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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

LAMOST Time-Domain survey: first results of four K2 plates

From Oct. 2019 to Apr. 2020, LAMOST performed a time-domain (TD) spectroscopic survey of four K2 plates with both low- and medium-resolution observations. The low-resolution spectroscopic survey acquired 282 exposures ( ≈ 46.6 h) over 25 nights, yielding a total of about 767 000 spectra, and the medium-resolution survey took 177 exposures ( ≈ 49.1 h) over 27 nights, collecting about 478 000 spectra. More than 70%/50% of low-resolution/medium-resolution spectra have signal-to-noise ratio higher than 10. We determine stellar parameters (e.g., T eff , log g, [Fe/H]) and radial velocity (RV) with different methods, including LASP, DD-Payne and SLAM. In general, these parameter estimations from different methods show good agreement, and the stellar parameter values are consistent with those of APOGEE. We use the Gaia DR2 RV values to calculate a median RV zero point (RVZP) for each spectrograph exposure by exposure, and the RVZP-corrected RVs agree well with the APOGEE data. The stellar evolutionary and spectroscopic masses are estimated based on the stellar parameters, multi-band magnitudes, distances and extinction values. Finally, we construct a binary catalog including about 2700 candidates by analyzing their light curves, fitting the RV data, calculating the binarity parameters from medium-resolution spectra and cross-matching the spatially resolved binary catalog from Gaia EDR3. In conclusion, the LAMOST TD survey is expected to represent a breakthrough in various scientific topics, such as binary systems, stellar activity, stellar pulsation, etc.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The role of international collaboration in the United States geologic disposal research program

Abstract. More than a decade ago, the United States disposal program discontinued all research activities focused on the unsaturated fractured tuff formation at Yucca Mountain as the geologic disposal site for spent fuel and high-level radioactive waste. A new research and development (R&D) program was initiated to provide a sound technical basis for alternative disposal options across clay, crystalline, and salt rocks. The goals of this broad program were (and still are) to (1) increase confidence in the robustness of generic disposal concepts, (2) develop the science and engineering tools needed to support disposal concept implementation, and (3) conduct R&D on the direct disposal of existing dual-purpose (storage and transportation) canisters. Recognizing the benefits of international collaboration toward the common goal of safely and efficiently managing the back end of the nuclear fuel cycle, the program emphasized international cooperation as an effective strategy for sharing information and knowledge. In a multi-laboratory effort coordinated by Lawrence Berkeley National Laboratory, the United States Department of Energy (DOE) program established formal and informal cooperation partnerships with several international initiatives and institutions and developed a number of collaborative R&D activities in important research areas, such as engineered barrier integrity, near-field perturbations, radionuclide transport, performance assessment, and methods for characterization and monitoring of engineered and natural barriers. This presentation gives an overview of these R&D activities, with a specific focus on activities that improve our current understanding of the coupled thermal–hydrological–mechanical–chemical (THMC) processes occurring in engineered and natural barriers. We start with a brief review of selected international collaboration initiatives and then describe a few specific collaboration projects. We focus specifically on such studies that use experimental data sets provided by international research cooperation for joint modeling work to increase confidence in performance-relevant predictions of coupled processes. Overall, the focus on international collaboration has allowed deep engagement of US researchers with the international waste management R&D community in terms of best practices, new scientific advances, state-of-the-art simulation tools, new monitoring and performance confirmation approaches, and lessons learned. The joint R&D with international researchers, worldwide sharing of knowledge and experience, and access to relevant data and experiments from a variety of host rocks have helped our researchers to significantly improve their understanding of the current technical basis for disposal in a range of potential host rock environments. International collaboration also provides ample opportunity for training and educating junior staff that are well suited to move the United States disposal research program forward into the next decades, a promising avenue for developing a next-generation workforce of disposal scientists.

Birkholzer, Jens T.↗
DOE OSTI2020

Effects of cluster expansion on the locations of phase transition boundary as a first step to quantify uncertainty in first principles statistical mechanics framework

Predicting phase diagrams from first principle calculations eliminates the need of tedious experimental trials and errors. Fully automating first principle phase diagram calculations without any sort of human intervention has been a long daunting task and troubling scientific communities for decades. This grand problem remains not fully resolved, largely due to the vastly high-dimensional parameter space associated with density functional theory, cluster expansion, lattice Monte Carlo, and the substantial uncertainty propagating through a set of complex simulations. As a first step to tackle this grand problem, we reported a first demonstration of how sensitive phase boundary locations can be to various cluster expansion fittings and input DFT training data. To the best knowledge of the authors, this study reported the first ever attempt to quantify uncertainty in first principles statistical mechanics framework. In addition, a semi-automated phase transition detection algorithm has been devised in this paper to deal with the associated statistical errors and uncertainties from Monte Carlo method and its predecessor DFT calculations and cluster expansions. This algorithm has been applied in a classical cluster expansion Mg-Cd binary alloy system to detect phase transitions at various locations of phase diagram using different cluster expansions to demonstrate its predictive power and quantify uncertainties. The results suggested that using Chebyshev basis function shifted the transition locations toward the dilute solid solution phase and expanded the phase stability of concentrated ordered phases to wider composition range. The addition of perturbed defect configurations into training data set lowered the order-disorder transition temperature to be away from true transition temperature, suggesting the transition nature is indeed configurational disorder dominated rather than defect assisted. Finally, we found that the weighting has negligible effect on the transition locations, except for the case of using Chebyshev basis function to fit all non-weighted configurations that can be susceptible to Monte Carlo sampling hysteresis.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Accelerator Physics at NSLS-II: Research Accomplishments in 2022

NSLS-II accelerator physicists are working on scientific support of the NSLS-II operations and start-up of the accelerator systems including Storage Ring, Injector, beam diagnostics, and top-off injection; improvement of beam stability and orbit feedbacks; commissioning of a superconducting wiggler for the HEX beamline; development of a new operation mode for time-resolved experiments. The routine lattice characterization is continued to keep tracking the machine, the storage ring lattice model including strong coupling is developed, and seasonal variations of the ring circumference are studied. The collaboration with the EIC project is ongoing. In the frameworks of three LDRD projects, the physicists are working on the lattice development, studies of collective effects, and specifications of alignment and stability for the NSLS-II accelerator upgrade; novel methods of lattice design and optimization; studies of free-electron laser options; ultrafast electron diffraction and microscopy. Research accomplishments achieved in 2022, are summarized in this report.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Accelerating Scientific Simulations with Bi-Fidelity Weighted Transfer Learning

High-fidelity modeling is an essential design tool for many engineering applications. However, for complex systems, computational cost can be a limiting factor. Analyzing parameter sensitivity, uncertainty quantification, and design optimization require many model evaluations. Surrogate models are often used to develop the relationship between model parameters and quantities of interest. However, in the case of complex systems, surrogate models require several degrees of freedom and, thus, a large number of data points to determine the correct dependencies. For many applications, this may be prohibitively expensive. The reduction of computational requirements can be achieved by leveraging low-fidelity models. Low-fidelity models represent the system at a coarser resolution with the advantage of computational efficiency. Therefore, a bi-fidelity modeling paradigm, which augments the accuracy of a low-fidelity model in a computationally efficient manner by invoking limited runs of a high-fidelity model, can be leveraged to sufficiently balance the accuracy and computational requirements. In this work, a bi-fidelity weighted transfer learning method using neural networks was applied to a computational fluid dynamics heat transfer modeling problem. The transfer learning advantage was investigated as a function of hyperparameters. Our main finding is that the use of a bi-fidelity modeling paradigm achieves accuracy close to that of a high-fidelity Gaussian process model while significantly reducing computational cost. The bi-fidelity model achieves comparable performance with 90 high-fidelity samples-that is, 60% less than the samples needed to achieve similar accuracy without the use of bi-fidelity modeling,

Borowiec, Katarzyna↗
DOE OSTI2024

Spectroscopic analysis of Pu-bearing compounds in double-walled cells

Spectroscopic analysis of radiological materials has been historically limited to radiological labs with older or less advanced scientific instrumentation. The development of double-walled cells (DWCs) at the Savannah River National Laboratory (SRNL) has enabled Pu-bearing compounds to be removed from radiological laboratories and studied in our radiologically clean spectroscopy laboratory with state-of-the-art instrumentation. In this manuscript, we discuss the contributions of DWCs that have allowed the application of Raman spectroscopy, diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), diffuse reflectance spectroscopy (DRS) in the shortwave infrared, and gamma spectroscopy at SRNL. Significant advances have been made in the understanding of the thermal decomposition of Pu(III) and Pu(IV) oxalates, alpha-induced damage to the PuO 2 crystal lattice, and the effect of calcination temperatures on the quality of PuO 2 . These techniques have enabled methods to conduct PuO 2 age dating since last calcination and estimate the calcination temperature with Raman spectroscopy and DRS. Additional spectroscopic information measured with DRIFTS has enabled the observation of the evolution of carbon species with calcination temperature, while gamma spectroscopy provides information on age dating since last purification.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Safety Analysis of FeCrAl Accident-Tolerant Fuels with Increased Enrichment and Extended Burnup

The U.S. nuclear industry is facing a strong challenge to maintain regulatory-required levels of safety while ensuring economic competitiveness to stay in business. Safety remains a key parameter for all aspects related to the operation of light water reactor nuclear power plants (NPPs), and it can be achieved more economically by using a risk-informed ecosystem, such as that being developed by the Risk-Informed Systems Analysis Pathway under the U.S. Department of Energy Light Water Reactor Sustainability Program. This program is promoting a wide range of research and development activities to maximize both the safety and economically efficient performance of NPPs through improved scientific understanding, especially given that many plants are considering a second license renewal. The Risk-Informed Systems Analysis Pathway has two main goals: (1) The deployment of methodologies and technologies that enable a better representation of the safety margins and factors that contribute to cost and safety, and (2) The development of advanced applications that enable cost-effective plant operation. As part of this pathway, the Enhanced Resilient Plant project refers to an NPP where safety is improved by implementing various measures, such as accident-tolerant fuels, diverse and flexible coping strategies, enhancements to plant components and systems, incorporation of augmented or new passive cooling systems, and utilization of advanced battery technologies. The objective of the Enhanced Resilient Plant project is to use novel methods and computational tools to enhance existing reactors’ safety while reducing operational costs. This report documents research and development conducted in support of deployment of accident-tolerant fuels. This project performed safety analyses for the steady-state normal operation, anticipated operational occurrences, and design-basis accidents of a representative four-loop pressurized water reactor model with Zr and FeCrAl accident-tolerant fuel clad with higher enrichment and burnup supporting plant refueling cycles of 18 and 24 months. The source terms and environmental impacts were studied for a large-break loss of coolant accident, including uncertainty analyses.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Effects of processing on the efficacy and metabolites of Cistanche tubulosa using ultra‐performance liquid chromatography coupled with quadrupole time‐of‐flight mass spectrometry

Abstract Cistanche tubulosa (CT), a well‐known traditional Chinese medicine, has always been processed with rice wine for the treatment of kidney‐yang deficiency syndrome (KYDS) since time immemorial. To explore the effect of processing on the efficacy and metabolites of CT in vivo , a comprehensive method using ultra‐performance liquid chromatography coupled with quadrupole time‐of‐flight mass spectrometry was established for the analysis of the altered endogenous metabolites in response to the intervention of the raw and processed CT in KYDS model and the metabolites of the absorbed compounds in rats after gastric perfusion. It was shown that CT could improve KYDS, and the effect of the processed product was more significant. A total of 47 differential metabolites were identified in urine. Pathway analysis proved that purine metabolism; alanine, aspartate, and glutamate metabolism; and citrate cycle were the main pathways. Furthermore, 53 prototypes and 48 metabolites have been detected in rats. This was the first systematic research focus on the metabolites of raw and processed CT in vivo , which could provide a scientific basis for explaining the increasing efficiency of the processed CT. Moreover, it provides a valuable strategy for analyzing the chemical components and metabolites of other TCM prescriptions.

Lei, Huibo↗
DOE OSTI2024

Causally‐Informed Deep Learning to Improve Climate Models and Projections

Abstract Climate models are essential to understand and project climate change, yet long‐standing biases and uncertainties in their projections remain. This is largely associated with the representation of subgrid‐scale processes, particularly clouds and convection. Deep learning can learn these subgrid‐scale processes from computationally expensive storm‐resolving models while retaining many features at a fraction of computational cost. Yet, climate simulations with embedded neural network parameterizations are still challenging and highly depend on the deep learning solution. This is likely associated with spurious non‐physical correlations learned by the neural networks due to the complexity of the physical dynamical system. Here, we show that the combination of causality with deep learning helps removing spurious correlations and optimizing the neural network algorithm. To resolve this, we apply a causal discovery method to unveil causal drivers in the set of input predictors of atmospheric subgrid‐scale processes of a superparameterized climate model in which deep convection is explicitly resolved. The resulting causally‐informed neural networks are coupled to the climate model, hence, replacing the superparameterization and radiation scheme. We show that the climate simulations with causally‐informed neural network parameterizations retain many convection‐related properties and accurately generate the climate of the original high‐resolution climate model, while retaining similar generalization capabilities to unseen climates compared to the non‐causal approach. The combination of causal discovery and deep learning is a new and promising approach that leads to stable and more trustworthy climate simulations and paves the way toward more physically‐based causal deep learning approaches also in other scientific disciplines.

Meteorology & Atmospheric Sciences↗
DOE OSTI2025

A bi-channel aided stitching of atomic force microscopy images

Microscopy is an essential tool in scientific research, enabling the visualization of structures at micro- and nanoscale resolutions. However, the field of microscopy often encounters limitations in field-of-view (FOV), restricting the amount of sample that can be imaged in a single capture. To overcome this limitation, image stitching techniques have been developed to seamlessly merge multiple overlapping images into a single, high-resolution composite. The images collected from microscope need to be optimally stitched before accurate physical information can be extracted from post analysis. However, the existing stitching tools either struggle to stitch images together when the microscopy images are feature sparse or cannot address all the transformations of images when performing image stitching. To address these issues, we propose a bi-channel aided feature-based image stitching method and demonstrate its use on Atomic Force Microscopy (AFM) generated Pantoea sp. YR343 biofilm and PTO thin film sample images as experimental data. The topographical channel image of AFM data captures the morphological details of the sample, and a stitched topographical image is desired for researchers. We utilize the amplitude and phase channels of AFM data to maximize the matching features and to estimate the position of the original topographical images and show that the proposed bi-channel aided stitching method outperforms the traditional direct stitching approach in AFM topographical image stitching task. Here, we demonstrated the application on AFM, but similar approaches could be employed of optical microscopy with brightfield and fluorescence channels. We believe this proposed workflow can serve as a valuable augmentation strategy for microscopy image stitching tasks and will benefit the experimentalist to avoid erroneous analysis and discovery due to incorrect stitching.

Atomic force microscopy↗
DOE OSTI2021

Estimation of the orientation of stress in the Earth’s crust without earthquake or borehole data

Abstract Mechanical stress acting in the Earth’s crust is a fundamental property that is important for a wide range of scientific and engineering applications. The orientation of maximum horizontal compressive stress can be estimated by inverting earthquake source mechanisms and measured directly from borehole-based measurements, but large regions of the continents have few or no observations. Here we present an approach to determine the orientation of maximum horizontal compressive stress by measuring stress-induced anisotropy of nonlinear susceptibility, which is the derivative of elastic modulus with respect to strain. Laboratory and Earth experiments show that nonlinear susceptibility is azimuthally dependent in an anisotropic stress field and is maximum in the orientation of maximum horizontal compressive stress. We observe this behavior in the Earth—in Oklahoma and New Mexico, U.S.A, where maximum nonlinear susceptibility coincides with the orientation of maximum horizontal compressive stress measured using traditional methods. Our measurements use empirical Green’s functions and solid-earth tides and can be applied at different temporal and spatial scales.

58 GEOSCIENCES↗
DOE OSTI2024

Regional climate change: consensus, discrepancies, and ways forward

Climate change has emerged across many regions. Some observed regional climate changes, such as amplified Arctic warming and land-sea warming contrasts have been predicted by climate models. However, many other observed regional changes, such as changes in tropical sea surface temperature and monsoon rainfall are not well simulated by climate model ensembles even when taking into account natural internal variability and structural uncertainties in the response of models to anthropogenic radiative forcing. This suggests climate model predictions may not fully reflect what our future will look like. The discrepancies between models and observations are not well understood due to several real and apparent puzzles and limitations such as the “signal-to-noise paradox” and real-world record-shattering extremes falling outside of the possible range predicted by models. Addressing these discrepancies, puzzles and limitations is essential, because understanding and reliably predicting regional climate change is necessary in order to communicate effectively about the underlying drivers of change, provide reliable information to stakeholders, enable societies to adapt, and increase resilience and reduce vulnerability. The challenges of achieving this are greater in the Global South, especially because of the lack of observational data over long time periods and a lack of scientific focus on Global South climate change. To address discrepancies between observations and models, it is important to prioritize resources for understanding regional climate predictions and analyzing where and why models and observations disagree via testing hypotheses of drivers of biases using observations and models. Gaps in understanding can be discovered and filled by exploiting new tools, such as artificial intelligence/machine learning, high-resolution models, new modeling experiments in the model hierarchy, better quantification of forcing, and new observations. Conscious efforts are needed toward creating opportunities that allow regional experts, particularly those from the Global South, to take the lead in regional climate research. This includes co-learning in technical aspects of analyzing simulations and in the physics and dynamics of regional climate change. Finally, improved methods of regional climate communication are needed, which account for the underlying uncertainties, in order to provide reliable and actionable information to stakeholders and the media.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Methods of Securing Chemical and Pharmaceutical Knowledge and Recommendations for International Institutions to Enhance Research Integrity

Here, this paper examines strategies for securing chemical and pharmaceutical expertise in a globalized research environment, focusing on safeguarding intellectual property and preventing the misuse of sensitive and potentially dual-use information. The product of collective efforts between Pacific Northwest National Laboratory, Carol Davila University of Medicine and Pharmacy, and New Bulgarian University, highlights the challenges and opportunities posed by cross-border research collaborations, particularly in the context of differing regulatory frameworks and research cultures. It explores current mechanisms to prevent data loss and unauthorized access to sensitive information while assessing the effectiveness of existing security measures, frameworks, and international export control regimes. The approach examines the differing methodologies for promoting transparency, trust-building, and mutual accountability in joint research projects to cultivate secure data-sharing practices and intellectual property. It provides recommendations for international institutions to implement security guidelines in framing research priorities, encourages continual training and education programs, and the integration of processes for monitoring research compliance. This partnership aims to advance scientific innovation while maintaining global stability, ensuring compliance with international norms, and safeguarding valuable intellectual property as measures in chemical and pharmaceutical research security practices continue to expand due to international collaboration and knowledge exchange.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Tetris-inspired detector with neural network for radiation mapping

Abstract Radiation mapping has attracted widespread research attention and increased public concerns on environmental monitoring. Regarding materials and their configurations, radiation detectors have been developed to identify the position and strength of the radioactive sources. However, due to the complex mechanisms of radiation-matter interaction and data limitation, high-performance and low-cost radiation mapping is still challenging. Here, we present a radiation mapping framework using Tetris-inspired detector pixels. Applying inter-pixel padding for enhancing contrast between pixels and neural networks trained with Monte Carlo (MC) simulation data, a detector with as few as four pixels can achieve high-resolution directional prediction. A moving detector with Maximum a Posteriori (MAP) further achieved radiation position localization. Field testing with a simple detector has verified the capability of the MAP method for source localization. Our framework offers an avenue for high-quality radiation mapping with simple detector configurations and is anticipated to be deployed for real-world radiation detection.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Utilization of protein film electrochemistry to characterize the mechanisms imparting aerotolerance and bidirectionality in soluble, multimeric [NiFe]-hydrogenases (Final Report for Grant No. DE-SC0008074)

The overall goal of this project was to better understand how structural features control functional aspects of enzymes involved in catalysis in which a substrate is oxidized or reduced. Two types of model enzymes were explored: the soluble [NiFe]-hydrogenase from Pyrococcus furiousus and the thiosulfate reductase from Pyrobaculum aerophilum. Both are models for complex, multielectron transformations such as nitrogen and carbon dioxide reduction, and parts of important biogeochemical cycles. In this project, electrochemical methods were used to define the activities of these enzymes and targeted variants designed to modulate activity. We showed that the catalytic activity of the soluble hydrogenase from Pyrococcus furiosus can be modulated by removing large parts of the enzyme far from the active site. This surprising result suggests that interactions between functional centers far apart within the enzyme may be essential for controlling and tuning activity. We also showed that the catalytic activity of thiosulfate reductase from Pyrobaculum aerophilum can be modulated by changing the metal at the active site to be either molybdenum or tungsten. These results contribute to our understanding of how the protein environment can tune the reactivity of an embedded metal, catalytic center. The results were and are being published in peer-reviewed, scientific publications.

08 HYDROGEN↗
DOE OSTI2025

Derivation of physical equations for high-speed laser welding using large language models

It is challenging to formulate complex physical phenomena that occur in a manufacturing process, particularly when the available data are limited, rendering conventional data-driven approaches ineffective. This study aims to predict humping onset in high-speed laser welding by introducing a novel framework, namely text-to-equations generative pre-trained transformer (T2EGPT). This method leverages the capabilities of large language models (LLMs), in combination with sparse experimental data and enriched literature data, to derive an interpretable and generalizable equation for predicting humping initiation. By capturing key correlations among physical parameters, T2EGPT generates a compact and dimensionless expression that accurately predicts hump formation. The equation reveals that humping arises from the interplay between inertia-driven backward melt flow and capillary-driven surface stabilization, where inertial forces drive molten metal backward and capillary forces resist surface deformation. Furthermore, compared to traditional data-driven models, T2EGPT demonstrates enhanced predictive accuracy and cross-material transferability. More broadly, this study highlights the potential of LLMs to integrate textual information with data-driven discovery, enabling the extraction of physical laws in data-scarce scientific domains.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Multi-objective Bayesian active learning for MeV-ultrafast electron diffraction

Ultrafast electron diffraction using MeV energy beams(MeV-UED) has enabled unprecedented scientific opportunities in the study of ultrafast structural dynamics in a variety of gas, liquid and solid state systems. Broad scientific applications usually pose different requirements for electron probe properties. Due to the complex, nonlinear and correlated nature of accelerator systems, electron beam property optimization is a time-taking process and often relies on extensive hand-tuning by experienced human operators. Algorithm based efficient online tuning strategies are highly desired. Here, we demonstrate multi-objective Bayesian active learning for speeding up online beam tuning at the SLAC MeV-UED facility. The multi-objective Bayesian optimization algorithm was used for efficiently searching the parameter space and mapping out the Pareto Fronts which give the trade-offs between key beam properties. Such scheme enables an unprecedented overview of the global behavior of the experimental system and takes a significantly smaller number of measurements compared with traditional methods such as a grid scan. This methodology can be applied in other experimental scenarios that require simultaneously optimizing multiple objectives by explorations in high dimensional, nonlinear and correlated systems.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗