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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↗
NASA NTRS1990

Dispersive and viscous scale lengths in the two-stage ion heating at quasi-parallel collisionless shocks

A simulation of quasi-parallel (QP) collisionless shock waves is used to deduce the dispersive and viscous scale lengths of QP shocks. The findings were found to be consistent with the observational results obtained by Scudder et al. (1984) and Kennel et al. (1984). It is shown that the upstream wavelength is the dispersive scale length which governs the magnetic-field structure of the shock. It is also shown that the two-stage ion heating obtained by Mandt and Kan (1988) is an intrinsic characteristic of the ion heating process in QP shocks.

Mandt, M. E.↗
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.↗
NASA NTRS1992

Radial profiles of quiet time magnetospheric parameters

The quiet time magnetosphere is studied using ion measurements covering energies from about 1 keV to about 4 MeV from selected passes of the Charge Composition Explorer during low geomagnetic activity. The quiet time plasma pressure in the midnight sector was found to be comparable to that deduced by Spence et al. (1989) and Kan et al. (1992) from inverting the magnetic field models of Tsyganenko and Usmanov (1982) and Tsyganenko (1987). The radial profile of the total plasma pressure exhibited a peak at L = 3-4 and decreased monotonically from L = 4 and L = 9. Contrary to theoretical expectations for the magnetospheric closure of the region 2 field-aligned current system, no large-scale earthward decrease in plasma pressure was found to occur in these outer L shells.

Lui, A. T. Y.↗
NASA NTRS2001

Institution Morphisms

Institutions formalize the intuitive notion of logical system, including both syntax and semantics. A surprising number of different notions of morphisim have been suggested for forming categories with institutions as objects, and a surprising variety of names have been proposed for them. One goal of this paper is to suggest a terminology that is both uniform and informative to replace the current rather chaotic nomenclature. Another goal is to investigate the properties and interrelations of these notions. Following brief expositions of indexed categories, twisted relations, and Kan extensions, we demonstrate and then exploit the duality between institution morphisms in the original sense of Goguen and Burstall, and the 'plain maps' of Meseguer, obtaining simple uniform proofs of completeness and cocompleteness for both resulting categories; because of this duality, we prefer the name 'comorphism' over 'plain map.' We next consider 'theoroidal' morphisms and comorphisims, which generalize signatures to theories, finding that the 'maps' of Meseguer are theoroidal comorphisms, while theoroidal morphisms are a new concept. We then introduce 'forward' and 'semi-natural' morphisms, and appendices discuss institutions for hidden algebra, universal algebra, partial equational logic, and a variant of order sorted algebra supporting partiality.

Goguen, Joseph↗
NASA NTRS2004

Integrated Financial Management Program

Having worked in the Employees and Commercial Payments Branch of the Financial Management Division for the past 3 summers, I have seen the many changes that have occurred within the NASA organization. As I return each summer, I find that new programs and systems have been adapted to better serve the needs of the Center and of the Agency. The NASA Agency has transformed itself the past couple years with the implementation of the Integrated Financial Management Program (IFMP). IFMP is designed to allow the Agency to improve its management of its Financial, Physical, and Human Resources through the use of multiple enterprise module applications. With my mentor, Joseph Kan, being the branch chief of the Employees and Commercial Payments Branch, I have been exposed to several modules, such as Travel Manager, WebTads, and Core Financial/SAP, which were implemented in the last couple of years under the IFMP. The implementation of these agency-wide systems has sometimes proven to be troublesome. Prior to IFMP, each NASA Center utilizes their own systems for Payroll, Travel, Accounts Payable, etc. But with the implementation of the Integrated Financial Management Program, all the "legacy" systems had to be eliminated. As a result, a great deal of enhancement and preparation work is necessary to ease the transformation from the old systems to the new. All this work occurs simultaneously; for example, e-Payroll will "go live" in several months, but a system like Travel Manager will need to have information upgraded within the system to meet the requirements set by Headquarters. My assignments this summer have given me the opportunity to become involved with such work. So far, I have been given the opportunity to participate in projects resulting from a congressional request, several bankcard reconciliations, updating routing lists for Travel Manager, updating the majordomo list for Travel Manager approvers and point of contacts, and a NASA Headquarters project involving improper payments on firm fixed price contracts. Each of the projects that I have worked on this summer presents a different aspect of the work performed on a regular basis by members of this branch. Not only do I get to see the "big picture" of what occurs within the organization, but I also get to experience the "little stuff" that goes on here and throughout the NASA Agency.

Pho, Susan↗
NASA NTRS2018

Snowballs in Euclid and WFIRST Detectors

Snowballs are transient events observed in HgCdTe detectors with a sudden increase of charge in a few pixels. They appear between consecutive reads of the detector, after which the affected pixels return to their normal behavior. The origin of the snowballs is unknown, but it was speculated that they could be the result of alpha decay of naturally radioactive contaminants in the detectors, but a cosmic ray origin cannot be ruled out. Even though previous studies predicted a low rate of occurrence of these events, and consequently, a minimal impact on science, it is interesting to investigate the cause or causes that may generate snowballs and their impact in detectors designed for future missions. We searched for the presence of snowballs in the dark current data in Euclid and Wide Field Infrared Survey Telescope (WFIRST) detectors tested in the Detector Characterization Laboratory at Goddard Space Flight Center. Our investigation shows that for Euclid and WFIRST detectors, there are snowballs that appear only one time, and others that repeat in the same spatial localization. For Euclid detectors, there is a correlation between the snowballs that repeat and bad pixels in the operational masks (pixels that do not fulfill the requirements to pass spectroscopy noise, photometry noise, quantum efficiency, and/or linearity). The rate of occurrence for a snowball event is about 0.9 snowballs/hr. in Euclid detectors (for the ones that do not have associated bad pixels in the mask), and about 0.7 snowballs/hr. in PV3 Full Array Lot WFIRST detectors.

Astronomy↗
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↗