Physics Model Calibration via Functional Kernel Regression and Multilevel Modeling
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Ohene-Obeng, Kwesi Appau [Sandia National Laborato↗
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Results for “KERNEL FUNCTION”
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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StOKeDMD: Streaming Occupation kernel dynamic mode decomposition
Dynamic mode decomposition (DMD) has become a common technique for constructing surrogate models for dynamical systems from observed system states. The Occupation Kernel DMD (OKDMD) method proposed in (Rosenfeld et al., 2022) and (Rosenfeld et al., 2024) is a Liouville operator based method that builds surrogate models from system state trajectories. Here, this paper proposes an extension of OKDMD to the case when the system states are observed in a streaming fashion, i.e., only a small fraction of the state trajectory is available at a given time. The developed method, Streaming Occupation Kernel DMD (StOKeDMD), accommodates the streaming data input by leveraging properties of specific choices of kernel functions and occupation kernels. We apply the StoKeDMD method as a compression method for streaming data, analyze the memory complexity, and demonstrate the performance of StoKeDMD in the compression of streaming data generated from a Lorenz system and a fluid flow simulation.
97 MATHEMATICS AND COMPUTING↗
Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method
Abstract An interface-modified reproducing kernel particle method (IM-RKPM) is introduced in this work to allow for a direct model construction from image pixels of heterogeneous polycrystalline Li-ion battery microstructures. The interface-modified reproducing kernel (IM-RK) approximation is constructed through scaling of a kernel function by a regularized distance function in conjunction with strategic placement of interface node locations. This leads to RK shape functions with either weak or strong discontinuities across material interfaces, suitable for modeling various interface mechanics. With the placement of a triple junction node and distance-based scaling of kernel functions, the resulting IM-RK shape function also possesses proper discontinuities at the triple junctions. This IM-RK approximation effectively remedies the well-known Gibb’s oscillation in the smooth approximation of discontinuities. Different from the conventional meshfree approaches for interface discontinuities, this IM-RK approach is done without additional degrees of freedom associated with the enrichment functions, and it is formulated with the standard procedures in the RK shape function construction. This work focuses on identifying the accuracy and convergence properties of IM-RKPM for modeling the coupled electro-chemo-mechanical system. A linear patch test is formulated and numerically tested for the electro-chemo-mechanical coupled problem with a Butler–Volmer boundary condition representing the physical conditions in Li-ion battery microstructures. This is followed by verification of the optimal rates of convergence of IM-RKPM for solving the coupled problem with higher order solutions. The image-based modeling of Li-ion battery microstructures in the numerical examples demonstrates the applicability of the proposed method to realistic Li-ion battery materials modeling.
25 ENERGY STORAGE↗
On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equation
The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation and related models is considered. Here, this work investigates the underlying Hamiltonian structure of such smoothed particle-based methods for Hamiltonian systems and the small-scale regularization such methods implicitly make in approximating the continuum theory. In the context of the Vlasov–Poisson equation and other mean-field Lie–Poisson systems, of which Vlasov–Poisson is a special case, smoothing amounts to a convolutive regularization of the Hamiltonian. This regularization may be interpreted as a change of the inner product structure used to identify the dual space in the Lie–Poisson Hamiltonian formulation. In particular, the shape function used for spatial smoothing may be identified as the kernel function of a reproducing kernel Hilbert space whose inner product is used to define the Lie–Poisson Hamiltonian structure. It is likewise possible to introduce smoothing in the Vlasov–Maxwell system, but in this case the Poisson bracket must be modified rather than the Hamiltonian. The smoothing applied to the Vlasov–Maxwell system is incorporated by inserting smoothing in the map from canonical to kinematic coordinates. In the filtered system, the Lorentz force law and the current, the two terms coupling the Vlasov equation with Maxwell’s equations, are spatially smoothed.
Hamiltonian mechanics↗
Data‐driven variational method for discrepancy modeling: Dynamics with small‐strain nonlinear elasticity and viscoelasticity
Abstract The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.
Masud, Arif↗
Physics-Informed Gaussian Process Inference of Liquid Structure from Scattering Data
We present a nonparametric Bayesian framework to infer radial distribution functions from experimental scattering measurements with uncertainty quantification using nonstationary Gaussian processes. The Gaussian process prior mean and kernel functions are designed to mitigate well-known numerical challenges with the Fourier transform, including discrete measurement binning and detector windowing, while encoding fundamental yet minimal physical knowledge of the liquid structure. We demonstrate uncertainty propagation of the Gaussian process posterior to unmeasured quantities of interest. Experimental radial distribution functions of liquid argon and water with uncertainty quantification are provided as both a proof of principle for the method and a benchmark for molecular models.
Chemical structure↗
Multiphysics Meshfree Degradation Modeling of Energy Storage Materials with Kernel Enrichment
Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. Reference: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.
25 ENERGY STORAGE↗
Kernel Enriched Meshfree Multiphysics Degradation Modeling of Energy Storage Materials
Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Laboratory of the Rockies (NLR), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. References: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.
97 MATHEMATICS AND COMPUTING↗
Learning error distribution kernel‐enhanced neural network methodology for multi‐intersection signal control optimization
Traffic congestion has substantially induced significant mobility and energy inefficiency. Many research challenges are identified in traffic signal control and management associated with artificial intelligence (AI)-based models. For example, developing AI-driven dynamic traffic system models that accurately capture high-resolution traffic attributes and formulate robust control algorithms for traffic signal optimization is difficult. Additionally, uncertainties in traffic system modeling and control processes can further complicate traffic signal system controllability. To partially address these challenges, this study presents a novel, hybrid neural network model enhanced with a probability density function kernel shaping technique to formulate traffic system dynamics better and improve comprehensive traffic network modeling and control. The numerical experimental tests were conducted, and the results demonstrate that the proposed control approach outperforms the baseline control strategies and reduces overall average delays by 11.64% on average. By leveraging the capabilities of this innovative model, this study aims to address major challenges related to traffic congestion and energy inefficiency toward more effective and adaptable AI-based traffic control systems.
Wang, Hong [Oak Ridge National Laboratory (ORNL), ↗
Particle Filter Based Inference Testing
The primary intent of PAR-FIT (Particle Filter based Inference Testing) is to provide hard inductive evidence that a machine learning model is capable and proven for an individual test input. By examining training data used to form the underlying model functional correlation, an estimate of the reliability that a model will make the correct prediction can be made. The Sequential Probability Ratio Test is used to derive a qualitative evaluation for reliability based on hypothesis testing. The PAR-FIT framework achieves this by implementing a particle filter and the sequential probability ratio test algorithms on the machine learning model training data to determine relevancy of new individual test samples to the training dataset. The kernel function evaluates the local proximity and density of training data used to derive a prediction outcome. Particles are used to probabilistically determine which training data to evaluate for proximity. For test samples that are within a close proximity to and surrounded by multiple training data points, the evaluated reliability of the prediction is high. For test samples that are anomalies not represented by the training dataset, in low density data clusters, or are far from existing data points, the evaluated reliability is low as insufficient training evidence exists to suggest the model is capable of making the correct prediction. Sequential Probability Ratio Test is further used to determine when a hypothesis on whether a signal can be rejected or accepted for use. The ratio test collects sequence information from the particle filter to test whether the signal is anomalous or normal via hypothesis testing of the underlying distributions.
Chen, Edward [Idaho National Laboratory (INL), Ida↗
Image-Based Failure Assessment of Li-Ion Batteries
In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. In this work, a digital twin is created to investigate the performance of a heterogeneous Li-ion battery cathode and simulate degradation accumulation. Pixel-based model construction is used to represent the complex material geometries from microstructural images supplied by the National Renewable Energy Laboratory (NREL). Because of the expected large deformation and crack opening, the reproducing kernel particle method (RKPM), a meshfree method with discretization at the image pixels, is used to approximate the field variables: electrostatic potential, concentration, and displacement. An interface modified reproducing kernel (IM-RK) is constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. IM-RK is additionally used to inform how crack evolution in turn affects the coupled electro-chemo-mechanical behavior of the Li-ion battery cathode.
image-based modeling↗
Signal Processing in SBND with Calibrated and Validated Electronics and Field Responses
SBND is a liquid argon time projection chamber in Fermilab’s Short-Baseline Neutrino Program, located 110 m from the neutrino source and operating in a high-rate environment with unprecedented statistics. Charged particles from neutrino interactions ionize the argon, and the resulting electrons drift to the anode wires, inducing current signals recorded as raw waveforms. These waveforms are a convolution of deposited charge with the electronics and TPC field responses, making accurate signal processing essential for recovering the true charge distribution. Signal processing forms the starting point for SBND reconstruction, directly impacting hit finding, charge calibration, clustering, and the reconstruction of tracks and showers, and therefore playing a key role in energy reconstruction and particle identification. In this poster, we present an overview of the SBND signal processing chain, including noise removal, channel-by-channel electronics correction, signal identification, and deconvolution using measured electronics and TPC field responses. We demonstrate that the two kernel functions—electronics and field responses—achieve high precision when compared to data, ensuring that the SBND signal processing chain provides a robust and accurate foundation for event reconstruction and precision physics measurements.
Singh, Prabhjot [Louisiana State U.] (ORCID:000000↗
Collins-Soper kernel and reduced soft function in lattice QCD
We evaluate the Collins-Soper kernel and the reduced soft function in lattice QCD, incorporating 𝒪(𝛼 𝑠 ) matching corrections. The calculation relies on the evaluation of the quasitransverse momentum–dependent wave function with asymmetric staple-shaped quark bilinear operators and four-point meson form factors. These quantities are computed nonperturbatively using two 𝑁 𝑓 =2 + 1 + 1 twisted-mass fermion ensembles with the same lattice spacing of 𝑎 = 0.093 fm: the first ensemble has a lattice size of 24 3 × 48 and a pion mass of 346 MeV, and the second one has a lattice size of 32 3 × 64 and a pion mass of 261 MeV. The Collins-Soper kernel and the soft function are needed for the determination of the transverse momentum–dependent parton distribution functions.
Lattice QCD↗
A meshless stochastic method for Poisson–Nernst–Planck equations
A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functions, kernel-independent fast multipole methods, and kernel density estimation to solve the PNP system in a meshless manner, capable of handling discontinuous initial states. The method is embarrassingly parallel, and the computational cost scales linearly with the number of particles and dimension. We use a series of numerical experiments to demonstrate both the method’s convergence with respect to the number of particles and computational cost vis-à-vis a traditional partial differential equation solver.
Chemistry↗
Gaussian processes for inferring parton distributions
The extraction of parton distribution functions (PDFs) from experimental or lattice QCD data is an ill-posed inverse problem, where regularization strongly impacts both systematic uncertainties and the reliability of the results. We study a framework based on Gaussian Process Regression (GPR) to reconstruct PDFs from lattice QCD matrix elements. Within a Bayesian framework, Gaussian processes serve as flexible priors that encode uncertainties, correlations, and constraints without imposing rigid functional forms. We investigate a wide range of kernel choices, mean functions, and hyperparameter treatments. We quantify information gained from the data using the Kullback-Leibler divergence. Synthetic data tests demonstrate the consistency and robustness of the method. Our study establishes GPR as a systematic and non-parametric approach to PDF reconstruction, offering controlled uncertainty estimates and reduced model bias in lattice QCD analyses.
hadronic spectroscopy↗
Gaussian Process Regression under Computational and Epistemic Misspecification
Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze Gaussian process regression under important classes of computational misspecification: Karhunen-Loève expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Furthermore, our theory also accounts for epistemic misspecification in the choice of kernel parameters.
Gaussian process regression↗
Enabling the Broader Use of MOOSE for Nuclear Energy and Other Simulation
This Final Scientific and Technical Report summarizes work performed under the Phase IIA SBIR project “Enabling the Broader Use of MOOSE for Nuclear Energy and Other Simulation” (DE-SC0020906) from August 2023 through August 2025. The objective of the Phase IIA effort was to mature and harden capabilities developed during Phase II, with the goal of enabling practical interoperability between Coreform’s isogeometric analysis (IGA) technologies and the Multiphysics Object-Oriented Simulation Environment (MOOSE), while improving robustness, performance, and scalability for complex, nuclear-relevant geometries. Over the course of Phase IIA, the project established and validated an extraction-based interoperability pathway between Coreform tools and MOOSE. A combined mesh and matrix format was defined collaboratively with MOOSE developers and integrated into the solver, enabling standard MOOSE workflows to operate on data exported from Coreform’s IGA and Flex Representation Method (FRM) pipelines. Early demonstrations validated architectural compatibility using linear solid mechanics problems, while later efforts focused on benchmark testing and external use. By the end of the project period, engineers at BWXT were able to independently set up and execute a simulation using the Coreform–MOOSE workflow and provide direct feedback that informed further refinement. In parallel, substantial effort was devoted to improving the robustness of trimmed U-spline construction for complex CAD geometries. A growing test suite of nuclear-relevant models was compiled through collaboration with multiple stakeholders and used to drive extensive bug fixing and reliability improvements. These efforts resulted in improved robustness and performance, including the addition of fallback capabilities that enhance reliability when the underlying commercial CAD kernel fails. Performance-oriented work progressed later in the project, with the development and demonstration of methods to decompose complex geometries into structured subregions and updated data representations to support more efficient solver processing. Additionally, extensive enhancements to threadsafe parallel data structures and trimming operations established a foundation for scalable processing of large assemblies. Collaboration with Sandia National Laboratories on the SGM geometric modeling kernel advanced to a functioning interface test case, positioning the workflow for future kernel integration. Overall, the Phase IIA effort successfully transitioned the project from architectural proof-of-concept to externally exercised, solver-integrated capability, while clarifying remaining technical challenges related to standardization, performance optimization, and kernel integration.
42 ENGINEERING↗
Effective Wang-Teter kernels for improved orbital-free density functional theory simulations
Not provided.
Materials Science↗