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A resolution independent neural operator

The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.

Deep operator network (DeepONet)

Heterogeneous Mixtures of Dictionary Functions to Approximate Subspace Invariance in Koopman Operators: Why Deep Koopman Operators Work

Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.

Johnson, Charles A.

Explainable and Differentiable Reinforcement Learning for Multi-objective Optimization in Particle Accelerators

Operating particle accelerators involves optimizing multiple goals simultaneously, which can be challenging due to trade-offs among objectives. While evolutionary algorithms like the genetic algorithm (GA) have been used for various Multi-Objective Optimization (MOO) tasks, they are not inherently suited for complex control problems. This talk highlights two variations of Reinforcement Learning (RL) for concurrently optimizing heat load and trip rates at the Continuous Electron Beam Accelerator Facility (CEBAF). The problem involves strict constraints on individual states, actions, and overall energy requirements of the beam. First, this talk highlights how differentiability can be harnessed through a Deep Differentiable Reinforcement Learning (DDRL) approach to address MOO issues within particle accelerators. We examine the DDRL method alongside Model Free Reinforcement Learning (MFRL), GA, and Bayesian Optimization (BO). The performance of these methods is assessed by generating a Pareto-front for two objectives. Our findings indicate that DDRL excels in handling high-dimensional problems more effectively than MFRL, BO, and GA. Next, we will show integration of explainable physics-based constraints into RL algorithms to enhance trans- parency and trust in decision-making processes by enabling users to verify that agents adhere to established physical principles. This surrogate function can be modeled using neural networks or sparse dictionary mod- els. By examining the mathematical form of the learned constraint function, we are able to confirm the agent has learned to use the established physics of each environment provided but the surrogate model. In addi- tion, we find that the introduction of a mathematical functional dictionary based surrogate model enables our reinforcement learning algorithms to reliably converge for difficult high-dimensional accelerator controls environments.

Rajput, Kishansingh [Thomas Jefferson National Acc

Machine learning model inputs, outputs, and scripts associated with “Artificial intelligence-guided iterations between observations and modeling significantly improve environmental predictions”

NOTE: The manuscript associated with this data package is currently in review. The data may be revised based on reviewer feedback. Upon manuscript acceptance, this data package will be updated with the final dataset and additional metadata. This data package is associated with the manuscript “Artificial intelligence-guided iterations between observations and modeling significantly improve environmental predictions” (Malhotra et al., in prep). This effort was designed following ICON (integrated, coordinated, open, and networked) principles to facilitate a model-experiment (ModEx) iteration approach, leveraging crowdsourced sampling across the contiguous United States (CONUS). New machine learning models were created every month to guide sampling locations. Data from the resulting samples were used to test and rebuild the machine learning models for the next round of sampling guidance. Associated sediment and water geochemistry and in situ sensor data can be found at https://data.ess-dive.lbl.gov/datasets/doi:10.15485/1923689, https://data.ess-dive.lbl.gov/datasets/doi:10.15485/1729719, and https://data.ess-dive.lbl.gov/datasets/doi:10.15485/1603775. This data package is associated with two GitHub repositories found at https://github.com/parallelworks/dynamic-learning-rivers and https://github.com/WHONDRS-Hub/ICON-ModEx_Open_Manuscript. In addition to this readme, this data package also includes two file-level metadata (FLMD) files that describes each file and two data dictionaries (DD) that describe all column/row headers and variable definitions. This data package consists of two main folders (1) dynamic-learning-rivers and (2) ICON-ModEx_Open_Manuscript which contain snapshots of the associated GitHub repositories. The input data, output data, and machine learning models used to guide sampling locations are within dynamic-learning-rivers. The folder is organized into five top-level directories: (1) “input_data” holds the training data for the ML models; (2) “ml_models” holds machine learning (ML) models trained on the data in “input_data”; (3) “examples” contains files for direct experimentation with the machine learning model, including scripts for setting up “hindcast” run; (4) “scripts” contains data preprocessing and postprocessing scripts and intermediate results specific to this data set that bookend the ML workflow; and (5) “output_data” holds the overall results of the ML model on that branch. Each trained ML model resides on its own branch in the repository; this means that inputs and outputs can be different branch-to-branch. There is also one hidden directory “.github/workflows”. This hidden directory contains information for how to run the ML workflow as an end-to-end automated GitHub Action but it is not needed for reusing the ML models archived here. Please see the top-level README.md in the GitHub repository for more details on the automation. The scripts and data used to create figures in the manuscript are within ICON-ModEx_Open_Manuscript. The folder is organized into four folders which contain the scripts, data, and pdf for each figure. Within the “fig-model-score-evolution” folder, there is a folder called “intermediate_branch_data” which contains some intermediate files pulled from dynamic-learning-rivers and reorganized to easily integrate into the workflows. NOTE: THIS FOLDER INCLUDES THE FILES AT THE POINT OF PAPER SUBMISSION. IT WILL BE UPDATED ONCE THE PAPER IS ACCEPTED WITH ANY REVISIONS AND WILL INCLUDE A DD/FLMD AT THAT POINT. We thank the United States Forest Service, Washington Department of Fish and Wildlife, Washington Department of Natural Resources, Cowiche Canyon Conservatory, Washington State Parks and Recreation Commission (Scientific Research Permit #210901), and the Confederated Tribes and Bands of the Yakama Nation for access to field locations where the samples labeled “SSS” were collected. We also thank the Yakama Nation Tribal Council and Yakama Nation Fisheries for working with us to facilitate sample collection and optimization of data usage according to their values and worldview. WHONDRS consortium members were asked to provide any acknowledgments for the collection of samples labeled “CM” and the following is a list of acknowledgments that were submitted with their corresponding Site IDs: (MART) Research activities were conducted in part on the Wind River Experimental Forest within the Gifford Pinchot National Forest; (MP- 100379) Philadelphia is part of Lenapehoking, the ancestral homelands of the Lenape peoples; (MP-102398) Land surveyed is the ancestral homelands of the Nookhose'iinenno (Arapaho), Tsis tsis'tas (Cheyenne), and Nuuchu (Ute); (MP-100749 and MP- 100747) Georgia Coastal Ecosystem LTER, OCE-1832178; (SP-70 and SP-72) Eastern Shoshone, Shoshone-Bannock; (MP- 102944) Funded by Oregon Watershed Enhancement Board. On the traditional lands of the Confederated Tribes of the Siletz, Confederated Tribes of the Grand Rhonde, and the Clatsop-Nehalem Confederated Tribe; (MP- 100607) Holiday Creek is located on the traditional territory of the Monacan Indian Nation; (SP-45) Lafayette Blue Springs State Park; (MP-102420) NSF DEB-2016749; (MP-100019) New Hampshire Agriculture Experiment Station; (SP-35) Rayonier (land owner; https://www.rayonier.com/); (MP- 101276) US Department of Energy, Office of Science, Biological and Environmental Research, Subsurface Biogeochemical Research, Watershed Dynamics and Evolution SFA at ORNL; (MP- 103224) Watershed Dynamics and Evolution SFA at ORNL; (MP- 101584) Traditional lands of the Oceti Sakowin (Dakota, Lakota, Nakoda) and Anishinaabe Peoples.

54 ENVIRONMENTAL SCIENCES

Physics-guided dual implicit neural representations for source separation

Significant challenges exist in efficient data analysis of most advanced experimental and observational techniques because the collected signals often include unwanted contributions, such as background and signal distortions, that can obscure the physically relevant information of interest. To address this, we have developed a self-supervised machine-learning approach for source separation using a dual implicit neural representation framework that jointly trains two neural networks: one for approximating distortions of the physical signal of interest and the other for learning the effective background contribution. Our method learns directly from the raw data by minimizing a reconstruction-based loss function without requiring labeled data or pre-defined dictionaries. We demonstrate the effectiveness of our framework by considering a challenging case study involving large-scale simulated, as well as experimental, momentum-energy-dependent inelastic neutron scattering data in a four-dimensional parameter space, characterized by heterogeneous background contributions and unknown distortions to the target signal. The method is found to successfully separate physically meaningful signals from a complex or structured background even when the signal characteristics vary across all four dimensions of the parameter space. An analytical approach that informs the choice of the regularization parameter is presented. Our method offers a versatile framework for addressing source separation problems across diverse domains, ranging from superimposed signals in astronomical measurements to structural features in biomedical image reconstructions.

47 OTHER INSTRUMENTATION

Explainable physics-based constraints on reinforcement learning for accelerator optimization

We present a reinforcement learning (RL) framework for optimizing particle accelerator experiments that builds explainable physics-based constraints on agent behavior. The goal is to increase transparency and trust by letting users verify that the agent’s decision-making process incorporates suitable physics. Our algorithm uses a learnable surrogate function for physical observables, such as energy, and uses them to fine-tune how actions are chosen. This surrogate can be represented by a neural network or by an interpretable sparse dictionary model. We test our algorithm on a range of particle accelerator optimization environments designed to emulate the Continuous Electron Beam Accelerator Facility at Jefferson Lab. By examining the mathematical form of the learned constraint function, we are able to confirm the agent has learned to use the established physics of each environment. In addition, we find that the introduction of a physics-based surrogate enables our RL algorithms to reliably converge for difficult high-dimensional accelerator optimization environments.

explainability

Leafweb: Leaf Gas Exchange and Pulse-Amplitude Modulated Fluorometry for C4 Species, June 2026 Release

This dataset contains leaf gas exchange and Pulse-Amplitude Modulated (PAM) fluorometry for 98 C4 species. The C4 photosynthetic pathway employs specialized CO2 concentration mechanisms and Kranz anatomy to enrich CO2 concentration around Rubisco, the enzyme that catalyzes carbon fixation in the Calvin-Benson cycle to suppress photorespiration and increase the use efficiencies of light, nitrogen, and water as compared to the C3 photosynthetic pathways. Large-scale C4 photosynthetic datasets are relatively scarce, which has affected C4 photosynthesis research. To improve C4 photosynthetic data availability, Leafweb organized an effort to systematically collect, compile, standardize, and organize measurements of leaf gas exchange and/or Pulse-Amplitude Modulated (PAM) fluorometry of C4 species. This derived a C4 photosynthetic dataset containing measurements made by independent researchers in multiple countries in various environments (field, garden, or greenhouse). It covers three biochemical subtypes – the nicotinamide adenine dinucleotide phosphate-malic enzyme (NADP-ME), nicotinamide adenine dinucleotide-malic enzyme (NAD-ME), and phosphoenolpyruvate carboxykinase (PEP-CK) subtypes. This dataset is useful for using Artificial Intelligence / Machine Learning and mechanistic models to study C4 photosynthesis and compare across different biochemical subtypes. This dataset contains 3 compressed (*.zip) folders containing 1,892 data files in comma-separate values (*.csv) format. Additional metadata are provided: one data dictionary and a file-level metadata file in comma-separate values (*.csv) format and a user guide in PDF (*.pdf) format.

Zhou, Haoran [Tianjin University, China]

Fully Homomorphic Encryption

This code implements a Fully Homomorphic Encryption (FHE) system, enabling secure computation on encrypted data without requiring decryption. It supports encryption, decryption, and homomorphic operations like matrix multiplication and addition. This code is adaptable for integrating FHE into linear-time invariant (LTI) systems, including digital control and filtering. With proper configuration from subject matter expertise, encrypted system parameters and signals can be manipulated to perform tasks like state updates, output calculations, and convolution in the encrypted domain. By preserving the structure of LTI systems while ensuring privacy, the framework facilitates secure applications in areas such as autonomous systems, signal processing, and industrial automation. The code initializes the encryption system using parameters provided in the env dictionary. These parameters include the ciphertext modulus, key dimension, plaintext fixed-point scaling factor, and noise bound. During initialization, a secret key is generated, which is essential for encrypting and decrypting data securely. The modular design allows users to tailor these parameters to specific use cases or security requirements. The code implements multiple cryptographic schemes. The learning with errors (LWE) encryption method encodes cleartext message to their plaintext fixed-point representation then encrypted into ciphertext space with additive noise. This noise ensures the security of the scheme, relying on the computational hardness of the LWE problem. The code also includes the Gentry-Sahai-Waters (GSW) scheme based off the LWE problem. Homomorphic matrix multiplication is performed between the LWE and GSW to encrypted data. This is achieved using a decomposition function on the LWE ciphertext during the multiplication operation. For higher-dimensional data, the code includes a method to encrypt entire matrices (GSWMat) using GSW encryption. These encrypted matrices can then be used for homomorphic matrix multiplications (MatMult). The decryption function uses the secret key to recover the original plaintext, removing the added noise and scaling that was originally applied during encryption.

Lois, Roberts [Idaho National Laboratory (INL), Id

Livewire: Automatic Annotations

Diogenes processes datasets to provide data quality metrics for the Livewire platform and creates standardized data dictionaries from data annotations. Diogenes needs data annotations that clearly outline thenformat and organization of the data. It also relies on the type, class, and unit of each data piece for comprehensive analysis, which it cannot determine independently. The Annotation Tool significantly reduces the time needed to create annotations for Diogenes by generating data annotations with the correct formatting and content. It also employs machine learning and hard-coded models to automatically annotate data class, quality type, and data units.

33 - ADVANCED PROPULSION SYSTEMS

Remote sensing images, DEM, and point clouds associated with “Accuracy evaluation of cost-effective 3D reconstruction approaches for hydrobiogeochemical processes in non-perennial stream riverbeds”

This data package is associated with the publication “Accuracy evaluation of cost-effective 3D reconstruction approaches for hydrobiogeochemical processes in non-perennial stream riverbeds” published in Frontiers in Environmental Science, Environmental Informatics and Remote Sensing (Bao et al., 2026; doi: 10.3389/fenvs.2026.1725258). This data package includes the drone photos for a section of Umtanum Creek in Washington, Unted States. The photos were used to reconstruct the 3-dimensional (3D) digital elevation model (DEM) of the riverbed for the investigated stream section. The reconstruction results from four approaches are provided: (1) unoccupied aerial vehicle (UAV, colloquially known as drone) imagery-based Structure-from-Motion (SfM), (2) a machine learning-based 3D reconstruction model, Visual Geometry Grounded Deep Structure from Motion (VGGSfM), (3) Visual Geometry Grounded Transformer for long sequence of images (VGGT-Long), and (4) handheld smartphone LiDAR scanning. The ground truth measurements by tripod-mounted optical level kit and ground control points GPS locations for evaluating the accuracy of the four reconstruction approaches are also provided in this data package. A preliminary version of this data package was published in October 2025 at the time of manuscript submission. It was updated in March 2026, at the time of manuscript acceptance, to include additional metadata (this readme, data dictionary, and file level metadata). The data did not change. For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. In addition to a readme, this data package also includes a file-level metadata (FLMD) file that describes each file and a data dictionary (DD) that describes all column/row headers and variable definitions. This dataset is comprised of (1) 8 folders; (2) the detailed flight configuration html files; (3) field metadata; (4) a readme; (5) a data dictionary; and (6) file-level metadata. The folders “2024_10_18_d01” and “2024_10_18_d02” contain the original drone photos for the two drone flights (d01 and d02) on October 18, 2024. The reconstruction results from each of the approaches are in the folders called “ODM_SfM”, “VGGSfM”, “VGGTLong”, and “LiDAR”. The ground truth measurements are in the folder called “optical_level_kit”. Lastly, results comparing the different approaches are in the folder called “comparisons”. All files are .csv, .html, .jpg, .obj, .txt, and .npy. For information on using the .obj and .npy files, see the readme files within the same folder as the files.

54 ENVIRONMENTAL SCIENCES

Data and Scripts associated with a manuscript on ecosystem responses to wildfires in the Columbia River Basin

This data package is associated with the publication “Ecosystem leaf area, gross primary production, and evapotranspiration responses to wildfire in the Columbia River Basin” submitted to Biogeosciences (Shi et al., 2024; doi: 10.22541/au.171053013.30286044/v1). In this research, data products, leaf area index (LAI), gross primary production (GPP), and evapotranspiration (ET), from the Moderate Resolution Imaging Spectroradiometer (MODIS) are used to quantify the resistance and resilience of different ecosystem types in the Columbia River Basin (CRB). A machine learning algorithm, random forest (RF), was used to examine the impacts of precipitation, vapor pressure deficit (VPD), and burn severity from Monitoring Trends in Burn Severity (MTBS) on ecosystem resilience. The data package includes the processed MODIS data products, precipitation, VPD, and burn severity in 138 fire regions in CRB and the input files for RF model training. This data package includes six folders. The MODIS products are included in three MODIS_* folders with shell scripts for data clipping and *ncl files for data processing: (1) “/MODIS_LAI_CRB”; (2) “/MODIS_GPP_CRB”; and (3) “/MODIS_ET_CRB”. All the processed data for each fire event are NetCDF formatted. The MTBS burn severity data and the shell and *ncl scripts used for data processing are in the folder named (4) “MTBS_fire”. The ERA meteorological fields and the data processing scritps are in (5) “ERA_Var_CR”. All the scripts for figure development are in the format of *ncl and in the folder (6) “paper_scripts”. See the file ending in “flmd.csv” for a list of all files contained in this data package and descriptions for each. Tabular column headers and units are described in the data dictionary file ending in “dd.csv”.

54 ENVIRONMENTAL SCIENCES

Direct NeTS sampling of nuclear graphite $S(α, β, T)$ in Serpent

For advanced reactor applications, Neural Thermal Scattering (NeTS) modules were developed to predict the thermal scattering law (TSL or $S(α, β, T)$) of a nuclear graphite neutron moderator. NeTS are multi-layer, feedforward artificial neural networks, which act as universal function approximators designed for TSL datasets. In this case, a 4-layer neural network with 164 neurons per layer is trained using FLASSH evaluated data in PyTorch and serialized as a torchscript dictionary to predict $S(α, β, T)$ on-the-fly. Relative, absolute and maximum percent deviations of NeTS from File 7 data generated using the FLASSH code are on the order of 0.01%, 0.1% and 1%, respectively, with low inference latencies of 0.000172 s per $S(α, β, T)$ at a given temperature. Capturing the full dimensionality of possible inelastic neutron-lattice interactions, NeTS functionality is embedded in the Serpent Monte Carlo code, where $S(α, β, T)_{NeTS}$ sampling is conducted on-the-fly and compared to ACE look-up-tables for predicting TREAT criticality. k-eff differences between sampling algorithms of 6 pcm are observed and are within the order of Monte Carlo uncertainty. Compared to discrete and continuous-energy ACE files (30 MB and 131 MB per temperature), the NeTS format is on the order of 200–300 kB for a continuous-temperature, interpolation-free representation of $S(α, β, T)$ and cross sections. NeTS-in-Serpent runtimes comparable with ACE look-up tables are achieved by scaling NeTS for high performance computing architectures with hybrid OpenMP + MPI parallelization. This work validates a novel, self-contained reactor physics framework for predictive cross sections, and demonstrates a general methodology for embedding modern machine learning libraries within existing neutronic analysis frameworks.

Nuclear Criticality Safety Program (NCSP)