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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the material is highly nonlinear in nature, as is common in biological tissue. In this work, we identify unknown material properties in continuum solid mechanics via physics-informed neural networks (PINNs). To improve the accuracy and efficiency of PINNs, we develop efficient strategies to nonuniformly sample observational data. We also investigate different approaches to enforce Dirichlet-type boundary conditions (BCs) as soft or hard constraints. Finally, we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space. The estimated material parameters achieve relative errors of less than 1%. As such, this work is relevant to diverse applications, including optimizing structural integrity and developing novel materials.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Methods for a blind analysis of isobar data collected by the STAR collaboration

In 2018, the STAR collaboration collected data from $_{44}^{96}{\mathrm{Ru}}+_{44}^{96}{\mathrm{Ru}}$ and $_{40}^{96}{\mathrm{Zr}}+_{40}^{96}{\mathrm{Zr}}$ at $\sqrt{s_\text {NN}}=200$ GeV to search for the presence of the chiral magnetic effect in collisions of nuclei. The isobar collision species alternated frequently between $_{44}^{96}{\mathrm{Ru}}+_{44}^{96}{\mathrm{Ru}}$ and $_{40}^{96}{\mathrm{Zr}}+_{40}^{96}{\mathrm{Zr}}$ . In order to conduct blind analyses of studies related to the chiral magnetic effect in these isobar data, STAR developed a three-step blind analysis procedure. Analysts are initially provided a “reference sample” of data, comprised of a mix of events from the two species, the order of which respects time-dependent changes in run conditions. After tuning analysis codes and performing time-dependent quality assurance on the reference sample, analysts are provided a species-blind sample suitable for calculating efficiencies and corrections for individual $\approx 30$-min data-taking runs. For this sample, species-specific information is disguised, but individual output files contain data from a single isobar species. Only run-by-run corrections and code alteration subsequent to these corrections are allowed at this stage. Following these modifications, the “frozen” code is passed over the fully un-blind data, completing the blind analysis. As a check of the feasibility of the blind analysis procedure, analysts completed a “mock data challenge,” analyzing data from Au + Au collisions at $\sqrt{s_\text {NN}}=27$ GeV, collected in 2018. The Au + Au data were prepared in the same manner intended for the isobar blind data. Finally, the details of the blind analysis procedure and results from the mock data challenge are presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Optical neural engine for solving scientific partial differential equations

Abstract Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations of PDEs. Although optical systems offer high-throughput and energy-efficient ML hardware, their demonstration for solving PDEs is limited. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time-dependent and time-independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson’s equation in demagnetization, the Navier-Stokes equation in incompressible fluid, Maxwell’s equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high-performance dual-space processing for outperforming traditional PDE solvers and being comparable with state-of-the-art ML models but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales and real-time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large-scale scientific and engineering computations.

Tang, Yingheng (ORCID:0009000153622546)↗

DOE OSTI2022

Survival analysis of localized prostate cancer with deep learning

In recent years, data-driven, deep-learning-based models have shown great promise in medical risk prediction. By utilizing the large-scale Electronic Health Record data found in the U.S. Department of Veterans Affairs, the largest integrated healthcare system in the United States, we have developed an automated, personalized risk prediction model to support the clinical decision-making process for localized prostate cancer patients. This method combines the representative power of deep learning and the analytical interpretability of parametric regression models and can implement both time-dependent and static input data. To collect a comprehensive evaluation of model performances, we calculate time-dependent C-statistics C td over 2-, 5-, and 10-year time horizons using either a composite outcome or prostate cancer mortality as the target event. The composite outcome combines the Prostate-Specific Antigen (PSA) test, metastasis, and prostate cancer mortality. Our longitudinal model Recurrent Deep Survival Machine (RDSM) achieved C td 0.85 (0.83), 0.80 (0.83), and 0.76 (0.81), while the cross-sectional model Deep Survival Machine (DSM) attained C td 0.85 (0.82), 0.80 (0.82), and 0.76 (0.79) for the 2-, 5-, and 10-year composite (mortality) outcomes, respectively. In addition to estimating the survival probability, our method can quantify the uncertainty associated with the prediction. The uncertainty scores show a consistent correlation with the prediction accuracy. We find PSA and prostate cancer stage information are the most important indicators in risk prediction. Our work demonstrates the utility of the data-driven machine learning model in prostate cancer risk prediction, which can play a critical role in the clinical decision system.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Hidden domain boundary dynamics toward crystalline perfection

A central paradigm of nonequilibrium physics concerns the dynamics of heterogeneity and disorder, impacting processes ranging from the behavior of glasses to the emergent functionality of active matter. Understanding these complex mesoscopic systems requires probing the microscopic trajectories associated with irreversible processes, the role of fluctuations and entropy growth, and the timescales on which nonequilibrium responses are ultimately maintained. Approaches that illuminate these processes in model systems may enable a more general understanding of other heterogeneous nonequilibrium phenomena, and potentially define ultimate speed and energy cost limits for information processing technologies. Here, we apply ultrafast single-shot X-ray photon correlation spectroscopy to resolve the nonequilibrium, heterogeneous, and irreversible mesoscale dynamics during a light-induced phase transition in a (PbTiO 3 ) 16 /(SrTiO 3 ) 16 superlattice. Such ferroelectric superlattice systems are a useful platform to study phase transitions and topological dynamics due to their high degree of tunability. This provides an approach for capturing the nucleation of the light-induced phase, the formation of transient mesoscale defects at the boundaries of the nuclei, and the eventual annihilation of these defects, even in systems with complex polarization topologies. We identify a nonequilibrium correlation response spanning >10 orders of magnitude in timescales, with multistep behavior similar to the plateaus observed in supercooled liquids and glasses. We further show how the observed time-dependent long-time correlations can be understood in terms of stochastic and non-Markovian dynamics of domain walls, encoded in waiting-time distributions with power-law tails. This work defines possibilities for probing the nonequilibrium and correlated dynamics of disordered and heterogeneous media.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Diminishing marginal effect in estimating the dissolved organic carbon export from a watershed

Dissolved organic carbon (DOC) can be initially moved from soils to inland waters with surface runoff, and then mineralized, buried, or eventually delivered to the coastal ocean. This land-to-ocean phase of the DOC flux must be accounted for to comprehensively understand the global carbon cycle. To estimate the terrestrial-aquatic DOC leaching, calculating the product of the riverine DOC concentration and the corresponding river discharge measured at the watershed outlet is a common method. However, it is challenging to frequently and exactly record riverine DOC concentrations, thus the relationship between DOC concentrations and discharges (C-Q relationship) are established and used to interpolate the time-series of DOC concentrations. We found that the widely used time-dependent and time-independent C-Q regression models are weak in representing their altered relationship when the discharge is extremely high, which was named as diminishing marginal effect. In this study, we evaluated the performance of two C-Q regression models and discussed possible reasons for the diminishing marginal effect. We suggest that repeated and long-term measurements of the DOC concentration are required to adequately analyze their relationships, especially during the early spring and seasons with heavy precipitations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains. The proposed framework, named eXtended PINNs ( X P I N N s ), further pushes the boundaries of both PINNs as well as conservative PINNs (cPINNs), which is a recently proposed domain decomposition approach in the PINN framework tailored to conservation laws. Compared to PINN, the XPINN method has large representation and parallelization capacity due to the inherent property of deployment of multiple neural networks in the smaller subdomains. Unlike cPINN, XPINN can be extended to any type of PDEs. Moreover, the domain can be decomposed in any arbitrary way (in space and time), which is not possible in cPINN. Thus, XPINN offers both space and time parallelization, thereby reducing the training cost more effectively. In each subdomain, a separate neural network is employed with optimally selected hyperparameters, e.g., depth/width of the network, number and location of residual points, activation function, optimization method, etc. A deep network can be employed in a subdomain with complex solution, whereas a shallow neural network can be used in a subdomain with relatively simple and smooth solutions. We demonstrate the versatility of XPINN by solving both forward and inverse PDE problems, ranging from one-dimensional to three-dimensional problems, from time-dependent to time-independent problems, and from continuous to discontinuous problems, which clearly shows that the XPINN method is promising in many practical problems. The proposed XPINN method is the generalization of PINN and cPINN methods, both in terms of applicability as well as domain decomposition approach, which efficiently lends itself to parallelized computation. The XPINN code is available on h t t p s : / / g i t h u b . c o m / A m e y a J a g t a p / X P I N N s .

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

The challenge to unify treatment of high-temperature fatigue - A partisan proposal based on strainrange partitioning

The strainrange partitioning concept divides the imposed strain into four basic ranges involving time-dependent and time-independent components. It is shown that some of the results presented at the symposium can be better correlated on the basis of this concept than by alternative methods. It is also suggested that methods of data generation and analysis can be helpfully guided by this approach. Potential applicability of the concept to the treatment of frequency and hold-time effects, environmental influence, crack initiation and growth, thermal fatigue, and code specifications are briefly considered. A required experimental program is outlined.

Manson, S. S.↗

NASA NTRS1973

The application of holography as a real-time three-dimensional motion picture camera

A historical introduction to holography is presented, as well as a basic description of sideband holography for stationary objects. A brief theoretical development of both time-dependent and time-independent holography is also provided, along with an analytical and intuitive discussion of a unique holographic arrangement which allows the resolution of front surface detail from an object moving at high speeds. As an application of such a system, a real-time three-dimensional motion picture camera system is discussed and the results of a recent demonstration of the world's first true three-dimensional motion picture are given.

Kurtz, R. L.↗

NASA NTRS1972

The challenge to unify treatment of high-temperature fatigue - A partisan proposal based on strainrange partitioning.

The strainrange partitioning concept divides the imposed strain into four basic ranges involving time-dependent and time-independent components. It is shown that some of the results presented at the Symposium can be better correlated on the basis of this concept than by alternative methods. It is also suggested that methods of data generation and analysis can be helpfully guided by this approach. Potential applicability of the concept to the treatment of frequency and hold-time effects, environmental influence, crack initiation and growth, thermal fatigue, and code specifications are then briefly considered. A required experimental program is outlined.

Manson, S. S.↗

NASA NTRS1973

Computational problems in three and four dimensional boundary layer theory

It is shown that three-dimensional and time-dependent boundary layer flows can be calculated in a reasonable amount of time with the current generation of computers. The physical problems used to illustrate this have a wide application, and are the following: (1) oscillating flows over cylinders with both the wall and the inviscid flow oscillating, and (2) time-dependent and three-dimensional flow over a rotating airfoil in forward flight.

Dwyer, H. A.↗

NASA NTRS1981

Semi-actuator disk theory for compressor choke flutter

A mathematical anaysis predict the unsteady aerodynamic utilizing semi actuator theory environment for a cascade of airfoils harmonically oscillating in choked flow was developed. A normal shock is located in the blade passage, its position depending on the time dependent geometry, and pressure perturbations of the system. In addition to shock dynamics, the model includes the effect of compressibility, interblade phase lag, and an unsteady flow field upstream and downstream of the cascade. Calculated unsteady aerodynamics were compared with isolated airfoil wind tunnel data, and choke flutter onset boundaries were compared with data from testing of an F100 high pressure compressor stage.

Micklow, J.↗

NASA NTRS1982

A parameterized model for the evolution of isotopic heterogeneities in a convecting system

It is experimentally shown that, although steady convective flows are efficient means to heterogeneity within a single cell, they do not produce a dispersal of heterogeneous material over scales that are large by comparison to their depth, which requires that the flow be time-dependent on a time scale comparable to the overturn time. Convection in an internally heated layer does possess this property, and numerical solutions are presently used to study the way in which it disperses a set of neutrally bouyant particles initially confined to a small space. The derived concept of effective diffusivity is applied to the isotopic evolution of the Sm-Nd and Rb-Sr systems, with spatial variations generated by horizontal variations in degree of melting 1.8 billion years ago.

Richter, F. M.↗

NASA NTRS1985

Unified constitutive material models for nonlinear finite-element structural analysis

Unified constitutive material models were developed for structural analyses of aircraft gas turbine engine components with particular application to isotropic materials used for high-pressure stage turbine blades and vanes. Forms or combinations of models independently proposed by Bodner and Walker were considered. These theories combine time-dependent and time-independent aspects of inelasticity into a continuous spectrum of behavior. This is in sharp contrast to previous classical approaches that partition inelastic strain into uncoupled plastic and creep components. Predicted stress-strain responses from these models were evaluated against monotonic and cyclic test results for uniaxial specimens of two cast nickel-base alloys, B1900+Hf and Rene' 80. Previously obtained tension-torsion test results for Hastelloy X alloy were used to evaluate multiaxial stress-strain cycle predictions. The unified models, as well as appropriate algorithms for integrating the constitutive equations, were implemented in finite-element computer codes.

Kaufman, A.↗

NASA NTRS1985

Unified constitutive material models for nonlinear finite-element structural analysis

Unified constitutive material models were developed for structural analyses of aircraft gas turbine engine components with particular application to isotropic materials used for high-pressure stage turbine blades and vanes. Forms or combinations of models independently proposed by Bodner and Walker were considered. These theories combine time-dependent and time-independent aspects of inelasticity into a continuous spectrum of behavior. This is in sharp contrast to previous classical approaches that partition inelastic strain into uncoupled plastic and creep components. Predicted stress-strain responses from these models were evaluated against monotonic and cyclic test results for uniaxial specimens of two cast nickel-base alloys, B1900+Hf and Rene 80. Previously obtained tension-torsion test results for Hastelloy X alloy were used to evaluate multiaxial stress-strain cycle predictions. The unified models, as well as appropriate algorithms for integrating the constitutive equations, were implemented in finite-element computer codes.

Kaufman, A.↗

NASA NTRS1992

The steady part of the secular variation of the Earth's magnetic field

The secular variation of the Earth's magnetic field results from the effects of magnetic induction in the fluid outer core and from the effects of magnetic diffusion in the core and the mantle. Adequate observations to map the magnetic field at the core-mantle boundary extend back over three centuries, providing a model of the secular variation at the core-mantle boundary. Here we consider how best to analyze this time-dependent part of the field. To calculate steady core flow over long time periods, we introduce an adaptation of our earlier method of calculating the flow in order to achieve greater numerical stability. We perform this procedure for the periods 1840-1990 and 1690-1840 and find that well over 90 percent of the variance of the time-dependent field can be explained by simple steady core flow. The core flows obtained for the two intervals are broadly similar to each other and to flows determined over much shorter recent intervals.

Bloxham, Jeremy↗

NASA NTRS1995

Tidal influence on O(1S) airglow emission rate distributions at the geographic equator as observed by WINDII

WINDII, the Wind Imaging Interferometer on the Upper Atmosphere Research Satellite, observes winds, temperatures and emission rates in the upper mesosphere and thermosphere. In this paper we report on nighttime observations of the vertical distribution of the O(1S) 557.7 nm emission near the geographic equator for March/April, 1993. The airglow volume emission rate distribution is found to be strongly dependent on local time. Beginning at dusk, an intense airglow emission layer descends from a mean altitude of 95 km, reaching 89 km by midnight after which the emission rapidly decays. Shortly after midnight it reappears weakly at a higher altitude and remains at this level as the emission rate gradually increases towards dawn. This strong local time dependence leads us to conclude that the effect is tidally driven. Comparison with the Forbes (1982a,b) model suggest that total density perturbations and changes in the atomic oxygen mixing ratio may the cause of the changes in emission rate distribution between dusk and midnight. The reappearance of the emission after midnight may be caused by downward winds bringing oxygen-rich air from above.

Shephere, G. G.↗

NASA NTRS1995

Time-domain approach for the transient responses in stratified viscoelastic Earth models

We have developed the numerical algorithm for the computation of transient viscoelastic responses in the time domain for a radially stratified Earth model. Stratifications in both the elastic parameters and the viscosity profile have been considered. The particular viscosity profile employed has a viscosity maximum with a constrast of O(100) in the mid lower mantle. The distribution of relaxation times reveals the presence of a continuous spectrum situated between O(100) and O(exp 4) years. The principal mode is embedded within this continuous spectrum. From this initial-value approach we have found that for the low degree harmonics the non-modal contributions are comparable to the modal contributions. For this viscosity model the differences between the time-domain and normal-mode results are found to decrease strongly with increasing angular order. These calculations also show that a time-dependent effective relaxation time can be defined, which can be bounded by the relaxation times of the principal modes.

Hanyk, L.↗