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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Supernova neutrino signals based on long-term axisymmetric simulations

ABSTRACT We study theoretical neutrino signals from core-collapse supernova (CCSN) computed using axisymmetric CCSN simulations that cover the post-bounce phase up to ∼4 s. We provide basic quantities of the neutrino signals such as event rates, energy spectra, and cumulative number of events at some terrestrial neutrino detectors, and then discuss some new features in the late phase that emerge in our models. Contrary to popular belief, neutrino emissions in the late phase are not always steady, but rather have temporal fluctuations, the vigour of which hinges on the CCSN model and neutrino flavour. We find that such temporal variations are not primarily driven by proto-neutron star convection, but by fallback accretion in exploding models. We assess the detectability of these temporal variations, and find that IceCube is the most promising detector with which to resolve them. We also update fitting formulae first proposed in our previous paper for which the total neutrino energy emitted at the CCSN source is estimated from the cumulative number of events in each detector. This will be a powerful technique with which to analyse real observations, particularly for low-statistics data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Sage: parallel semi-asymmtric graph algorithms for NVRAMs

Non-volatile main memory (NVRAM) technologies provide an attractive set of features for large-scale graph analytics, including byte-addressability, low idle power, and improved memory-density. NVRAM systems today have an order of magnitude more NVRAM than traditional memory (DRAM). NVRAM systems could therefore potentially allow very large graph problems to be solved on a single machine, at a modest cost. However, a significant challenge in achieving high performance is in accounting for the fact that NVRAM writes can be much more expensive than NVRAM reads. In this paper, we propose an approach to parallel graph analytics using the Parallel Semi-Asymmetric Model (PSAM), in which the graph is stored as a read-only data structure (in NVRAM), and the amount of mutable memory is kept proportional to the number of vertices. Similar to the popular semi-external and semi-streaming models for graph analytics, the PSAM approach assumes that the vertices of the graph fit in a fast read-write memory (DRAM), but the edges do not. In NVRAM systems, our approach eliminates writes to the NVRAM, among other benefits. To experimentally study this new setting, we develop Sage, a parallel semi-asymmetric graph engine with which we implement provably-efficient (and often work-optimal) PSAM algorithms for over a dozen fundamental graph problems. We experimentally study Sage using a 48--core machine on the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) equipped with Optane DC Persistent Memory, and show that Sage outperforms the fastest prior systems designed for NVRAM. Importantly, we also show that Sage nearly matches the fastest prior systems running solely in DRAM, by effectively hiding the costs of repeatedly accessing NVRAM versus DRAM.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Effect of reactor radiation on the thermal conductivity of TREAT fuel

The Transient Reactor Test Facility (TREAT) at the Idaho National Laboratory is resuming operations after more than 20 years in latency in order to produce high-neutron-flux transients for investigating transient-induced behavior of reactor fuels and their interactions with other materials and structures. A parallel program is ongoing to develop a replacement core in which the fuel, historically containing highly-enriched uranium (HEU), is replaced by low-enriched uranium (LEU). Both the HEU and prospective LEU fuels are in the form of UO 2 particles dispersed in a graphite matrix, but the LEU fuel will contain a much higher volume of UO 2 particles, which may create a larger area of interphase boundaries between the particles and the graphite. This may lead to a higher volume fraction of graphite exposed to the fission fragments escaping from the UO 2 particles, and thus may induce a higher volume of fission-fragment damage on the fuel graphite. In this work, we analyzed the reactor-radiation induced thermal conductivity degradation of graphite-based dispersion fuel. A semi-empirical method to model the relative thermal conductivity with reactor radiation was proposed and validated based on the available experimental data. Prediction of thermal conductivity degradation of LEU TREAT fuel during a long-term operation was performed, with a focus on the effect of UO 2 particle size on fission-fragment damage. Lastly, the proposed method can be further adjusted to evaluate the degradation of other properties of graphite-based dispersion fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2016

Near-Earth Magnetic Field Effects of Large-Scale Magnetospheric Currents

Magnetospheric currents play an important role in the electrodynamics of near- Earth space. This has been the topic of many space science studies. Here we focus on the magnetic fields they cause close to Earth. Their contribution to the geomagnetic field is the second largest after the core field. Significant progress in interpreting the magnetic fields from the different sources has been achieved thanks to magnetic satellite missions like Ørsted, CHAMP and now Swarm. Of particular interest for this article is a proper representation of the magnetospheric ring current effect. Uncertainties in modelling its effect still produce the largest residuals between observations and present-day geomagnetic field models. A lot of progress has been achieved so far, but there are still open issues like the characteristics of the partial ring current. Other currents discussed are those flowing in the magnetospheric tail. Also their magnetic contribution at LEO orbits is non-negligible. Treating them as an independent source is a more recent development, which has cured some of the problems in geomagnetic field modelling. Unfortunately there is no index available for characterizing the tail current intensity. Here we propose an approach that may help to properly quantify the magnetic contribution from the tail current for geomagnetic field modelling. Some open questions that require further investigation are mentioned at the end.

Magnetospheric currents↗
DOE OSTI2013

Benchmark analysis of high temperature engineering test reactor core using McCARD code

A benchmark calculation has been performed for a startup core physics test of Japan's High Temperature Engineering Test Reactor (HTTR). The calculation is carried out by the McCARD code, which adopts the Monte Carlo method. The cross section library is ENDF-B/VII.0. The fuel cell is modeled by the reactivity-equivalent physical transform (RPT) method. Effective multiplication factors with different numbers of fuel columns have been analyzed. The calculation shows that the HTTR becomes critical with 19 fuel columns with an excess reactivity of 0.84% Δk/k. The discrepancies between the measurements and Monte Carlo calculations are 2.2 and 1.4 % Δk/k for 24 and 30 columns, respectively. The reasons for the discrepancy are thought to be the current version of cross section library and the impurity in the graphite which is represented by the boron concentration. In the future, the depletion results will be proposed for further benchmark calculations. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2015

Large Scale Frequent Pattern Mining using MPI One-Sided Model

In this paper, we propose a work-stealing runtime --- Library for Work Stealing LibWS --- using MPI one-sided model for designing scalable FP-Growth --- {\em de facto} frequent pattern mining algorithm --- on large scale systems. LibWS provides locality efficient and highly scalable work-stealing techniques for load balancing on a variety of data distributions. We also propose a novel communication algorithm for FP-growth data exchange phase, which reduces the communication complexity from state-of-the-art O(p) to O(f + p/f) for p processes and f frequent attributed-ids. FP-Growth is implemented using LibWS and evaluated on several work distributions and support counts. An experimental evaluation of the FP-Growth on LibWS using 4096 processes on an InfiniBand Cluster demonstrates excellent efficiency for several work distributions (87\% efficiency for Power-law and 91% for Poisson). The proposed distributed FP-Tree merging algorithm provides 38x communication speedup on 4096 cores.

Vishnu, Abhinav↗
DOE OSTI2017

BISON Fuel Performance Analysis of IFA-796 Rod 3 & 4 and Investigation of the Impact of Fuel Creep

In order to improve the accident tolerance of light water reactor (LWR) fuel, alternative cladding materials have been proposed to replace the currently used zirconium (Zr)-based alloys. Of these materials, there is a particular focus on iron-chromiumaluminum (FeCrAl) alloys because they exhibit slower oxidation kinetics in high-temperature steam than Zr-alloys. This should decrease the energy release due to oxidation and slow cladding consumption in the presence of high temperature steam. These alloys should also exhibit increased “coping time” in the event of an accident scenario by improving the mechanical performance at high temperatures, allowing greater flexibility to achieve core cooling. As a continuation of the development of these alloys, in-reactor irradiation testing of FeCrAl cladded fuel rods has started. In order to provide insight on the possible behavior of these fuel rods as they undergo irradiation in the Halden Boiling Water Reactor, engineering analysis has been performed using FeCrAl material models implemented into the BISON fuel performance code. This milestone report provides an update on the ongoing development of modeling capability to predict FeCrAl cladding fuel performance and to provide an early look at the possible behavior of planned in-reactor FeCrAl cladding experiments. In particular, this report consists of two separate analyses. The first analysis consists of fuel performance simulations of IFA-796 rod 4 and two segments of rod 3. These simulations utilize previously implemented material models for the C35M FeCrAl alloy and UO2 to provide a bounding behavior analysis corresponding to variation of the initial fuel cladding gap thickness within the fuel rod. The second analysis is an assessment of the fuel and cladding stress states after modification of the fuel creep model that is currently implemented in the BISON fuel performance code. Effects from modifying the fuel creep model were identified for the BISON simulations of the IFA-796 rod 4 experiment, but show that varying the creep model (within the range investigated here) only provide a minimal increase in the fuel radius and maximum cladding hoop stress. Continued investigation of fuel behavioral models will include benchmarking the modified fuel creep model against available experimental data, as well as an investigation of the role that fuel cracking will play in the compliance of the fuel. Correctly calculating stress evolution in the fuel is key to assessing fuel behavior up to gap closure and the subsequent deformation of the cladding due to PCMI. The inclusion of frictional contact should also be investigated to determine the axial elongation of the fuel rods for comparison with data from this experiment.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Modeling the effect of nitrogen recycling on the erosion and leakage of tungsten impurities from the SAS-VW divertor in DIII-D during nitrogen gas injection

The new SAS-VW divertor in DIII-D has tungsten-coated components to enable the study of tungsten erosion and leakage from a closed, slot-like divertor. A proposed method of actively managing the tungsten impurities is to inject low-Z impurities, such as nitrogen, into the Scrape-off-Layer (SOL) to modify the conditions in the plasma boundary and in turn manipulate both the erosion and subsequent transport of tungsten. Nitrogen injection from the SOL crown has been modeled using SOLPS-ITER to calculate the background plasma including the intrinsic carbon and the injected nitrogen impurities, and subsequently DIVIMP has been used to calculate the tungsten erosion and transport on top of the background plasma solution. This workflow has been used to model scenarios at a variety of nitrogen injection rates with different assumptions about the nitrogen recycling at the target. In the scenario modeled here, an optimal nitrogen injection rate around 3-4 x 10 20 N/s is found to reduce the amount of tungsten reaching the core by a factor of about 2.4. However, when the nitrogen recycling rate at the divertor targets is high, the nitrogen redistributes within the slot leading to increased tungsten sputtering, and the range of injection rates resulting in tungsten mitigation becomes narrower.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

sRecovery Act: Geologic Characterization of the South Georgia Rift Basin for Source Proximal CO 2 Storage

This study focuses on evaluating the feasibility and suitability of using the Jurassic/Triassic (J/TR) sediments of the South Georgia Rift basin (SGR) for CO 2 storage in southern South Carolina and southern Georgia The SGR basin in South Carolina (SC), prior to this project, was one of the least understood rift basin along the east coast of the U.S. In the SC part of the basin there was only one well (Norris Lightsey #1) the penetrated into J/TR. Because of the scarcity of data, a scaled approach used to evaluate the feasibility of storing CO 2 in the SGR basin. In the SGR basin, 240 km (~149 mi) of 2-D seismic and 2.6 km2 3-D (1 mi2) seismic data was collected, process, and interpreted in SC. In southern Georgia 81.3 km (~50.5 mi) consisting of two 2-D seismic lines were acquired, process, and interpreted. Seismic analysis revealed that the SGR basin in SC has had a very complex structural history resulting the J/TR section being highly faulted. The seismic data is southern Georgia suggest SGR basin has not gone through a complex structural history as the study area in SC. The project drilled one characterization borehole (Rizer # 1) in SC. The Rizer #1 was drilled but due to geologic problems, the project team was only able to drill to 1890 meters (6200 feet) instead of the proposed final depth 2744 meters (9002 feet). The drilling goals outlined in the original scope of work were not met. The project was only able to obtain 18 meters (59 feet) of conventional core and 106 rotary sidewall cores. All the conventional core and sidewall cores were in sandstone. We were unable to core any potential igneous caprock. Petrographic analysis of the conventional core and sidewall cores determined that the average porosity of the sedimentary material was 3.4% and the average permeability was 0.065 millidarcy. Compaction and diagenetic studies of the samples determined there would not be any porosity or permeability at depth in SC. In Georgia there appears to be porosity in the J/TR section based on neutron log porosity values. The only zones in Rizer #1 that appear to be porous were fractured diabase units where saline formation water was flowing into the borehole. Two geocellular models were created for the SC and GA study area. Flow simulation modeling was performed on the SC data set. The injection simulation used the newly acquired basin data as well as the Petrel 3-D geologic model that included geologic structure. Due to the new basin findings as a result of the newly acquired data, during phase two of the modeling the diabase unit was used as reservoir and the sandstone units were used as caprock. Conclusion are: 1) the SGR basin is composed of numerous sub-basins, 2) this study only looked at portions of two sub-basins, 3) in SC, 30 million tonnes of CO 2 can be injected into the diabase units if the fracture network is continuous through the units, 4) due to the severity of the faulting there is no way of assuring the injected CO 2 will not migrate upward into the overlying Coastal Plain aquifers, 5) in Georgia there appears to porous zones in the J/TR sandstones, 6) as in SC there is faulting in the sub-basin and the seismic suggest the faulting extends upward into the Coastal Plain making that area not suitable for CO 2 sequestration, 7) the complex faulting observed at both study areas appear to be associated with transfer fault zones (Heffner 2013), if sub-basins in the Georgia portion of the SGR basin can be located that are far away from the transfer fault zones there is a strong possibility of sequestering CO 2 in these areas, and 9) the SGR basin covers area in three states and this project only studied two small areas so there is enormous potential for CO 2 sequestration in other portions the basin and further research needs to be done to find these areas.

58 GEOSCIENCES↗
DOE OSTI2024

Strategy to Develop a Control Scheme for Core Thermal Performance Optimization

This report outlines a three-year research plan for optimizing reactor core thermal performance through use of a Digital Twin (DT) model and a set of neutron detectors to correspondingly adapt the reactor control strategy. It identifies reactor features and achievable neutron measurements that factor into this optimization task. It considers spatial effects that are important and how they can be managed by a real-time algorithm that controls reactivity actuators. The report presents a set of tasks, along with corresponding methods, for accomplishing this objective. The final task in this set is to validate the combined optimization procedure in the Purdue University’s PUR-1 reactor, for which we have an agreement of understanding. Additionally, we describe an alternative approach for overcoming some of the limitations inherent in the above approach, which includes the computational costs of high-fidelity simulations and achievable integration of neutron measurements into the DT. The proposed algorithms lower the technology readiness level (TRL) of the overall approach as some additional analysis and the development of a new neutron detector concept are necessary. In particular, a sensor measuring the gradient of the neutron flux is required, and the prototype is expected to be validated in the PUR-1 reactor. The potential benefits and the opportunity to significantly push forward the state-of-the-art make this approach worthy of further exploration in the upcoming years.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1984

Changes in the High-latitude Ocean as Possible Causes of Atmospheric CO2 Variations

Measurements on air enclosed in old polar ice have indicated that the atmospheric CO2 concentration was ca. 50 to 70 ppm lower in late glacial times than during the Holocene. Similar measurements performed on samples from a Greenland ice core, dating ca. 30,000 to 40,000 B.P., and have yielded evidence of several CO2 oscillations with an amplitude of ca. 50 ppm. Each change lasted on the order of a few centuries. A mechanism by which circulation changes in the high-latitude ocean could lead to rapid variations in atmospheric CO2 is proposed. In the Antarctic Ocean a slowing down of the vertical mixing would imply a smaller upward flux of sigma CO2 and nutrients. Assuming constant productivity, sigma CO2 and nutrients would be more completely used which would imply lower CO2 in these high-latitude surface waters. In areas with a warm surface, a slowing down of the circulation would not have a direct impact on CO2 because productivity would automatically decrease by the same factor as the upwelling rate of nutrients. Studies with a simple box model of the ocean-atmosphere system suggest that a suddent decrease by a factor of 2 of the water exchange between the surface and deep sea in high latitudes could lead to a CO2 decrease of ca. 40 to 50 ppm with a time constant of ca. 200 years. Deep-sea sediment studies indicate rapid changes in the high-latitude surface conditions of the North Atlantic and the Antarctic Oceans at the end of the last glaciation. Studies of carbon isotope ratios should help ascertain whether this proposed mechanism was indeed responsible for the CO2 variation.

Siegenthaler, U.↗
DOE OSTI2022

Designing optimal core–shell MOFs for direct air capture

Metal–organic frameworks (MOFs), along with other novel adsorbents, are frequently proposed as candidate materials to selectively adsorb CO 2 for carbon capture processes. However, adsorbents designed to strongly bind CO 2 nearly always bind H 2 O strongly (sometimes even more so). Given that water is present in significant quantities in the inlet streams of most carbon capture processes, a method that avoids H 2 O competition for the CO 2 binding sites would be technologically valuable. Here, in this paper, we consider a novel core–shell MOF design strategy, where a high-CO 2 -capacity MOF “core” is protected from competitive H 2 O-binding via a MOF “shell” that has very slow water diffusion. We consider a high-frequency adsorption/desorption cycle that regenerates the adsorbents before water can pass through the shell and enter the core. To identify optimal core–shell MOF pairs, we use a combination of experimental measurements, computational modeling, and multiphysics modeling. Our library of MOFs is created from two starting MOFs-UiO-66 and UiO-67-augmented with 30 possible functional group variations, yielding 1740 possible core–shell MOF pairs. After defining a performance score to rank these pairs, we identified 10 core–shell MOF candidates that significantly outperform any of the MOFs functioning alone.

42 ENGINEERING↗
DOE OSTI2017

Structural dissection of an interaction between transcription initiation and termination factors implicated in promoter-terminator cross-talk

Functional cross-talk between the promoter and terminator of a gene has long been noted. Promoters and terminators are juxtaposed to form gene loops in several organisms, and gene looping is thought to be involved in transcriptional regulation. The general transcription factor IIB (TFIIB) and the C-terminal domain phosphatase Ssu72, essential factors of the transcription preinitiation complex and the mRNA processing and polyadenylation complex, respectively, are important for gene loop formation. TFIIB and Ssu72 interact both genetically and physically, but the molecular basis of this interaction is not known. Here we present a crystal structure of the core domain of TFIIB in two new conformations that differ in the relative distance and orientation of the two cyclin-like domains. The observed extraordinary conformational plasticity may underlie the binding of TFIIB to multiple transcription factors and promoter DNAs that occurs in distinct stages of transcription, including initiation, reinitiation, and gene looping. We mapped the binding interface of the TFIIB-Ssu72 complex using a series of systematic, structure-guided in vitro binding and site-specific photocross-linking assays. Our results indicate that Ssu72 competes with acidic activators for TFIIB binding and that Ssu72 disrupts an intramolecular TFIIB complex known to impede transcription initiation. We also show that the TFIIB-binding site on Ssu72 overlaps with the binding site of symplekin, a component of the mRNA processing and polyadenylation complex. Here, we propose a hand-off model in which Ssu72 mediates a conformational transition in TFIIB, accounting for the role of Ssu72 in transcription reinitiation, gene looping, and promoter-terminator cross-talk.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

WE-G-BRF-04: Robust Real-Time Volumetric Imaging Based On One Single Projection

Purpose: Real-time volumetric imaging is highly desirable to provide instantaneous image guidance for lung radiation therapy. This study proposes a scheme to achieve this goal using one single projection by utilizing sparse learning and a principal component analysis (PCA) based lung motion model. Methods: A patient-specific PCA-based lung motion model is first constructed by analyzing deformable vector fields (DVFs) between a reference image and 4DCT images at each phase. At the training stage, we “learn” the relationship between the DVFs and the projection using sparse learning. Specifically, we first partition the projections into patches, and then apply sparse learning to automatically identify patches that best correlate with the principal components of the DVFs. Once the relationship is established, at the application stage, we first employ a patchbased intensity correction method to overcome the problem of different intensity scale between the calculated projection in the training stage and the measured projection in the application stage. The corrected projection image is then fed to the trained model to derive a DVF, which is applied to the reference image, yielding a volumetric image corresponding to the projection. We have validated our method through a NCAT phantom simulation case and one experiment case. Results: Sparse learning can automatically select those patches containing motion information, such as those around diaphragm. For the simulation case, over 98% of the lung region pass the generalized gamma test (10HU/1mm), indicating combined accuracy in both intensity and spatial domain. For the experimental case, the average tumor localization errors projected to the imager are 0.68 mm and 0.4 mm on the axial and tangential direction, respectively. Conclusion: The proposed method is capable of accurately generating a volumetric image using one single projection. It will potentially offer real-time volumetric image guidance to facilitate lung radiotherapy. This study is supported in part by NIH (1R01CA154747-01), The Core Technology Research in Strategic Emerging Industry, Guangdong, China(2011A081402003)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Developing Upscaling Approach for Swarming Hydraulic Fractures Observed at Hydraulic Fracturing Test Site through Multiscale Simulations

We show that this work aims to address a challenge posed by recent observations of tightly spaced hydraulic fractures in core samples from the hydraulic fracturing test site (HFTS) in the Middle Wolfcamp Formation. Many fractures in retrieved cores have subfoot spacing, which is at odds with conventional models in which usually one hydraulic fracture is initiated per cluster. Models assuming a single fracture at each cluster, although a common practice, often predict excessive fracture propagation that is inconsistent with microseismic observation. Here, we aim to develop a numerical approach to effectively account for densely spaced hydraulic fractures in field-scale simulations. Because it is impractical to explicitly model all aforementioned fractures, we develop a new upscaling law that enables existing simulation tools to predict reservoir response to fracture swarms. The upscaling law is derived based on an energy equivalence argument and validated through multiscale simulations using a high-fidelity code, GEOS. The swarming fractures are first modeled with a spacing that is much smaller than the cluster spacing; these fractures are then approximated by an upscaled, single fracture based on the proposed upscaling law. The upscaled fracture is shown to successfully match the energy input rate and produce the total fracture aperture and average propagation length of the explicitly simulated swarm. Afterward, the upscaling approach is further implemented in 3D field-scale simulations and validated against the HFTS microseismic data of a horizontal well. Our results show that hydraulic fracture swarming can significantly affect fracture propagation behaviors compared with the propagation of single fractures as assumed by conventional modeling approaches. Under the considered situations, the conventional treatment yields fast propagation speed that far exceeds that indicated by the microseismic data. We also illustrate that this discrepancy can be reduced readily through the implementation of the upscaling law. Our results demonstrate the importance of accounting for the fracture swarming effect in field-scale simulations and the efficacy of this approach to enable realistic predictions of reservoir responses to fracture swarms, without the need to model tightly spaced fractures individually.

02 PETROLEUM↗
NASA NTRSDate not supplied

2040 Vision Study: NASA’s T3 Implementation Activities

Over the last few decades, advances in high-performance computing, new materials characterization methods, and, more recently, an emphasis on integrated computational materials engineering (ICME) and additive manufacturing have been a catalyst for multiscale modeling and simulation-based design of materials and structures in the aerospace industry. As a result, NASA’s Transformational Tools and Technology (TTT) Project sponsored a study (performed by a team led by Pratt & Whitney) to define the potential 25-year future state required for integrated multiscale modeling of materials and systems (e.g., load-bearing structures) to accelerate the pace and reduce the expense of innovation in future aerospace and aeronautical systems. This talk will briefly review the findings of this 2040 Vision study (e.g., the 2040 vision state; the required interdependent core technical work areas, Key Element (KE); associated critical gaps and actions to close those gaps; and major recommendations) and discuss NASA’s TTT implementation activities, with special emphasis on recent accomplishments. The study, NASA CR 2018- 219771, envisions the development of a cyber-physical-social ecosystem comprised of experimentally verified and validated computational models, tools, and techniques, along with the associated digital tapestry, that marries two non-mutually exclusive paradigms – “design of the materials” (material scientist viewpoint) and “design with the materials” (structural analyst viewpoint) – into a concurrent transformational paradigm that impacts the entire supply chain to enable cost-effective, rapid, and revolutionary design of fit-for-purpose materials, components, and systems. Although the vision focused on aeronautics and space applications, it is believed that other engineering communities (e.g., automotive, biomedical, etc.) can benefit as well from the proposed framework with only minor modifications. Finally, it is TTT’s hope and desire that this vision provides the strategic guidance to both public and private research and development decision makers to make the proposed 2040 vision state a reality and thereby provide a significant advancement in the United State's global competitiveness

Materials↗
DOE OSTI2026

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING↗