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DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗

DOE OSTI2021

A new method to compute periodic orbits in general symplectic maps

The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples include reversible maps with symmetry lines. The present work proposes a new method to compute high-order periodic orbits in twist maps without the use of symmetries. The method is a combination of the parameterization method in Fourier space and a Newton–Gauss multiple shooting scheme. The parameterization method has been successfully used in the past to compute quasi-periodic invariant circles. However, this is the first time that this method is used in the context of periodic orbits. Numerical examples are presented showing the accuracy and efficiency of the proposed method. Furthermore, the method is also applied to verify the renormalization prediction of the residues’ convergence at criticality (extensively studied in reversible maps) in the relatively unexplored case of maps without symmetries.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

Understanding how chemical structure affects ignition-delay-time $\phi$-sensitivity

$\phi$-sensitivity is the change in ignition delay time (IDT) with respect to the fuel-to-air equivalence ratio ($\phi$). High $\phi$-sensitivity is a desirable fuel property for applications in advanced compression ignition and multi-mode engine designs. Understanding how $\phi$-sensitivity depends on chemical structure is essential for selecting promising biofuels from the ever-growing list of proposed candidates. Here, we investigate the effect of chemical structure on $\phi$-sensitivity with experiment, simulation, and theory. Experimental Advanced Fuel Ignition Delay Analyzer (AFIDA) measurements for 2,4-dimethylpentane and diisopropyl ether provide evidence that branching and functional groups strongly impact $\phi$-sensitivity. Further insights into this dependence are obtained with 0-D kinetic simulations with existing mechanisms for n-pentane, diethyl ether, 3-pentanone, n-heptane, 2-methylhexane, 2,4-dimethylpentane, and 2,2,3-trimethylbutane. Quantum mechanical (QM) G4 calculations of low-temperature reactions help explain the observed experimental and simulation trends. Specifically, these QM calculations provide theoretical estimates of the ketohydroperoxide (KHP) dissociation rates, the HO 2 formation rates from peroxy radical (ROO), and the “cross-over” temperatures, i.e., the temperature at which ROO dissociation is favored compared to hydroperoxyl radical (QOOH) formation. Each of these reaction rates is compared to the n-alkane reference point to determine the impact of branching and different functional groups. Although kinetic mechanisms typically assume that KHP dissociation rates are invariant of chemical environment, our QM results suggest that this rate can span a range of roughly two orders of magnitude. We also discuss the importance of including the peroxy-hydroperoxy (OO-OOH) hydrogen transfer reaction for branched ethers. Finally, the insights gained assist in proposing a highly $\phi$-sensitive compound, namely, isopropyl propyl ether.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Towards physics-informed explainable machine learning and causal models for materials research

From emergent material descriptions to estimation of properties stemming from structures to optimization of process parameters for achieving best performance – all key facets of materials science and related fields have experienced tremendous growth with the introduction of data-driven models. This gradual progression goes at par with developments of machine learning workflows, from purely data-driven shallow models to those that are well-capable in encoding more complex graphs, symbolic representations, invariances, and positional embeddings. Furthermore, this perspective aims at summarizing strategic aspects of such transitions while providing insights into the requirements of bringing in explainable, interpretable predictive models, and causal learning to aid in materials design and discovery. Although the focus remains on a variety of functional materials by providing a handful of case studies, the applications of such integrated methodologies are universal to facilitate fundamental understandings of materials physics while enabling autonomous experiments.

36 MATERIALS SCIENCE↗

DOE OSTI2021

An adaptive adversarial domain adaptation approach for corn yield prediction

Recently, statistical machine learning and deep learning methods have been widely explored for corn yield prediction. Though successful, machine learning models generated within a specific spatial domain often lose their validity when directly applied to new regions. To address this issue, we designed an unsupervised adaptive domain adversarial neural network (ADANN). Specifically, through domain adversarial training, the ADANN model reduced the impact of domain shift by projecting data from different domains into the same subspace. Also, the ADANN model was designed to be trained in an adaptive way, which guaranteed the model can learn the domain-invariant features and perform accurate yield prediction simultaneously. Informative variables including time-series vegetation indices and sequential weather observations were first collected from multiple data sources and aggregated to the county level. Then, we trained the ADANN model with the extracted features and corresponding reported county-level corn yield from the U.S. Department of Agriculture (USDA). Finally, the trained model was evaluated in four testing years 2016–2019. The U.S. corn belt was used as the study area and counties under study were grouped into two diverse ecological regions. Overall, the experimental results showed that the developed ADANN model had better performance than three other state-of-the-art machine learning models in both local experiments (train and test in the same region) and transfer experiments (train and test in different regions). As the first study using adversarial learning for crop yield prediction, this research demonstrates a novel solution for improving model transferability on crop yield prediction.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Using dorsal surface for individual identification of dairy calves through 3D deep learning algorithms

Advances in machine learning techniques have allowed the development of computer vision systems (CVS) that can accurately predict several phenotypes of interest for livestock operations. In this context, 3D images taken from a top-down view are particularly useful for estimating body condition score, growth development, and body biometrics in cattle. Frequently, such CVS rely on identification (ID) systems, such as electronic tags, as a way to match animal ID and the predicted phenotype. However, the same 3D images used to predict body weight and other animal biometrics could be adopted for animal recognition as well. Such alternative would optimize CVS to recognize animal ID and monitor growth development simultaneously while leveraging the same hardware infrastructure. Furthermore, this strategy could be used to recognize animals with similar color patterns. Nonetheless, growing animals are continuously changing body shape, which could limit its use as an invariant feature for pattern recognition. Thus, the objectives of this study were: (1) to compare algorithms for different 3D object representations to identify individual animals; and (2) to evaluate how short-term changes in body shape due to animal growth affect the predictive performance of these algorithms. For objective 1, the algorithms were trained (n = 4,558) and tested (n = 1,139) using images from 38 Holstein calves. For objective 2, we designed three different experiments using images (n = 2,347) from five Holstein calves taken over six weeks during their growing period, always training and testing on different weeks. Each experiment evaluated how changing a different parameter of the image capturing procedure affected the predictive ability of the trained algorithms. In the first experiment, we varied the total number of images per animal in the training set; in the second experiment, we varied the number of weeks while keeping a fixed number of images in the training set; and in the third experiment, we skipped weeks between images in the training and test sets. The F 1 score for objective (1) was up to 0.804 when testing with the last frames of each video, and up to 0.959 when using random frames for testing. For objective (2), the F 1 score was up to 0.947 for the first experiment when using 130 images per animal; up to 0.979 for the second experiment when using all five weeks; and up to 0.917 when not skipping weeks between training and testing. In conclusion, these results show that deep learning algorithms can be used to identify individual animals through their dorsal area 3D surfaces, and, from our experiments using calves in their growing period, that they are robust enough to account for changes in body shape and size, making them a promising tool for animal recognition during growth.

3D neural networks↗

DOE OSTI2020

Particlization in fluid dynamical simulations of heavy-ion collisions: The IS3D module

The IS3D particlization module simulates the emission of hadrons from heavy-ion collisions via Monte-Carlo sampling of the Cooper–Frye formula which converts fluid dynamical information into local phase-space distributions for hadrons. The code package includes multiple choices for the non-equilibrium correction to these distribution functions: the 14-moment approximation, first-order Chapman–Enskog expansion, and two types of modified equilibrium distributions. This makes it possible to explore to what extent heavy-ion experimental data are sensitive to different choices for δf n , presently the main source of theoretical uncertainty in the particlization stage. Here, we validate our particle sampler with a high degree of precision by generating several million hadron emission events from a longitudinally boost-invariant hypersurface and comparing the event-averaged particle spectra and space–time distributions to the Cooper–Frye formula.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Ensemble Monte Carlo calculations with five novel moves

We introduce five novel types of Monte Carlo (MC) moves that brings the number of moves of ensemble MC calculations from three to eight. So far such calculations have relied on affine invariant stretch moves that were originally introduced by Christen (2007), walk moves by Goodman and Weare (2010) and quadratic moves by Militzer (2023). Ensemble MC methods have been very popular because they harness information about the fitness landscape from a population of walkers rather than relying on expert knowledge. Here we modified the affine method and employed a simplex of points to set the stretch direction. We adopt the simplex concept to quadratic moves. We also generalize quadratic moves to arbitrary order. Finally, we introduce directed moves that employ the values of the probability density while all other types of moves rely solely on the location of the walkers. We apply all algorithms to the Rosenbrock density in 2 and 20 dimensions and to the ring potential in 12 and 24 dimensions. We evaluate their efficiency by comparing error bars, autocorrelation time, travel time, and the level of cohesion that measures whether any walkers were left behind. Our code is open source.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Regression models using shapes of functions as predictors

Functional variables are often used as predictors in regression problems. A commonly used parametric approach, called scalar-on-function regression, uses the $\mathbb L^2$ inner product to map functional predictors into scalar responses. This method can perform poorly when predictor functions contain undesired phase variability, causing phases to have disproportionately large influence on the response variable. One past solution has been to perform phase–amplitude separation (as a pre-processing step) and then use only the amplitudes in the regression model. In this paper, we propose a more integrated approach, termed elastic functional regression model (EFRM), where phase-separation is performed inside the regression model, rather than as a pre-processing step. This approach generalizes the notion of phase in functional data, and is based on the norm-preserving time warping of predictors. Due to its invariance properties, this representation provides robustness to predictor phase variability and results in improved predictions of the response variable over traditional models. We demonstrate this framework using a number of datasets involving gait signals, NMR data, and stock market prices.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Graviton-photon oscillations in an expanding universe

Through the Gertsenshtein effect, the presence of a large external B-field may allow photons and gravitons to mix in a way that resembles neutrino oscillations and is even more similar to axion-photon mixing. Assuming a background B-field (or any field that behaves like one), we examine the Gertsenshtein mechanism in the context of FLRW expanding universe models, as well as de Sitter space. The conformal invariance of Maxwell’s equations and the conformal noninvariance of the Einstein equations preclude the operation of the Gertsenshtein effect at all scales. In general we find for the matter- and radiation-dominated cases, graviton-oscillations are possible only at late conformal times or when the wavelengths are much shorter than the horizon (kn $\gg$ 1), but that the time-dependent oscillations eventually damp out in any case. Further, the presence of charged particles additionally damps out the oscillations. For the de Sitter universe, we find that oscillations are possible only at early conformal times (n $\ll$ H -1 ) and for wavelengths short compared to the Hubble radius, but eventually freeze in when wavelengths become longer than the Hubble radius. In principle a Gertsenshtein-like mechanism might influence the balance of particle species in an inflationary phase before freezing in; however, we find that in all our models the mixing length is larger than the Hubble radius. We discuss several possible remedies to this situation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Sequence2Self: Self-supervised image sequence denoising of pixel-level spray breakup morphology

Optical imaging of fast and transient phenomena such as the turbulent breakup of liquid sprays exhibit low signal-to-noise ratios due to the limited illumination intensity relative to the short exposure time. Image denoising is required to facilitate physical studies over these data but is challenging due to the absence of clean ground-truths and the stringency of the denoising task (e.g., strong and complex noise, limited resolution, preserving physical fidelity), preventing supervised and existing un-/self-supervised deep learning methods. To this end, Sequence2Self (Seq2S) is proposed, an extension of Self2Self (S2S) to image sequences that leverages both the signal’s spatial and temporal correlation. Seq2S is demonstrated on time-resolved x-ray phase contrast imaging of liquid jet fuel sprays in a gas turbine combustor, which possesses all of challenges detailed above. Experiments are conducted across four fuels with different breakup morphology using various state-of-the-art methods. Overall, many of the methods failed and Seq2S was most successful: (1) Accurate spray structures were reconstructed with consistent evolution across frames void of artifacts. (2) The performance was robust, invariant to the hyperparameter choice. (3) Computational time is short and can be made eligible for real-time denoising. In particular, the images denoised by Seq2S showed spray droplet diameter distributions with near-zero Kullback–Leibler divergence (0.01 ± 0.01) to a cleaner reference, whereas the second best method yielded 0.06 ± 0.03. In conclusion, this suggests that Seq2S can be reliably used prior to subsequent quantitative spray analyses as it retains (if not, improves) the statistical physical properties of the data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

New data-driven approach to bridging power system protection gaps with deep learning

Protection is a critical function in power systems to avoid equipment damage, maintain personnel safety, and support system reliability. However, current protective relay technology cannot adequately protect equipment and personnel from effects of some events; these deficiencies are termed protection gaps. In this paper, a data-driven approach is proposed to complement traditional protection technology and distinguish fault conditions from transients caused by normal operations. A combined convolutional neural network and long short-term memory (CNN-LSTM) network is implemented to achieve data translation invariance and capture the temporal correlation of the time-series input data. As a result, the data-driven method can accurately detect system faults despite variation and noise in the input data. In addition, using the CNN-LSTM--based method avoids the complicated, manual feature extraction procedure required by many traditional data-driven methods. The effectiveness of the proposed approach is tested on two kinds of protection gaps: high-impedance faults and transformer inter-turn faults. Lastly, a transfer learning method is also proposed to address the common issue of data-driven methods for which real-world training data are scarce. Extensive study results demonstrate that the proposed approach can accurately bridge power system protection gaps.

42 ENGINEERING↗

DOE OSTI2025

Hyperelastic nature of the Hoek–Brown criterion

In this article, we propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or hyperelastic) behavior with plasticity obeying the associated flow rule. Interestingly, we find that a linear yield criterion on the thermodynamical force associated with plasticity results in a quadratic yield criterion in the stress space. This suggests a specific hyperelastic connection between Mohr–Coulomb and Hoek–Brown (or alternatively between Drucker–Prager and Pan–Hudson) yield criteria. We compare the elasto-plastic responses of standard tests for the Drucker–Prager yield criterion using either linear or the suggested hyperbolic elasticity. Notably, the nonlinear case stands out due to dilatancy saturation observed during cyclic loading in the triaxial compression test. We conclude this study with structural finite element simulations that clearly demonstrate the numerical applicability of the proposed model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Verification of nonperturbative guiding center theory in symmetric fields

We verify a recently-developed nonperturbative guiding center formalism to charged particle dynamics in fields with two-parameter continuous symmetry groups. This entails finding exact constants of motion, valid in the nonperturbative regime, that agree with Kruskal’s adiabatic invariant series to all orders in the perturbative regime, when the field scale length is large compared with a typical gyroradius. We demonstrate that the nonperturbative guiding center model makes exact predictions in these cases, even though it eliminates the cyclotron timescale, thereby establishing a theoretical baseline for performance of the nonperturbative formalism.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Weighted Composition Operators for Learning Nonlinear Dynamics

Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Physics augmented machine learning discovery of composition-dependent constitutive laws for 3D printed digital materials

Multi-material 3D printing, particularly through polymer jetting, enables the fabrication of digital materials by mixing distinct photopolymers at the micron scale within a single build to create a composite with tunable mechanical properties. Here, this work presents an integrated experimental and computational investigation into the composition-dependent mechanical behavior of 3D printed digital materials. We experimentally characterize five formulations, combining soft and rigid UV-cured polymers under uniaxial tension and torsion across three strain and twist rates. The results reveal nonlinear and rate-dependent responses that strongly depend on composition. To model this behavior, we develop a physics-augmented neural network (PANN) that combines a partially input convex neural network (pICNN) for learning the composition-dependent hyperelastic strain energy function with a quasi-linear viscoelastic (QLV) formulation for time-dependent response. The pICNN ensures convexity with respect to strain invariants while allowing non-convex dependence on composition. To enhance interpretability, we apply $L_0$ sparsification. For the time-dependent response, we introduce a multilayer perceptron (MLP) to predict viscoelastic relaxation parameters from composition. The proposed model accurately captures the nonlinear, rate-dependent behavior of 3D printed digital materials in both uniaxial tension and torsion, achieving high predictive accuracy for interpolated material compositions. This approach provides a scalable framework for automated, composition-aware constitutive model discovery for multi-material 3D printing.

Constitutive modeling↗

DOE OSTI2024

A robust spectral element implementation of the $k - τ$ RANS model in Nek5000/NekRS

The $k - ω$ Reynolds Averaged Navier Stokes (RANS) model is one of the industry standard approaches for modeling of turbulent flows. It performs better than the $k - ϵ$ model for low Reynolds number flows and is also more suitable for boundary layers with adverse pressure gradients. Major drawback of the model, however, is that the asymptotic value of $ω$ at the walls is singular, necessitating the use of a contrived “sufficiently” large value for $ω$ as the boundary condition for its transport equation. Here, this invariably leads to the solution being sensitive to near wall grid spacing. While an acceptable solution for low order (finite volume) methods, the excessive near wall gradients lead to persistent numerical stability issues in high order codes. To alleviate the problem, specifically in the context of the high order spectral element code Nek5000, a regularized $k - ω$ approach was formulated in our prior work (Tomboulides et al., 2018). The formulation, however, relies on the use of wall distance and its gradients for modeling the closure terms and can pose problems for simulations in complex geometries. This work presents a novel implementation of the $k - τ$ RANS model in Nek5000, where $τ = 1/ω$, eliminating the need for regularization, owing to the asymptotically bounded behavior of the source terms in the $τ$ transport equation, and also eliminating dependence on wall distance. Robustness and stability of the $k - τ$ model is ensured through implicit treatment of the source terms and their careful numerical implementation and demonstrated through several cases aimed at verification and validation. Studies include both canonical and engineering relevant problems, viz., turbulent channel flow, pipe flow, backward facing step, flow over NACA 0012 airfoil and flow in a T-junction. Results from the $k - τ$ model are shown to be consistent with regularized $k - ω$ model and also with the $k - ω$ SST model in OpenFOAM (for select studies). Comparison with experimental data is also shown, where available, to bolster validation efforts for the $k - τ$ model implementation through prediction of key turbulent quantities of interest.

Nek5000↗

DOE OSTI2025

Additional considerations in analytical solution for time-dependent heat conduction in a three-dimensional multilayer sphere

This work presents an analytical method to solve the heat conduction equation in three dimensions for problems consisting of multilayer concentric spheres. The method can be used to treat time-varying heat conduction problems where the heat source that drives the transient is time-invariant. Equally applicable to all Poisson-type problems with concentric spherical geometry, the method consists of representing the solution as a summation of weighted eigenfunctions. The weights for each eigenfunction are computed algebraically. Previous work has already established the core constituents of the methodology. The current work augments the existing methods by including consideration of nonzero interface resistance between layers and explicit discussion on the boundary condition homogenization required to treat inhomogeneous problems. Also, two demonstration problems are presented. One demonstration problem is based on the method of manufactured solutions and therefore allows for comparison with exact expressions for the solution temperature distribution. The second, more complex, demonstration problem relies on the finite element method for comparisons. The expected convergence behavior is observed for both demonstration problems.

97 - MATHEMATICS AND COMPUTING↗