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Universal Workflow Language and Software Enable Geometric Learning and FAIR Scientific Protocol Reporting

Written language and conventional data structures for representing scientific procedures suffer from low process detail, often fail to accurately represent protocols, and lack universality. New strategies for the handling of experimental data are needed to provide viable process information for both humans and machines. In this work, we present the universal workflow language (UWL) and interface (UWLi). UWL is a findable, accessible, interoperable, and reusable (FAIR)-compatible, graph-based data architecture that can capture arbitrary scientific procedures through workflow representation, and UWLi is an accompanying software package for building, manipulating, and interpreting UWL entries. The UWL format was found to be highly effective in identifying deficiencies in the reported process details of high-impact, peer-reviewed scientific journals, and in simulated scenarios, the graph format was shown to be more effective than conventional methods in predictively modeling the outcome of diverse scientific protocols. Implementation of UWL could enable more accurate scientific communication and more impactful process datasets.

14 SOLAR ENERGY

Reduced‐Order Modeling of Energetic Materials Using Physics‐Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)

Physics-aware deep learning (PADL) has gained popularity for use in spatiotemporal dynamics simulations, such as those in computational modeling of energetic materials (EM). We show that the challenge PADL methods face while learning complex field evolution problems can be simplified and accelerated by decoupling it into two tasks: learning complex geometric features in evolving fields and modeling dynamics over these features in a lower-dimensional feature space. We build upon our previous work on physics-aware recurrent convolutional neural networks (PARC). PARC embeds knowledge of underlying physics into its neural network architecture for more robust and accurate prediction of evolving physical fields. PARC was shown to effectively learn complex nonlinear features such as the formation of hotspots and coupled shock fronts in various initiation scenarios of EMs, as a function of microstructures, serving effectively as a microstructure-aware burn model. Here, we further accelerate PARC and reduce its computational cost by projecting the original dynamics onto a lower-dimensional invariant manifold, or “latent space.” The projected latent representation encodes the complex geometry of evolving fields (e.g., temperature and pressure) in a set of data-driven features. The reduced dimension of this latent space allows us to learn the dynamics during the initiation of EM with a lighter and more efficient model. We observe a significant decrease in training and inference time while maintaining results comparable to PARC at inference. This work takes steps towards enabling rapid prediction of EM thermomechanics at larger scales and characterization of EM structure–property–performance linkages at a full application scale.

Mathematics and Computing

On the hardness of learning ground state entanglement of geometrically local Hamiltonians

Characterizing the entanglement structure of ground states of local Hamiltonians is a fundamental problem in quantum information. In this work we study the computational complexity of this problem, given the Hamiltonian as input. Our main result is that to show it is cryptographically hard to determine if the ground state of a geometrically local, polynomially gapped Hamiltonian on qudits (d=O(1)) has near-area law vs near-volume law entanglement. This improves prior work of Bouland et al. (arXiv:2311.12017) showing this for non-geometrically local Hamiltonians. In particular we show this problem is roughly factoring-hard in 1D, and LWE-hard in 2D. Our proof works by constructing a novel form of public-key pseudo-entanglement which is highly space-efficient, and combining this with a modification of Gottesman and Irani's quantum Turing machine to Hamiltonian construction. Our work suggests that the problem of learning so-called "gapless" quantum phases of matter might be intractable.

Computational Complexity (cs.CC)

Generative learning for slow manifolds and bifurcation diagrams

In dynamical systems characterized by separation of time scales, the approximation of so called “slow manifolds”, on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms (like the equation-free approach) alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams (curves for one-parameter continuation, and more generally, on manifolds in state parameter space. Sampling these manifolds gives us representative attractors (here, steady states of ODEs or PDEs) at different parameter values. Algorithms for the systematic construction of these manifolds (slow manifolds, bifurcation diagrams) are required parts of the “traditional” numerical nonlinear dynamics toolkit. In more recent years, as the field of Machine Learning develops, conditional score-based generative models (cSGMs) have been demonstrated to exhibit remarkable capabilities in generating plausible data from target distributions that are conditioned on some given label. It is tempting to exploit such generative models to produce samples of data distributions (points on a slow manifold, steady states on a bifurcation surface) conditioned on (consistent with) some quantity of interest (QoI, observable). In this work, we present a framework for using cSGMs to quickly (a) initialize on a low-dimensional (reduced-order) slow manifold of a multi-time-scale system consistent with desired value(s) of a QoI (a “label”) on the manifold, and (b) approximate steady states in a bifurcation diagram consistent with a (new, out-of-sample) parameter value. This conditional sampling can help uncover the geometry of the reduced slow-manifold and/or approximately “fill in” missing segments of steady states in a bifurcation diagram. Finally, the quantity of interest, which determines how the sampling is conditioned, is either known a priori or identified using manifold learning-based dimensionality reduction techniques applied to the training data.

Dynamical systems

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps

Exascale granular microstructure reconstruction in 3D volumes of arbitrary geometries with generative learning

Reconstructing 3D granular microstructures within volumes of arbitrary geometries from limited 2D image data is crucial for predicting the material properties, as well as performances of structural components accounting for material microstructural effects. We present a novel generative learning framework that enables exascale reconstruction of granular microstructures within complex 3D geometric volumes. Building upon existing transfer learning techniques using pre-trained convolutional neural networks (CNN), we introduce several key innovations to overcome the difficulties inherent in arbitrary geometries. Our framework incorporates periodic boundary conditions using circular padding techniques, ensuring continuity and representativeness of the reconstructed microstructures. We also introduce a novel seamless transition reconstruction (STR) method that creates statistically equivalent transition zones to integrate multiple pre-existing 3D microstructure volumes. Based on STR, we propose a cost-effective strategy for reconstructing microstructures within complex geometric volumes, minimizing computational waste. Validation through numerical experiments using kinetic Monte Carlo simulations demonstrates accurate reproduction of grain statistics, including grain size distributions and morphology. A case study involving the reconstruction of a 4-blade propeller microstructure illustrates the method’s capability to efficiently handle complex geometries. In conclusion, the proposed framework significantly reduces computational demands while maintaining high reconstruction quality, paving the way for scalable microstructure reconstruction in materials design and analysis.

36 MATERIALS SCIENCE

“Understanding Robustness Lottery”: A Geometric Visual Comparative Analysis of Neural Network Pruning Approaches

Deep learning approaches have provided state-of-the-art performance in many applications by relying on large and overparameterized neural networks. However, such networks are very brittle and are difficult to deploy on resource-limited platforms. Model pruning, i.e., reducing the size of the network, is a widely adopted strategy that can lead to a more robust and compact model. Many heuristics exist for model pruning, but our understanding of the pruning process remains limited due to the black-box nature of a neural network model. Empirical studies show that some heuristics improve performance whereas others can make models more brittle. Here, this work aims to shed light on how different pruning methods alter the network’s internal feature representation and the corresponding impact on model performance. To facilitate a comprehensive comparison and characterization of the high-dimensional model feature space, we introduce a visual geometric analysis of feature representations. We evaluated a set of critical geometric concepts decomposed from the commonly adopted classification loss and used them to design a visualization system to compare and highlight the impact of pruning on model performance and feature representation. The proposed tool provides an environment for an in-depth comparison of pruning methods and a comprehensive understanding of how the model responds to common data corruption. By leveraging the proposed visualization, machine learning researchers can reveal the similarities between pruning methods and redundancy in robustness evaluation benchmarks, obtain geometric insights about the differences between pruned models that achieve superior robustness performance, and identify samples that are robust or fragile to model pruning and common data corruption.

Li, Zhimin [Univ. of Utah, Salt Lake City, UT (Uni

DONUT: physics-aware machine learning for real-time X-ray nanodiffraction analysis

Coherent X-ray scattering techniques are critical for investigating the fundamental structural properties of materials at the nanoscale. While advancements have made these experiments more accessible, real-time analysis remains a significant bottleneck, often hindered by artifacts and computational demands. In scanning X-ray nanodiffraction microscopy, which is widely used to spatially resolve structural heterogeneities, this challenge is compounded by the convolution of the divergent beam with the sample’s local structure. To address this, we introduce DONUT (Diffraction with Optics for Nanobeam by Unsupervised Training), a physics-aware neural network designed for the rapid and automated analysis of nanobeam diffraction data. By incorporating a differentiable geometric diffraction model directly into its architecture, DONUT learns to predict crystal lattice strain and orientation in real-time. Crucially, this is achieved without reliance on labeled datasets or pre-training, overcoming a fundamental limitation for supervised machine learning in X-ray science. We demonstrate experimentally that DONUT accurately extracts all features within the data over 200 times more efficiently than conventional fitting methods.

Materials science

DONUT: Physics-aware Machine Learning for Real-time X-ray Nanodiffraction Analysis

SF-25-088 Coherent X-ray scattering techniques are critical for investigating the fundamental structural properties of materials at the nanoscale. While advancements have made these experiments more accessible, real-time analysis remains a significant bottleneck, often hindered by artifacts and computational demands. In scanning X-ray nanodiffraction microscopy, which is widely used to spatially resolve structural heterogeneities, this challenge is compounded by the convolution of the divergent beam with the sample’s local structure. To address this, we introduce DONUT (Diffraction with Optics for Nanobeam by Unsupervised Training), a physics-aware neural network designed for the rapid and automated analysis of nanobeam diffraction data. By incorporating a differentiable geometric diffraction model directly into its architecture, DONUT learns to predict crystal lattice strain and orientation in real-time. Crucially, this is achieved without reliance on labeled datasets or pre-training, overcoming a fundamental limitation for supervised machine learning in X-ray science. We demonstrate experimentally that DONUT accurately extracts all features within the data over 200 times more efficiently than conventional fitting methods.

Zhou, Tao [Argonne National Laboratory (ANL), Argo

Oak Ridge National Laboratory Building Envelope Library (ORNOBEL)

The Oak Ridge National Laboratory Building Envelope Library (ORNOBEL) is a collection of dense exterior building-facade point clouds acquired using a survey-grade terrestrial laser scanner. Each file represents an individual facade from a building on the Oak Ridge National Laboratory (ORNL) campus or in Knoxville, Tennessee, with an average point-cloud resolution of approximately 3 mm. The points in each facade are semantically labeled into three classes: (1) window/door, representing openings in the building envelope; (2) wall, representing planar opaque envelope surfaces; and (3) other, representing the remaining facade-adjacent elements, architectural features, and protrusions. ORNOBEL supports the development, training, and evaluation of advanced deep-learning methods for automated building-envelope segmentation, geometric reconstruction, and building information modeling (BIM).

Maldonado Puente, Bryan [ORNL] (ORCID:000000033880

Geometry-aware framework for deep energy method: An application to structural mechanics with hyperelastic materials

Here, in this work, we introduce a novel physics-informed framework named the Geometry-Aware Deep Energy Method (GADEM) for solving structural mechanics problems on different geometries. As the weak form of the physical system equation (or the energy-based approach) has demonstrated clear advantages compared to the strong form for solving solid mechanics problems, GADEM employs the weak form and aims to infer the solution on multiple shapes of geometries. Integrating a geometry-aware framework into an energy-based method results in an effective physics-informed deep learning model in terms of accuracy and computational cost. Different ways to represent the geometric information and to encode the geometric latent vectors are investigated in this work. We introduce a loss function of GADEM which is minimized based on the potential energy of all considered geometries. An adaptive learning method is also employed for the sampling of collocation points to enhance the performance of GADEM. We present some applications of GADEM to solve solid mechanics problems, including a loading simulation of a toy tire involving contact mechanics and large deformation hyperelasticity. The numerical results of this work demonstrate the remarkable capability of GADEM to infer the solution on various and new shapes of geometries using only one trained model.

97 MATHEMATICS AND COMPUTING

Generative learning of densities on manifolds

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an Itô stochastic differential equation in the latent space. Additional realizations of the data are generated by lifting the samples back to the ambient space using Double Diffusion Maps , a recently introduced technique typically employed in studying dynamical system reduction; here the focus lies in sampling densities rather than system dynamics. The proposed approaches enable sampling high dimensional data densities restricted to low-dimensional, a priori unknown manifolds. The efficacy of the proposed framework is demonstrated through a benchmark problem and a material with multiscale structure.

Double diffusion maps

On learning what to learn: Heterogeneous observations of dynamics and establishing possibly causal relations among them

Abstract Before we attempt to (approximately) learn a function between two sets of observables of a physical process, we must first decide what the inputs and outputs of the desired function are going to be. Here we demonstrate two distinct, data-driven ways of first deciding “the right quantities” to relate through such a function, and then proceeding to learn it. This is accomplished by first processing simultaneous heterogeneous data streams (ensembles of time series) from observations of a physical system: records of multiple observation processes of the system. We determine (i) what subsets of observables are common between the observation processes (and therefore observable from each other, relatable through a function); and (ii) what information is unrelated to these common observables, therefore particular to each observation process, and not contributing to the desired function. Any data-driven technique can subsequently be used to learn the input–output relation—from k-nearest neighbors and Geometric Harmonics to Gaussian Processes and Neural Networks. Two particular “twists” of the approach are discussed. The first has to do with the identifiability of particular quantities of interest from the measurements. We now construct mappings from a single set of observations from one process to entire level sets of measurements of the second process, consistent with this single set. The second attempts to relate our framework to a form of causality: if one of the observation processes measures “now,” while the second observation process measures “in the future,” the function to be learned among what is common across observation processes constitutes a dynamical model for the system evolution.

Sroczynski, David W.

A machine learning method of modern urban building energy modeling: A case study of Chicago

Urban-scale building energy modeling is vital for urban planning. However, it can be challenging to assimilate reliable non-geometry building data for urban-scale modeling without extensive investment. Here, this study introduces a novel approach to developing modern urban-scale building energy stock data using geographic information systems and machine learning algorithms without necessarily requiring pre-supplied non-geometric metadata. The proposed framework integrates building footprint and height data to estimate gross floor areas, and matches each building to a pool of candidate records from ComStock or ResStock—filtered to the same county and ranked by geometric similarity—demonstrate a proof-of-concept case study in Chicago for predicting energy use intensity (EUI) using scalable datasets. The model achieved a mean bias error (MBE) of 0.08 kWh/m² and root mean square error (RMSE) of 14.84 kWh/m² under full metadata input for EUI prediction. With only location inputs, the model captured 69.2 % of EUI within predicted ranges. These results demonstrate the model’s potential to support early-stage urban planning, identify candidates for energy-efficient retrofits. By removing the dependency on detailed pre-surveys or extensive building metadata, the approach overcomes a key barrier in traditional urban-scale building energy modeling, illustrating a pathway toward broader and more cost-effective application, though further multi-city validation and improved treatment of pre-1925 buildings are needed.

Energy Use Intensity

Accelerating multilevel Markov Chain Monte Carlo using machine learning models

Here, this work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian inference often substitute computationally expensive high-fidelity models with machine learning models, thereby introducing approximation errors, our approach offers a computationally efficient alternative by augmenting high-fidelity models with low-fidelity ones within a hierarchical framework. The multilevel approach utilizes the low-fidelity machine learning model (MLM) for inexpensive evaluation of proposed samples thereby improving the acceptance of samples by the high-fidelity model. The hierarchy in our multilevel algorithm is derived from geometric multigrid hierarchy. We utilize an MLM to accelerate the coarse level sampling. Training machine learning model for the coarsest level significantly reduces the computational cost associated with generating training data and training the model. We present an MCMC algorithm to accelerate the coarsest level sampling using MLM and account for the approximation error introduced. We provide theoretical proofs of detailed balance and demonstrate that our multilevel approach constitutes a consistent MCMC algorithm. Additionally, we derive the expression for cost reduction due to machine learning model to facilitate cost analysis of the hierarchical sampling algorithm. Our technique is demonstrated on a standard benchmark inference problem in groundwater flow, where we estimate the probability density of a quantity of interest using a four-level MCMC algorithm. Our proposed algorithm accelerates multilevel sampling by a factor of two while achieving similar accuracy compared to sampling using the standard multilevel algorithm.

97 MATHEMATICS AND COMPUTING

Development and Evaluation of a General Drag Model for Gas-Solid Flows via Deep Learning

This project presents the development and evaluation of a general drag model for gas–solid multiphase flows using deep learning techniques. A comprehensive database of more than 4,000 experimental and numerical data points for spherical and non spherical particles was compiled, incorporating geometric features such as sphericity, aspect ratio, and orientation. Several predictive approaches—including traditional em pirical correlations, machine learning, and deep neural networks—were benchmarked, with the proposed Drag Coefficient Correlation-aided Deep Neural Network (DCC DNN) demonstrating superior accuracy. To account for particle–particle interactions, additional drag data were generated using CFD-based simulations of packed and flu idized beds, leading to the development of a retrained model capable of incorporat ing volume fraction effects. Integration of the trained model with the MFiX CFD solver was achieved using FTorch, enabling drag predictions during discrete element method (DEM) simulations. Validation against experimental data for single particles and fluidized beds confirmed the model’s improved predictive ability, particularly for non-spherical geometries. While the model performed strongly under fluidized con ditions, limitations remained in unfluidized regimes, suggesting a need for expanded datasets. Overall, this study demonstrates the feasibility of combining deep learning with physics-informed CFD to improve drag modeling for gas–solid flows, with promis ing implications for scaling multiphase simulations in industrial applications.

42 ENGINEERING