancements have explored alternative neural network structures. One such innovation is the Kolmogorov–Arnold Network (KAN), which has demonstrated benefits over traditional MLPs, including faster neural scaling and better interpretability. The application of KANs to physics-informed learning has led to the development of Physics-Informed KANs (PIKANs), enabling the use of KANs to solve PDEs. However, despite their advantages, KANs often suffer from slower training speeds, particularly in higher-dimensional problems where the number of collocation points grows exponentially with the dimensionality of the system. To address this challenge, we introduce Separable Physics-Informed Kolmogorov–Arnold Networks (SPIKANs). This novel architecture applies the principle of separation of variables to PIKANs, decomposing the problem such that each dimension is handled by an individual KAN. This approach drastically reduces the computational complexity of training without sacrificing accuracy, facilitating their application to higher-dimensional PDEs. Through a series of benchmark problems, we demonstrate the effectiveness of SPIKANs, showcasing their superior scalability and performance compared to PIKANs and highlighting their potential for solving complex, high-dimensional PDEs in scientific computing.

Kolmogorov-Arnold networks↗
DOE OSTI2025

SineKAN: Kolmogorov-Arnold Networks using sinusoidal activation functions

Recent work has established an alternative to traditional multi-layer perceptron neural networks in the form of Kolmogorov-Arnold Networks (KAN). The general KAN framework uses learnable activation functions on the edges of the computational graph followed by summation on nodes. The learnable edge activation functions in the original implementation are basis spline functions (B-Spline). Here, we present a model in which learnable grids of B-Spline activation functions are replaced by grids of re-weighted sine functions (SineKAN). We evaluate numerical performance of our model on a benchmark vision task. We show that our model can perform better than or comparable to B-Spline KAN models and an alternative KAN implementation based on periodic cosine and sine functions representing a Fourier Series. Further, we show that SineKAN has numerical accuracy that could scale comparably to dense neural networks (DNNs). Compared to the two baseline KAN models, SineKAN achieves a substantial speed increase at all hidden layer sizes, batch sizes, and depths. Current advantage of DNNs due to hardware and software optimizations are discussed along with theoretical scaling. Additionally, properties of SineKAN compared to other KAN implementations and current limitations are also discussed.

Reinhardt, Eric↗
DOE OSTI2025

Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks

Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they often suffer from overfitting due to their large number of parameters. Kolmogorov-Arnold networks (KANs) offer an alternative solution with fewer parameters. However, gradient-based inference methods, such as Hamiltonian Monte Carlo (HMC), may result in computational inefficiency when applied to KANs, especially for large-scale datasets, due to the high cost of back-propagation. To address these challenges, we propose a novel approach, combining the dropout Tikhonov ensemble Kalman inversion (DTEKI) with Chebyshev KANs. This gradient-free method effectively mitigates overfitting and enhances numerical stability. In addition, we incorporate the active subspace method to reduce the parameter-space dimensionality, allowing us to improve the accuracy of predictions and obtain more reliable uncertainty estimates. Extensive experiments demonstrate the efficacy of our approach in various test cases, including scenarios with large datasets and high noise levels. Our results show that the new method achieves comparable or better accuracy, much higher efficiency as well as stability compared to HMC, in addition to scalability. Moreover, by leveraging the low-dimensional parameter subspace, our method preserves prediction accuracy while substantially reducing further the computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Scattering-based structural inversion of soft materials via Kolmogorov–Arnold networks

Small-angle scattering techniques are indispensable tools for probing the structure of soft materials. However, traditional analytical models often face limitations in structural inversion for complex systems, primarily due to the absence of closed-form expressions of scattering functions. To address these challenges, we present a machine learning framework based on the Kolmogorov–Arnold Network (KAN) for directly extracting real-space structural information from scattering spectra in reciprocal space. This model-independent, data-driven approach provides a versatile solution for analyzing intricate configurations in soft matter. By applying the KAN to lyotropic lamellar phases and colloidal suspensions—two representative soft matter systems—we demonstrate its ability to accurately and efficiently resolve structural collectivity and complexity. Here, our findings highlight the transformative potential of machine learning in enhancing the quantitative analysis of soft materials, paving the way for robust structural inversion across diverse systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Kolmogorov-Arnold wavefunctions

Here, this work investigates Kolmogorov-Arnold network-based (KAN) wave-function Ansätz as viable representations for quantum Monte Carlo simulations. Through systematic analysis of one-dimensional model systems, we evaluate their computational efficiency and representational power against established methods. Our numerical experiments suggest some efficient training methods and we explore how the computational cost scales with desired precision, particle number, and system parameters. Roughly speaking, KANs seem to be 10 times cheaper computationally than other neural-network-based Ansätz . We also introduce a novel approach for handling strong short-range potentials—a persistent challenge for many numerical techniques—which generalizes efficiently to higher-dimensional, physically relevant systems with short-ranged strong potentials common in atomic and nuclear physics.

1-dimensional systems↗
DOE OSTI2025

Moltensaltpropnet

MoltenSaltPropnet is a physics-informed machine learning framework that aims to predict the thermophysical properties of molten fluoride and chloride salt mixtures, which are crucial for the design and safety of Generation IV molten salt reactors. The code processes data from the Molten-Salt Thermal Properties Database (MSTDB-TP) and the Janz compendium, converting critically evaluated correlations into fast, differentiable surrogate models for density, viscosity, thermal conductivity, and heat capacity across 448 distinct salt systems. The implementation consists of several key components: 1. Data Curation: The code parses and cleans the raw data, normalizing elemental mole fractions and extracting relevant regression coefficients for various thermophysical properties. 2. Feature Engineering: It generates fixed-length numerical descriptors that encapsulate the composition and temperature, incorporating polynomial interaction terms and dimensionality-reduction techniques to optimize model performance. 3. Coefficient Learning: Four different machine learning architectures are employed: a deep residual network (ResNet), a Kolmogorov–Arnold network (KAN), a sparsity-inducing neural network (SNN), and classical regression models. Each model learns to predict coefficients that define the temperature-dependent correlations for the thermophysical properties. 4. Property Reconstruction: The predicted coefficients are used to compute temperature-dependent property values, ensuring positivity and monotonic trends through a composite loss function that enforces physical constraints. 5. User Interface: An open-source web application enables users to filter the database, train task-specific models, and visualize the results, allowing for rapid exploration of candidate salt mixtures. MoltenSaltPropnet bridges the gap between limited experimental data and high-fidelity reactor simulations, providing a powerful tool for researchers in the field of molten salt reactors and advanced nuclear energy systems.

Retamales, Mauricio Eduardo Tano [Idaho National L↗
DOE OSTI2025

MassIVE MSV000095714

Proteomic analysis reveals translation-related proteins are significantly altered in response to stabilized G4s. Identification of the importance of translation factors in overcoming G4s led to the question of how E. coli cells generally respond to chemicals that stabilize such structures. As a first step in addressing this question, a proteomic analysis was carried out to measure the quantitative effects of NMM on the levels of individual proteins in E. coli. Protein levels from early log-phase cultures of delta-tolC and delta-tolC tufA::kan strains grown in the presence or absence of NMM were measured to assess how reduced EF- Tu levels and NMM impacted expression.

Bottom-up proteomics↗
DOE OSTI2024

Altering translation allows E. coli to overcome chemically stabilized G-quadruplexes

To investigate the effects of stabilizing G-quadruplexes on Escherichia coli, cells were grown in the presence of the G-quadruplex stabilizing compound, NMM, and RNA-seq was performed. This was done for the control cell strain (MG1655 dtolC) as well as a strain with a decrease in a translation elongation factor (MG1655 dtolC tufA::kan). TPM values were used for differential gene expression analysis between each growth condition. All samples were grown and sequenced in triplicate.

Keck, James L.↗
DOE OSTI2024

Direct and Inverse Photoelectron Spectroscopy Evidence for a Revised Picture of Electronic States of Negative Polarons in n‐Doped C 60

Abstract Determining the electronic levels associated with polarons, the fundamental charge carriers in organic semiconductors, is key to understanding the charge transport properties of these materials. Recent findings challenge the traditional view of these electronic levels by highlighting the importance of intra‐molecular Coulomb interactions in polarons. Experimental evidence was previously presented for a revised model of the negative polaron in the case of the polymer semiconductor poly(NDI2OD‐T 2 ); there, the addition of an excess electron was seen to lead to the emergence of a singly occupied state within the energy gap of the undoped material and an unoccupied state above the edge of the conduction states . Here, focus is on a small‐molecule semiconductor, C 60 , and spectral evidence is provided of a similar picture for the new states appearing upon polaron formation. Specifically, direct and inverse photoemission spectroscopy is used to investigate the density of states in C 60 films n‐doped with two dimeric dopants. The Coulomb interaction energy (Hubbard U ) of the C 60 anion is experimentally determined to be ≈1.1 eV, a value that aligns closely with theoretical predictions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Regulation of Side‐Chain Symmetry for Delaying Triplet Formation and Suppressing Non‐Radiative Loss in Organic Solar Cells

Abstract The structural revolutions of non‐fullerene acceptors (NFAs) have driven continuous efficiency breakthroughs in organic solar cells (OSCs). Rational regulation of NFA structures toward efficient exciton dissociation and mitigated non‐radiative recombination is pivotal for OSCs. The incorporation of asymmetric side chains on NFAs can often achieve these goals by inducing a desirable aggregate state. However, it lacks the studies to directly correlate the side‐chain symmetry of NFAs with the exciton delocalization and triplet dynamics in OSCs. Herein, The influence of structural symmetry on the aggregate properties is systematically investigated and exciton/charge dynamics based on two developed biaxial‐conjugated NFAs with varied side‐chain symmetry. The symmetric NFA having diverse molecular packing orientations can form multiple charge transfer channels in its blend with polymer donor, which cannot be found in that comprising the asymmetric ones. Moreover, a slower rate and lower ratio of the spin‐triplet state are formed in the blend of symmetric NFA, resulting in a much lower non‐radiative voltage loss in corresponding OSCs. This study reveals the distinct advantages of symmetric NFAs in both aggregate properties and exciton/charge dynamics over those of asymmetric ones, paving the way for developing high‐performance OSCs using easier‐to‐prepare, low‐cost symmetric materials.

Chemistry↗
DOE OSTI2025

In situ self-ion (Fe + ) irradiation of ODS-FeCrAl alloy fuel cladding materials with different Cr contents: The early stages of Cr-rich α’ phase precipitation

Oxide-dispersion-strengthened FeCrAl (ODS-FeCrAl) alloys are candidate accident-tolerant fuel cladding materials for light water reactors because they demonstrate satisfactory resistance to materials degradation effects such as high-temperature oxidation, radiation-induced swelling, and creep. Their perspective deployment to market is challenged, however, by their inherent susceptibility to irradiation embrittlement caused by the precipitation of the brittle Cr-rich α’ phase at relatively low temperatures (≤475 °C). This work used in situ self-ion irradiation (150 keV Fe + ) in a transmission electron microscope to elucidate the early stages of Cr-rich α’ phase precipitation in three candidate ODS-FeCrAl alloy fuel cladding materials with different Cr contents (10, 12, and 20 wt.%) and microstructures. The early stages of the process resulting in the precipitation of the Cr-rich α’ phase in these three ODS-FeCrAl alloys under Fe + irradiation were investigated at room temperature and 300 °C up to total fluences of 1.7 × 10 15 ions·cm -2 (2 dpa) and 3.4 × 10 15 ions·cm -2 (4 dpa), using three damage dose rates (5 × 10 –5 , 3.3 × 10 –4 , and 2 × 10 –3 dpa·s -1 ). Post-irradiation examination via scanning transmission electron microscopy, energy-dispersive X-ray spectroscopy and electron energy loss spectroscopy suggested that the precipitation of the Cr-rich α’ phase might be promoted by the phase separation of the alloy matrix into Cr-rich and Fe-rich regions. Interestingly, oxygen impurities segregated preferentially in the Cr-rich regions, possibly promoting the radiation-assisted formation of the Cr-rich α’ phase. α’ phase precipitation was more pronounced at room temperature when compared to 300 °C, and it was clearly promoted by the progressive increase in the Cr content of the ODS-FeCrAl alloy.

36 MATERIALS SCIENCE↗
DOE OSTI2025

The ladder and readout cables of intermediate silicon strip detector for sPHENIX

A new silicon-strip-type detector was developed for precise charged-particle tracking in the central rapidity region of heavy ion collisions. A new detector and collaboration at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory is sPHENIX, which is a major upgrade of the PHENIX detector. The intermediate tracker (INTT) is part of the advanced tracking system of the sPHENIX detector complex together with a CMOS monolithic-active-pixel-sensor based silicon-pixel vertex detector, a time-projection chamber, and a micromegas-based detector. The INTT detector is barrel shaped and comprises 56 silicon ladders. Two different types of strip sensors of 78 micron pitch and 320 micron thick are mounted on each half of a silicon ladder. Each strip sensor is segmented into 8 × 2 and 5 × 2 blocks with lengths of 16 and 20 mm. Strips are read out with a silicon strip-readout (FPHX) chip. In order to transmit massive data from the FPHX to the down stream readout electronics card (ROC), a series of long and high speed readout cables were developed. This document focuses on the silicon ladder, the readout cables, and the ROC of the INTT. The radiation hardness is studied for some parts of the INTT devices in the last part of this document, since the INTT employed some materials from the technology frontier of the industry whose radiation hardness is not necessarily well known.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

A model to assess Zircaloy’s mechanical property changes following a transient beyond critical heat flux

Maintaining the integrity of nuclear fuel rods is essential for ensuring public health and safety in nuclear power generation. During reactor operation, this integrity is confirmed by demonstrating compliance with established regulatory acceptance criteria. For moderate-frequency events, such as limiting transients and anticipated operational occurrences (AOOs), the current fuel integrity criterion is based on preventing boiling transition. This criterion assumes that prevention of boiling transition will prevent excessive cladding heating and, thus, fuel failure during normal operations. While conservative, this approach places significant constraints on core design, fuel cycle economics, and a plant’s ability to perform major power uprates, leading to suboptimal fuel utilization and inefficient carbon-free energy production. A more efficient approach could be achieved by revising the failure criterion to a material-specific limit rather than strictly preventing the boiling transition, since boiling transition per se is not a cause of fuel cladding failure. Here, as a result, a new licensing framework based on material properties, termed time-at-temperature (t@T), is needed. This approach would allow for brief periods of post–critical heat flux operation during an AOO without compromising safety. Implementing the t@T licensing strategy requires a robust technical foundation in material properties, which must be established through comprehensive data collection on both unirradiated and irradiated fuel and cladding materials. This foundation would enable the development of a safety basis that ensures safe operation while providing greater flexibility and efficiency for reactor operation. This paper documents a thorough review of the available data to establish a baseline knowledge that can inform the development of cladding mechanical models, as well as identify experimental data gaps that need to be addressed in future research. Machine learning and data informatics were utilized to extract the importance of parameters on the t@T parameter. Industry tools were used to perform baseline analyses to define the relevant transient conditions for data analysis. The subsequent review successfully identified applicable experimental data, as well as sufficient data to evaluate changes in cladding mechanical properties following an AOO transient. Rather than developing new models, this work coupled existing irradiation annealing and recrystallization models to calculate changes in hardness, yield stress, and ultimate tensile stress following an AOO event. The findings from this review were summarized to highlight the experimental data needs required to fill remaining gaps and support the development of future t@T licensing methodologies.

Cladding performance↗