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Medical Aspects of Gemini Extravehicular Activities

The medical aspects of Gemini extravehicular activities are principally concerned with the physiological responses to high workloads, high thermal stresses, and low fatigue tolerance. Analysis of physiological instrumentation data. from extravehicular flights and training operations contributed significantly to the understanding of extra-vehicular workloads and the means of controlling these workloads.

G Fred Kelly

Fourth International Microgravity Combustion Workshop

This proceedings document is a compilation about work performed by a community of researchers from universities, industry and government laboratories across the United States and in Europe and Japan who have recognized the value of the reduced-gravity environment in attacking the fundamental and practical problems of combustion science. On their behalf, I am pleased to present this document to the assembled participants at the Fourth International Microgravity Combustion Workshop, to be held near the NASA Lewis Research Center in Cleveland, Ohio, on May 19-21, 1997.

Microgravity

Learning Nonlinear Reduced Models from Data with Operator Inference

This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example.

Mechanics

"Long Life" Dc Brush Motor for Use on the Mars Surveyor Program

DC brush motors have several qualities which make them very attractive for space flight applications. Their mechanical commutation is simple and lightweight, requiring no external sensing and control in order to function properly. They are extremely efficient in converting electrical energy into mechanical energy. Efficiencies over 80% are not uncommon, resulting in high power throughput to weight ratios. However, the inherent unreliability and short life of sliding electrical contacts, especially in vacuum, have driven previous programs to utilize complex brushless DC or the less efficient stepper motors. The Mars Surveyor Program (MSP'98) and the Shuttle Radar Topography Mission (SRTM) have developed a reliable "long life" brush type DC motor for operation in low temperature, low pressure CO2 and N2, utilizing silver-graphite brushes. The original intent was to utilize this same motor for SRTM's space operation, but the results thus far have been unsatisfactory in vacuum. This paper describes the design, test, and results of this development.

David Braun

Uncovering obscured phonon dynamics from powder inelastic neutron scattering using machine learning

The study of phonon dynamics is pivotal for understanding material properties, yet it faces challenges due to the irreversible information loss inherent in powder inelastic neutron scattering spectra and the limitations of traditional analysis methods. In this study, we present a machine learning framework designed to reveal obscured phonon dynamics from powder spectra. Using a variational autoencoder, we obtain a disentangled latent representation of spectra and successfully extract force constants for reconstructing phonon dispersions. Notably, our model demonstrates effective applicability to experimental data even when trained exclusively on physics-based simulations. The fine-tuning with experimental spectra further mitigates issues arising from domain shift. Analysis of latent space underscores the model’s versatility and generalizability, affirming its suitability for complex system applications. Furthermore, our framework’s two-stage design is promising for developing a universal pre-trained feature extractor. This approach has the potential to revolutionize neutron measurements of phonon dynamics, offering researchers a potent tool to decipher intricate spectra and gain valuable insights into the intrinsic physics of materials.

domain adaptation

HydraGNN_Predictive_GFM_2026 - Ensemble of predictive graph foundation models for atomistic materials modeling

This release contains data and parameters of HydraGNN-based graph foundation models trained as a result of the work published in the pre-print "Exascale Multi-Task Graph Foundation Models for Imbalanced, Multi-Fidelity Atomistic Data" by M. Lupo Pasini et al. (https://arxiv.org/abs/2604.15380). We jointly train on 16 open first-principles datasets (544+ million structures covering 85+ elements) using a multi-task architecture with per-dataset heads and a scalable ADIOS2/DDStore data pipeline. On Frontier, we execute six large-scale DeepHyper hyperparameter optimization campaigns in FP64 and promote the top-performing message-passing models to sustained 2,048-node training, yielding a PaiNN-based lead model. The version of HydraGNN used to generate the outputs provided in this release is HydraGNN v5.0 (https://github.com/ORNL/HydraGNN/releases/tag/v5.0) The list of datasets used for the training of the graph foundation model is the following: 1) Alexandria [1] 2) ANI1x [2] 3) MPTrj [3] 4) Open Catalyst 2020 (OC20) [4] 5) Open Catalyst 2022 (OC22) [5] 6) Open Catalyst 2025 (OC25) [6] 7) Open Direct ir Capture 2023 (ODAC23) [7] 8) Open Materials 2024 (OMat24) [8] 9) Open Molecules 2025 (OMol25) [9] 10) OMol25-neutral (subset of OMol25 that contains only molecules with zero total charge) 11) OMol25-non-neutral (subset of OMol25 that contains only molecules with non-zero total charge) 12) Open Polymers 2026 (OPoly2026) [10] 13) Nabla2DFT [11] 14) QCML [12] 15) QM7X [reference 13] 16) transition1x [14] Dataset references: [1] J. Schmidt et al., “A dataset of 175k stable and metastable materials calculated with the PBEsol and SCAN functionals,” Scientific Data, vol. 9, p. 64, 2022. [2] J. S. Smith et al., “The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules,” Scientific Data, vol. 7, p. 134, 2020. [Online]. Available: https: //www.nature.com/articles/s41597-020-0473-z [3] A. Jain et al., “Commentary: The Materials Project: A materials genome approach to accelerating materials innovation,” APL Materials, vol. 1, no. 1, p. 011002, 07 2013. [Online]. Available: https://doi.org/10.1063/1.4812323 [4] L. Chanussot et al., “Open catalyst 2020 (oc20) dataset and community challenges,” ACS Catalysis, vol. 11, no. 10, pp. 6059–6072, 2021. [Online]. Available: https://doi.org/10.1021/acscatal.0c04525 [5] K. Tran et al., “Open catalyst 2022 (oc22) dataset and challenges for oxidation electrocatalysts,” ACS Catalysis, vol. 13, no. 5, pp. 3066–3084, 2023. [Online]. Available: https://doi.org/10.1021/acscatal.2c05426 [6] S. J. Sahoo et al., “The open catalyst 2025 (oc25) dataset and models for solid-liquid interfaces,” arXiv preprint arXiv:2509.17862, 2025. [Online]. Available: https://arxiv.org/abs/2509.17862 [7] A. Sriram et al., “The open DAC 2023 dataset and challenges for sorbent discovery in direct air capture,” ACS Central Science, vol. 10, no. 5, pp. 923–941, 2024. [8] L. Barroso-Luque et al., “Open materials 2024 (omat24) inorganic materials dataset and models,” 2024. [Online]. Available: https://arxiv.org/abs/2410.12771 [9] D. S. Levine et al., “The open molecules 2025 (OMol25) dataset, evaluations, and models,” 2025. [Online]. Available: https://arxiv.org/abs/2505.08762 [10] D. S. Levine et al., The open polymers 2026 (OPoly26) dataset and evaluations,” arXiv preprint arXiv:2512.23117, 2025. [Online]. Available: https://arxiv.org/abs/2512.23117 [11] K. Khrabrov et al., “Nabla2dft: A universal quantum chemistry dataset of drug-like molecules and a benchmark for neural network potentials,” in NeurIPS 2024 Datasets and Benchmarks Track, 2024. [Online]. Available: https://openreview.net/forum?id=ElUrNM9U8c [12] S. Ganscha et al., “The QCML dataset, quantum chemistry reference data from 33.5M DFT and 14.7B semi-empirical calculations,” Scientific Data, vol. 12, p. 406, 2025. [13] J. Hoja et al., “QM7-X, a comprehensive dataset of quantum-mechanical properties spanning the chemical space of small organic molecules,” Scientific Data, vol. 8, p. 43, 2021. [Online]. Available: https://www.nature.com/articles/s41597-021-00812-2 [14] M. Schreiner et al., “Transition1x - a dataset for building generalizable reactive machine learning potentials,” Scientific Data, vol. 9, p. 779, 2022. The folder "datasets_ADIOS2_format" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "datasets_ADIOS2_format" directory contains 2 sub-directories, one for the version "v1" of the datasets and one for the version "v2" of the datasets. The version "v1" of the datasets provides values of the total energy as they are extracted from the original data as it was released by the respective institutions. The version "v2" of the datasets provides values of the energy that have been realigned. The realignment was performed by training a linear regression model that predicts the total energy as a function of the chemical composition of the atomistic structure, and then subtract such prediction from the original value of the total energy. Both folders "v1" and "v2" contain 16 sub-directories, each corresponding to an ADIOS2-formatted dataset The folder "DeepHyper-results" contains the configurational files and model's parameters for all the 186 HPO trials that were successfully completed by the scalable hyperparameter optimization (HPO) runs on Frontier. The content of the folder "DeepHyper-results" I structured as follows: 1) task-list.txt: list of mpnn name, jobid, and deephyper task id 2) gfm_${MPNN}_${JOBID}_0.${TASKID}: run directory with checkpoint files 3) gfm_${MPNN}: deephyper summary directory (*.csv) for each specific MPNN type 4) deephyper-experiment-${JOBID}: output and error logs for each job The file "deephyper-sorted.csv" contains the details of each HydraGNN model built and tested by HPO, obtained by merging the (*.csv) filed from each HPO run executed. Out of all the HPO trials, we selected 10 to continue the training of the respective HydraGNN models. Due to limited computational budget available in the LRN070 allocation we could not complete the training till convergence for all these 10 selected models. The folder "models" contains multiple sub-folders, one per each HydraGNN model trained. Each model sub-folder contains the parameters of each HydraGNN model, with multiple checkpoint-restarts. The list of sub-folders are as follows: 1) multidataset_hpo-BEST1-fp64 2) multidataset_hpo-BEST2-fp64 3) multidataset_hpo-BEST3-fp64 4) multidataset_hpo-BEST4-fp64 5) multidataset_hpo-BEST5-fp64 6) multidataset_hpo-BEST6-fp64 7) multidataset_hpo-BEST7-fp64 8) multidataset_hpo-BEST8-fp64 9) multidataset_hpo-BEST9-fp64 10) multidataset_hpo-BEST10-fp64 Within each one of these folders, additional auxiliary log files are provided with descriptions about how the training proceeded. The lead PaiNN-model is contained inside "multidataset_hpo-BEST6-fp64". The file "mlp_branch_weights" contains the parameters of the multi-layer perceptron (MLP) used to reconcile the predictions of the 16 output decoding heads of the HydragNN architectures. The MLP takes in input the chemical composition of the atomistic structure and predicts averaging weights to linearly mix the predictions of each output decoding head toward consolidating them into a single one. The folder "1.1billion-structure-inference" contains 1.1 billion atomistic structures randomly generated. Each structures is associated with energy and forces predicted with the lead-PaiNN model combined with the MLP model for reconciliation of the multi-branch predictions generated by the 16 output decoding heads. The folder "1.1billion-structure-inference" contains 9,300 (*.tar.gz) subdirectories, one per Frontier compute node used to execute the inference at exascale. Once uncompressed, each (*.tar.gz) subdirectory contains an ADIOS2 (*.bp) file container, where each atomistic structure is stored as a PyTorch-Geometric Data object. The file "export_dataset_environment_variables.sh" contains the environment variables that need to be set before running the HydraGNN code to reproduce the results provided in this dataset release. The code that can be used to load the ADIOS2 files, load HydraGNN models, and run inference is available at: https://github.com/ORNL/HydraGNN/releases/tag/v5.0

36 MATERIALS SCIENCE

Structure–Property Linkage in Alloys Using Graph Neural Network and Explainable Artificial Intelligence

Deep learning tools have recently shown significant potential for accelerating the prediction of microstructure–property linkage in materials. While deep neural networks like convolution neural networks (CNNs) can extract physics information from 3D microstructure images, they often require a large network architecture and substantial training time. In this research, we trained a graph neural network (GNN) using phase field generated microstructures of Ni-Al alloys to predict the evolution of mechanical properties. We found that a single GNN is capable of accurately predicting the strengthening of Ni-Al alloys with microstructures of varying sizes and dimensions, which cannot otherwise be done with a CNN. Additionally, GNN requires significantly less GPU utilization than CNN and offers more interpretable explanation of predictions using saliency analysis as features are manually defined in the graph. We also utilize explainable artificial intelligence tool Bayesian Inference to determine the coefficients in the power law equation that governs coarsening of precipitates. Overall, our work demonstrates the ability of the GNN to accurately and efficiently extract relevant information from material microstructures without having restrictions on microstructure size or dimension and offers an interpretable explanation.

Chemistry

Microstructure prediction for Ti-22Al-25Nb in laser powder bed fusion

This work presents a physics-informed framework for predicting solidification morphology and defect susceptibility in additively manufactured Ti–22Al–25Nb across a broad processing space. The framework integrates solidification microstructure selection (SMS) analysis with a single-track defect-based printability map to establish a unified methodology linking processing parameters to both interfacial morphology and manufacturability. Thermal gradients G and solidification rates R are first computed using the Thermo-Calc Additive Manufacturing (TC-AM) module, a finite-interface-dissipation (FID) phase-field (PF) model coupled with CALPHAD method is then employed to systematically distinguish planar and dendritic regimes as functions of $G$ and $R$. By superimposing the printability map onto the morphology projections, a comprehensive process–structure framework is obtained. Across most processing conditions, the predicted microstructure is predominantly dendritic, while planar growth emerges only under selected laser power $P$ and scan speed $v$ combinations. In addition to morphology classification, the framework quantifies the dendritic area fraction and introduces a width-based morphology descriptor to characterize the spatial extent of planar/dendritic regions within the melt pool. It provides mechanistic insight into the interplay between solidification physics and defect formation, offering practical guidance for parameter selection and microstructural control in Ti–22Al–25Nb additive manufacturing (AM).

36 MATERIALS SCIENCE

Multi-Agent Swarm State of the Art Report

The Next-Generation Multi-Agent Swarm (NGS) Study conducted by NASA’s Ames Research Center for NASA’s Space Technology Mission Directorate (STMD) will develop a comprehensive understanding of emerging multi-agent swarm capabilities. The study aims to identify existing swarm capabilities and asses their potential for persistent lunar space situational awareness, surface monitoring, and distributed autonomy demonstrations. A key objective is to inform the design of a next-generation multi-agent swarm that can perform autonomous distributed remote sensing, position, navigation, and timing (PNT) services, automated deployment that leverages autonomy, edge computing, and interoperable networking to enable cooperative operations without the need for immediate human operation. This study will address specific shortfalls identified by STMD, including intelligent multi-agent constellations, autonomy, edge computation, position, navigation, and timing for small spacecraft, small spacecraft propulsion, and space situational awareness (1625, 1438, 1433, 1557, 1431, 1430, 1589). The NASA Ames Mission Design Center (MDC) will provide subject matter expertise to support systems engineering trades, while experts in autonomy and spacecraft swarms in NASA’s Intelligent Systems Division will lead the study and focus on identifying emerging next-generation swarm capabilities. The study objectives include: capturing the current state-of-the-art for multi-agent swarm capabilities, evaluating technologies and creating technology roadmaps, and developing at least one new technology demonstration mission concept. This initial NGS study report surveys the current state of the art in technology areas relevant for the next-generation multi-agent swarm design. Our primary focus is on surveying relevant deployed space systems1, supplemented with selective analysis of relevant proposed missions and technology developments that have yet to fly.

agent

Challenge of Fielding Experiments at the Annular Core Research Reactor

Conference is the annual Test, Research &Training Reactors (TRTR) meeting. Typically attended by dozens of research reactor operators, educators, trainers, maintenance & service contractors Also, members of the Nuclear Regulatory Commission (NRC) attend. Presentation highlights ACRRs capability and the process used to submit and approve experimental activities. This presentation is adapted from my previous presentation to the Material Test and Research conference, SAND2025-1775526.

Martin, Lonnie E. [Sandia National Laboratories (S

Mercury Corrosion Loop Testing Program

The Mercury Corrosion Loop Testing Program continued through the second quarter. Materials to be tested in the 10 forced-convection test loops were selected; the materials are: Haynes 25, 9 Cr-1Mo alloy clad with Type 316 stainless steel, AM 350 stainless steel, and columbium (niobium) clad with Type 316 stainless steel. The eight-test-cell facility was completed and all utilities were installed. Pneumatic and electronic instrumentation for all test cells was installed and calibrated. Fabrication was initiated on the first four Haynes 25 loops. The first loop was 85% assembled at the end of the quarter. A centrifugal pump made from Type 316 stainless steel was tested; bearing modifications were made to improve operation.

Corrosion

Nuclear Safety [Vol. 34, No. 1, January-March 1993]

Nuclear Safety is a review journal that covers significant developments in the field of nuclear safety. Its scope includes the analysis and control of hazards associated with nuclear energy, operations involving fissionable materials, and the products of nuclear fission and their effects on the environment. Primary emphasis is on safety in reactor design, construction, and operation; however, the safety aspects of the entire fuel cycle, including fuel fabrication, spent-fuel processing, nuclear waste disposal, handling of radioisotopes, and environmental effects of these operations, are also treated. Table of Contents for this issue follows. GENERAL SAFETY CONSIDERATIONS: 1 An Integrated Regional Approach To Risk Management of Industrial Systems, S. Chakraborty and R. Stratton; 9 Annual Technical Meeting of the NRC Cooperative Severe Accident Research Program, E. G. Silver; ACCIDENT ANALYSIS: 13 Deterministic Severe Accident Criteria as Severe Accident Design Criteria and Policy for the New Production Reactor-Heavy Water Reactor, P. T. Rhoads; 20 Proposed Deterministic Severe Accident Criteria for the Heavy Water Reactor-New Production Reactor Containment, K. D. Bergeron, S. E. Slezak, and C. E. Leach; 33 Quasi-Static Core Liquid Level Depression and Long-Term Core Uncovery During a PWR LOCA, Y. Kukita, R. R. Schultz, H. Nakamura, and J. Katayama; 49 LIRA: An Advanced Containment System to Minimize the Accidental Radioactivity Releases, A. Turricchia; 63 Errata to “A Review of Hydrogen Production During Melt/Water Interaction in LWRs,” Vol. 33, No. 4; CONTROL AND INSTRUMENTATION: 64 The Nuplex 80+™ Advanced Control Complex from ABB Combustion Engineering, F. Ridolfo, D. Harmon, and K. Scarola; DESIGN FEATURES: 76 A Scheme for Passive Isolation of the Containment of a Reactor, A. K. Ghosh, V. V. Raj, and K. Kakodkar; 84 Utility Requirements for Safety in the Passive Advanced Light-Water Reactor, T. U. Marston, W. H. Layman, and G. Bockhold, Jr.; WASTE AND SPENT FUEL MANAGEMENT: 91 Activities Related to Waste and Spent Fuel Management, Compiled by M. D. Muhlheim and E. G. Silver; OPERATING EXPERIENCES: 103 Testing Deficiencies in Auxiliary Systems Feedwater Systems, J. D. Kueck; 110 Reactor Shutdown Experience, Compiled by J. W. Cletcher; 113 Selected Safety-Related Events, Compiled by G. A. Murphy; 115 Operating U.S. Power Reactors, Compiled by M. D. Muhlheim and E. G. Silver; RECENT DEVELOPMENTS: 133 General Administrative Activities, Compiled by M. D. Muhlheim and E. G. Silver; 145 Reports, Standards, and Safety Guides, D. S. Queener; 150 Proposed Rule Changes as of Sept. 30, 1992; ANNOUNCEMENTS: 75 Harvard Short Course on Risk: Science, Assessment, and Management; 102 International Conference on Reactor Physics and Reactor Computations; 102 The Fourth International Conference on Nuclear Waste Reprocessing and Waste Management [RECOD ’94]; 132 International Symposium on the Radiological Exposure of the Population of the European Community from Radioactivity in the Mediterranean Sea [MARINA-MED]; 162 International High-Level Radioactive Waste Conference ‘Technology Integration—Above and Below”; 154 The Authors; 158 Indexes to Nuclear Safety, Volume 33.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

NASA Agile Community of Practice 2024-2026 Report

This 2024-2026 report provides a summary of the products and activities executed by the NASA Agile Community of Practice (CoP) during its second and third years. Building on the foundation established in its inaugural year, the CoP continued to advance Agile values and principles across NASA centers. The report highlights key initiatives, including specialized framework training, AI integration in Agile toolkits, and active participation in agency-wide project management and systems engineering workshops.

Agile

Technology Demonstrator of an Americium-Fuelled Radioisotope Stirling Generator

Americium-241 is used as the fuel of choice in European Radioisotope Power Systems. The University of Leicester have developed a number of systems using this fuel type, including a 200 Wth heat source. To maximise the electrical output that can be generated from the heat source, the University of Leicester and NASA Glenn Research Center have collaborated on a radioisotope Stirling generator concept, building on the long heritage of dynamic power conversion developments at NASA GRC. Here we present the design of a technology demonstrator of the Americium-fuelled Radioisotope Stirling Generator (Am-RSG).

Americium-241

Astrophysical science with a spaceborne photometric telescope

The FRESIP Project (FRequency of Earth-Sized Inner Planets) is currently under study at NASA Ames Research Center. The goal of FRESIP is the measurement of the frequency of Earth-sized extra-solar planets in inner orbits via the photometric signature of a transit event. This will be accomplished with a spaceborne telescope/photometer capable of photometric precision of two parts in 100,000 at a magnitude of m(sub v) = 12.5. To achieve the maximum scientific value from the FRESIP mission, an astrophysical science workshop was held at the SETI Institute in Mountain View, California, November 11-12, 1993. Workshop participants were invited as experts in their field of astrophysical research and discussed the astrophysical science that can be achieved within the context of the FRESIP mission.

Granados, Arno F.

Machine learning approach for vibronically renormalized electronic band structures

Here, we present a machine learning (ML) method for efficient computation of vibrational thermal expectation values of physical properties from first principles. Our approach is based on the nonperturbative frozen phonon formulation in which stochastic Monte Carlo algorithm is employed to sample configurations of nuclei in a supercell at finite temperatures based on a first-principles phonon model. A deep-learning neural network is trained to accurately predict physical properties associated with sampled phonon configurations, thus bypassing the time-consuming ab initio calculations. To incorporate the point-group symmetry of the electronic system into the ML model, group-theoretical methods are used to develop a symmetry-invariant descriptor for phonon configurations in the supercell. We apply our ML approach to compute the temperature dependent electronic energy gap of silicon based on density functional theory (DFT). We show that, with less than a hundred DFT calculations for training the neural network model, an order of magnitude larger number of sampling can be achieved for the computation of the vibrational thermal expectation values. Our work highlights the promising potential of ML techniques for finite temperature first-principles electronic structure methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Electronic structure prediction of medium and high entropy alloys across composition space

We propose machine learning (ML) models to predict the electron density — the fundamental unknown of a material’s ground state — across the composition space of concentrated alloys. From this, other physical properties can be inferred, enabling accelerated exploration. A significant challenge is that the number of descriptors and sampled compositions required for accurate prediction grows rapidly with species. To address this, we employ Bayesian Active Learning (AL), which minimizes training data requirements by leveraging uncertainty quantification capabilities of Bayesian Neural Networks. Compared to the strategic tessellation of the composition space, Bayesian-AL reduces the number of training data points by a factor of 2.5 for ternary (SiGeSn) and 1.7 for quaternary (CrFeCoNi) systems. We also introduce easy-to-optimize, body-attached-frame descriptors, which respect physical symmetries while keeping descriptor-vector size nearly constant as alloy complexity increases. Our ML models demonstrate high accuracy and generalizability in predicting both electron density and energy across composition space.

materials science

Echo state network for coarsening dynamics of charge density waves

An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its training process. Yet, despite the seemingly restricted learnable parameters, ESN has been shown to successfully capture the spatial-temporal dynamics of complex patterns. Here we build an ESN to model the coarsening dynamics of charge-density waves (CDWs) in a semiclassical Holstein model, which exhibits a checkerboard electron density modulation at half-filling stabilized by a commensurate lattice distortion. The inputs to the ESN are local CDW order parameters in a finite neighborhood centered around a given site, while the output is the predicted CDW order of the center site at the next time step. Special care is taken in the design of couplings between hidden layer and input nodes to ensure lattice symmetries are properly incorporated into the ESN model. Since the model predictions depend only on CDW configurations of a finite domain, the ESN is scalable and transferrable in the sense that a model trained on dataset from a small system can be directly applied to dynamical simulations on larger lattices. Furthermore, our work opens avenues for efficient dynamical modeling of pattern formations in functional electron materials.

2-dimensional systems