Results for “Equation learning” — Page 31

DOE OSTI2023

Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging: Theory, algorithms, and applications

Plug-and-play (PnP) priors constitute one of the most widely used frameworks for solving computational imaging problems through the integration of physical models and learned models. PnP leverages high-fidelity physical sensor models and powerful machine learning methods for prior modeling of data to provide state-of-the-art reconstruction algorithms. PnP algorithms alternate between minimizing a data fidelity term to promote data consistency and imposing a learned regularizer in the form of an image denoiser. Recent highly successful applications of PnP algorithms include biomicroscopy, computerized tomography (CT), magnetic resonance imaging (MRI), and joint ptychotomography. This article presents a unified and principled review of PnP by tracing its roots, describing its major variations, summarizing main results, and discussing applications in computational imaging. Additionally, we also point the way toward further developments by discussing recent results on equilibrium equations that formulate the problem associated with PnP algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Calibrating constitutive models with full‐field data via physics informed neural networks

Abstract The calibration of solid constitutive models with full‐field experimental data is a long‐standing challenge, especially in materials that undergo large deformations. In this paper, we propose a physics‐informed deep‐learning framework for the discovery of hyperelastic constitutive model parameterizations given full‐field surface displacement data and global force‐displacement data. Contrary to the majority of recent literature in this field, we work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. The approach presented in this paper is computationally efficient, suitable for irregular geometric domains, and readily ingests displacement data without the need for interpolation onto a computational grid. A selection of canonical hyperelastic material models suitable for different material classes is considered including the Neo–Hookean, Gent, and Blatz–Ko constitutive models as exemplars for general non‐linear elastic behaviour, elastomer behaviour with finite strain lock‐up, and compressible foam behaviour, respectively. We demonstrate that physics informed machine learning is an enabling technology and may shift the paradigm of how full‐field experimental data are utilized to calibrate constitutive models under finite deformations.

Hamel, Craig M.↗

DOE OSTI2021

Encoder–decoder neural network for solving the nonlinear Fokker–Planck–Landau collision operator in XGC

An encoder–decoder neural network has been used to examine the possibility for acceleration of a partial integro-differential equation, the Fokker–Planck–Landau collision operator. This is part of the governing equation in the massively parallel particle-in-cell code XGC, which is used to study turbulence in fusion energy devices. The neural network emphasizes physics-inspired learning, where it is taught to respect physical conservation constraints of the collision operator by including them in the training loss, along with the ℓ 2 loss. In particular, network architectures used for the computer vision task of semantic segmentation have been used for training. A penalization method is used to enforce the ‘soft’ constraints of the system and integrate error in the conservation properties into the loss function. During training, quantities representing the particle density, momentum and energy for all species of the system are calculated at each configuration vertex, mirroring the procedure in XGC. This simple training has produced a median relative loss, across configuration space, of the order of 10 –4 , which is low enough if the error is of random nature, but not if it is of drift nature in time steps. The run time for the current Picard iterative solver of the operator is O(n 2 ), where n is the number of plasma species. As the XGC1 code begins to attack problems including a larger number of species, the collision operator will become expensive computationally, making the neural network solver even more important, especially since its training only scales as O(n). Here, a wide enough range of collisionality has been considered in the training data to ensure the full domain of collision physics is captured. An advanced technique to decrease the losses further will be subject of a subsequent report. Eventual work will include expansion of the network to include multiple plasma species.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Turbulent field fluctuations in gyrokinetic and fluid plasmas

A key uncertainty in the design and development of magnetic confinement fusion energy reactors is predicting edge plasma turbulence. An essential step in overcoming this uncertainty is the validation in accuracy of reduced turbulent transport models. Drift-reduced Braginskii two-fluid theory is one such set of reduced equations that has for decades simulated boundary plasmas in experiment, but significant questions exist regarding its predictive ability. To this end, using a novel physics-informed deep learning framework, we demonstrate the first ever direct quantitative comparisons of turbulent field fluctuations between electrostatic two-fluid theory and electromagnetic gyrokinetic modeling with good overall agreement found in magnetized helical plasmas at low normalized pressure. This framework presents a new technique for the numerical validation and discovery of reduced global plasma turbulence models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Turbulent field fluctuations in gyrokinetic and fluid plasmas

A key uncertainty in the design and development of magnetic confinement fusion energy reactors is predicting edge plasma turbulence. An essential step in overcoming this uncertainty is the validation in accuracy of reduced turbulent transport models. Drift-reduced Braginskii two-fluid theory is one such set of reduced equations that has for decades simulated boundary plasmas in experiment, but significant questions exist regarding its predictive ability. To this end, using a novel physics-informed deep learning framework, we demonstrate the first ever direct quantitative comparisons of turbulent field fluctuations between electrostatic two-fluid theory and electromagnetic gyrokinetic modelling with good overall agreement found in magnetized helical plasmas at low normalized pressure. This framework is readily adaptable to experimental and astrophysical environments, and presents a new technique for the numerical validation and discovery of reduced global plasma turbulence models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1989

Evolution of the solar nebula. I - Nonaxisymmetric structure during nebula formation

Numerical solutions of the equations of hydrodynamics, gravitation, and radiative transfer in three spatial dimensions are used to model the formation and time evolution of the early solar nebula in order to learn whether or not gravitational torques between nonaxisymmetric structures in the solar nebula can transport angular momentum rapidly enough to produce nebula clearing on astronomically indicated (10 to the 5 to 10 to the 7 yr) time scales. The models involve solutions for the collapse of spherical clouds with assumed initial density and rotation profiles onto protosuns of variable mass. Most of the models assume uniform initial density and rotation, and have variations in the initial parameters of cloud mass, cloud rotation rate, and protosun mass which are chosen to simulate a range of possible phases of early solar nebula evolution. The models show little tendency for directly forming small numbers of giant gaseous protoplanets through gaseous gravitational instability.

Boss, Alan P.↗

NASA NTRS2008

Sensing a Changing Chemical Mixture Using an Electronic Nose

A method of using an electronic nose to detect an airborne mixture of known chemical compounds and measure the temporally varying concentrations of the individual compounds is undergoing development. In a typical intended application, the method would be used to monitor the air in an inhabited space (e.g., the interior of a building) for the release of solvents, toxic fumes, and other compounds that are regarded as contaminants. At the present state of development, the method affords a capability for identifying and quantitating one or two compounds that are members of a set of some number (typically of the order of a dozen) known compounds. In principle, the method could be extended to enable monitoring of more than two compounds. An electronic nose consists of an array of sensors, typically made from polymer carbon composites, the electrical resistances of which change upon exposure to a variety of chemicals. By design, each sensor is unique in its responses to these chemicals: some or all of the sensitivities of a given sensor to the various vapors differ from the corresponding sensitivities of other sensors. In general, the responses of the sensors are nonlinear functions of the concentrations of the chemicals. Hence, mathematically, the monitoring problem is to solve the set of time-dependent nonlinear equations for the sensor responses to obtain the time dependent concentrations of individual compounds. In the present developmental method, successive approximations of the solution are generated by a learning algorithm based on independent-component analysis (ICA) an established information theoretic approach for transforming a vector of observed interdependent signals into a set of signals that are as nearly statistically independent as possible.

Duong, Tuan↗

NASA NTRS2014

High Efficiency Centrifugal Compressor for Rotorcraft Applications

The report "High Efficiency Centrifugal Compressor for Rotorcraft Applications" documents the work conducted at UTRC under the NRA Contract NNC08CB03C, with cost share 2/3 NASA, and 1/3 UTRC, that has been extended to 4.5 years. The purpose of this effort was to identify key technical barriers to advancing the state-of-the-art of small centrifugal compressor stages; to delineate the measurements required to provide insight into the flow physics of the technical barriers; to design, fabricate, install, and test a state-of-the-art research compressor that is representative of the rear stage of an axial-centrifugal aero-engine; and to acquire detailed aerodynamic performance and research quality data to clarify flow physics and to establish detailed data sets for future application. The design activity centered on meeting the goal set outlined in the NASA solicitation-the design target was to increase efficiency at higher work factor, while also reducing the maximum diameter of the stage. To fit within the existing Small Engine Components Test Facility at NASA Glenn Research Center (GRC) and to facilitate component re-use, certain key design parameters were fixed by UTRC, including impeller tip diameter, impeller rotational speed, and impeller inlet hub and shroud radii. This report describes the design effort of the High Efficiency Centrifugal Compressor stage (HECC) and delineation of measurements, fabrication of the compressor, and the initial tests that were performed. A new High-Efficiency Centrifugal Compressor stage with a very challenging reduction in radius ratio was successfully designed, fabricated and installed at GRC. The testing was successful, with no mechanical problems and the running clearances were achieved without impeller rubs. Overall, measured pressure ratio of 4.68, work factor of 0.81, and at design exit corrected flow rate of 3 lbm/s met the target requirements. Polytropic efficiency of 85.5 percent and stall margin of 7.5 percent were measured at design flow rate and speed. The measured efficiency and stall margin were lower than pre-test CFD predictions by 2.4 percentage points (pt) and 4.5 pt, respectively. Initial impressions from the experimental data indicated that the loss in the efficiency and stall margin can be attributed to a design shortfall in the impeller. However, detailed investigation of experimental data and post-test CFD simulations of higher fidelity than pre-test CFD, and in particular the unsteady CFD simulations and the assessment with a wider range of turbulence models, have indicated that the loss in efficiency is most likely due to the impact of unfavorable unsteady impeller/diffuser interactions induced by diffuser vanes, an impeller/diffuser corrected flow-rate mismatch (and associated incidence levels), and, potentially, flow separation in the radial-to-axial bend. An experimental program with a vaneless diffuser is recommended to evaluate this observation. A subsequent redesign of the diffuser (and the radial-to-axial bend) is also recommended. The diffuser needs to be redesigned to eliminate the mismatching of the impeller and the diffuser, targeting a slightly higher flow capacity. Furthermore, diffuser vanes need to be adjusted to align the incidence angles, to optimize the splitter vane location (both radially and circumferentially), and to minimize the unsteady interactions with the impeller. The radial-to-axial bend needs to be redesigned to eliminate, or at least minimize, the flow separation at the inner wall, and its impact on the flow in the diffuser upstream. Lessons were also learned in terms of CFD methodology and the importance of unsteady CFD simulations for centrifugal compressors was highlighted. Inconsistencies in the implementation of a widely used two-equation turbulence model were identified and corrections are recommended. It was also observed that unsteady simulations for centrifugal compressors require significantly longer integration times than what is current practice in industry.

Gorazd Medic↗

NASA NTRS2014

High Efficiency Centrifugal Compressor for Rotorcraft Applications

The report "High Efficiency Centrifugal Compressor for Rotorcraft Applications" documents the work conducted at UTRC under the NRA Contract NNC08CB03C, with cost share 2/3 NASA, and 1/3 UTRC, that has been extended to 4.5 years. The purpose of this effort was to identify key technical barriers to advancing the state-of-the-art of small centrifugal compressor stages; to delineate the measurements required to provide insight into the flow physics of the technical barriers; to design, fabricate, install, and test a state-of-the-art research compressor that is representative of the rear stage of an axial-centrifugal aero-engine; and to acquire detailed aerodynamic performance and research quality data to clarify flow physics and to establish detailed data sets for future application. The design activity centered on meeting the goal set outlined in the NASA solicitation-the design target was to increase efficiency at higher work factor, while also reducing the maximum diameter of the stage. To fit within the existing Small Engine Components Test Facility at NASA Glenn Research Center (GRC) and to facilitate component re-use, certain key design parameters were fixed by UTRC, including impeller tip diameter, impeller rotational speed, and impeller inlet hub and shroud radii. This report describes the design effort of the High Efficiency Centrifugal Compressor stage (HECC) and delineation of measurements, fabrication of the compressor, and the initial tests that were performed. A new High-Efficiency Centrifugal Compressor stage with a very challenging reduction in radius ratio was successfully designed, fabricated and installed at GRC. The testing was successful, with no mechanical problems and the running clearances were achieved without impeller rubs. Overall, measured pressure ratio of 4.68, work factor of 0.81, and at design exit corrected flow rate of 3 lbm/s met the target requirements. Polytropic efficiency of 85.5 percent and stall margin of 7.5 percent were measured at design flow rate and speed. The measured efficiency and stall margin were lower than pre-test CFD predictions by 2.4 percentage points (pt) and 4.5 pt, respectively. Initial impressions from the experimental data indicated that the loss in the efficiency and stall margin can be attributed to a design shortfall in the impeller. However, detailed investigation of experimental data and post-test CFD simulations of higher fidelity than pre-test CFD, and in particular the unsteady CFD simulations and the assessment with a wider range of turbulence models, have indicated that the loss in efficiency is most likely due to the impact of unfavorable unsteady impeller/diffuser interactions induced by diffuser vanes, an impeller/diffuser corrected flow-rate mismatch (and associated incidence levels), and, potentially, flow separation in the radial-to-axial bend. An experimental program with a vaneless diffuser is recommended to evaluate this observation. A subsequent redesign of the diffuser (and the radial-to-axial bend) is also recommended. The diffuser needs to be redesigned to eliminate the mismatching of the impeller and the diffuser, targeting a slightly higher flow capacity. Furthermore, diffuser vanes need to be adjusted to align the incidence angles, to optimize the splitter vane location (both radially and circumferentially), and to minimize the unsteady interactions with the impeller. The radial-to-axial bend needs to be redesigned to eliminate, or at least minimize, the flow separation at the inner wall, and its impact on the flow in the diffuser upstream. Lessons were also learned in terms of CFD methodology and the importance of unsteady CFD simulations for centrifugal compressors was highlighted. Inconsistencies in the implementation of a widely used two-equation turbulence model were identified and corrections are recommended. It was also observed that unsteady simulations for centrifugal compressors require significantly longer integration times than what is current practice in industry.

Gorazd Medic↗

NASA NTRS2017

High Efficiency Centrifugal Compressor for Rotorcraft Applications

The report "High Efficiency Centrifugal Compressor for Rotorcraft Applications" documents the work conducted at UTRC under the NRA Contract NNC08CB03C, with cost share 2/3 NASA, and 1/3 UTRC, that has been extended to 4.5 years. The purpose of this effort was to identify key technical barriers to advancing the state-of-the-art of small centrifugal compressor stages; to delineate the measurements required to provide insight into the flow physics of the technical barriers; to design, fabricate, install, and test a state-of-the-art research compressor that is representative of the rear stage of an axial-centrifugal aero-engine; and to acquire detailed aerodynamic performance and research quality data to clarify flow physics and to establish detailed data sets for future application. The design activity centered on meeting the goal set outlined in the NASA solicitation-the design target was to increase efficiency at higher work factor, while also reducing the maximum diameter of the stage. To fit within the existing Small Engine Components Test Facility at NASA Glenn Research Center (GRC) and to facilitate component re-use, certain key design parameters were fixed by UTRC, including impeller tip diameter, impeller rotational speed, and impeller inlet hub and shroud radii. This report describes the design effort of the High Efficiency Centrifugal Compressor stage (HECC) and delineation of measurements, fabrication of the compressor, and the initial tests that were performed. A new High-Efficiency Centrifugal Compressor stage with a very challenging reduction in radius ratio was successfully designed, fabricated and installed at GRC. The testing was successful, with no mechanical problems and the running clearances were achieved without impeller rubs. Overall, measured pressure ratio of 4.68, work factor of 0.81, and at design exit corrected flow rate of 3 lbm/s met the target requirements. Polytropic efficiency of 85.5 percent and stall margin of 7.5 percent were measured at design flow rate and speed. The measured efficiency and stall margin were lower than pre-test CFD predictions by 2.4 percentage points (pt) and 4.5 pt, respectively. Initial impressions from the experimental data indicated that the loss in the efficiency and stall margin can be attributed to a design shortfall in the impeller. However, detailed investigation of experimental data and post-test CFD simulations of higher fidelity than pre-test CFD, and in particular the unsteady CFD simulations and the assessment with a wider range of turbulence models, have indicated that the loss in efficiency is most likely due to the impact of unfavorable unsteady impeller/diffuser interactions induced by diffuser vanes, an impeller/diffuser corrected flow-rate mismatch (and associated incidence levels), and, potentially, flow separation in the radial-to-axial bend. An experimental program with a vaneless diffuser is recommended to evaluate this observation. A subsequent redesign of the diffuser (and the radial-to-axial bend) is also recommended. The diffuser needs to be redesigned to eliminate the mismatching of the impeller and the diffuser, targeting a slightly higher flow capacity. Furthermore, diffuser vanes need to be adjusted to align the incidence angles, to optimize the splitter vane location (both radially and circumferentially), and to minimize the unsteady interactions with the impeller. The radial-to-axial bend needs to be redesigned to eliminate, or at least minimize, the flow separation at the inner wall, and its impact on the flow in the diffuser upstream. Lessons were also learned in terms of CFD methodology and the importance of unsteady CFD simulations for centrifugal compressors was highlighted. Inconsistencies in the implementation of a widely used two-equation turbulence model were identified and corrections are recommended. It was also observed that unsteady simulations for centrifugal compressors require significantly longer integration times than what is current practice in industry.

Centrifugal compressor↗

NASA NTRSDate not supplied

Clifford Neural Operators on Atmospheric Data Influenced Partial Differential Equations

Mathematical representations of the atmosphere are key to forecasting and research tasks across Earth science. Numerically solving the underlying partial differential equations(PDEs) of the atmosphere, however, can be difficult and computationally expensive with numerous trade-offs between computing efficiency and accuracy. Utilizing neural net-works to learn approximations of the PDE solutions from the data can help us model complex phenomena more efficiently than traditional numerical schemes. Here, we have applied Clifford algebra-based neural operators for predicting atmospheric variables. Clifford Fourier neural operators are used with two different backbone architectures, ResNet and UNet, on custom data of U10, V10 and surface pressure as well as U500, V500 and Z500. Clifford Fourier neural operators, coupled with ResNet and UNet architectures, are applied to a key reanalysis dataset. Model performance is initially strong, but we observe increasing errors, resulting in the model becoming highly unstable.

Sujit Roy↗

DOE OSTI2023

Using Co-Optimized Machine Learned Manifolds for Modeling Chemically Reacting Flows

Chemically reacting flows play a key role in a wide range of engineered systems, from chemical and polymer processing to combustion-based energy conversion technologies. Simulations of these flows involve solving a coupled set of partial differential equations for mass, momentum, energy, and all relevant chemical species in the system. Chemical reaction pathways may be extremely complex and involve hundreds or more intermediate species, with reactions that occur over timescales varying by several orders of magnitude - presenting a significant numerical stiffness challenge. The combination of these factors makes simulation of chemically reacting flows vastly more expensive than nonreactive simulations, and often makes direct solution of the governing equations intractable. It is necessary to apply lower-fidelity models in place of the detailed governing equations in order to reduce computational cost to enable reacting flow simulation tools to be used in the engineering design process. Many of the models employed for this purpose are based on reducing the dimension of the thermochemical state, motivated by the observation that the observed thermochemical states in a system lie on a low-dimensional manifold in thermochemical state space. This behavior occurs due to the fast equilibration of certain reactive and transport processes, and physics-based manifold models rely on idealized assumptions about the balance of timescales and the way in which chemistry and transport are coupled. In this work, we apply a novel method for data-driven manifold-based modeling that can leverage data from high-fidelity reacting flow simulations to improve model accuracy in cases where the physics-based modeling assumptions break down. The approach is designed to be broadly applicable across chemically reacting flow systems but is applied here to turbulent combustion modeling.

machine learning↗

DOE OSTI2025

DS-TIDE: Harnessing Dynamical Systems for Efficient Time-Independent Differential Equation Solving

Time-Independent Differential Equations (TIDEs) are central to modeling equilibrium behavior across a wide range of scientific and engineering domains, from electrostatics to porous media flow. Conventional numerical solvers offer reliable solutions but incur significant computational costs due to fine-grained discretization and iterative procedures. Machine learning-based approaches address this by replacing iterative solving processes with one-time inference; however, their sophisticated models require extensive training resources that often exceed those of traditional solvers. Consequently, designing a TIDE solver that achieves high accuracy, broad applicability, and exceptional computational efficiency remains a fundamental challenge. In this paper, we propose DS-TIDE, a novel hardware solver that is inspired by, and subsequently leverages, the intrinsic connection between Dynamical Systems (DS) and Differential Equations (DEs) to efficiently and accurately solve TIDEs. DS-TIDE employs a CMOS-compatible DS-based processor, whose physical states evolve under carefully designed DE-driven dynamics and naturally converge to equilibrium -- the solution of the target TIDE -- within ~1µs on a ~1-watt DS-TIDE processor. To enhance expressivity, DS-TIDE incorporates Heterogeneous Dynamics with Temporal Layering (HDTL), which solves TIDEs through a three-stage DS evolution -- conditioning, solving, and decoding -- each governed by specialized dynamics. The entire evolution process is analogous to an infinitely deep neural network temporally unrolled, offering the system the capability of representing complex equations. Furthermore, DS-TIDE is equipped with an on-device DS-DE Auto-Alignment mechanism that dynamically adapts intrinsic hardware dynamics within milliseconds, effectively aligning the system’s dynamics to diverse target DEs. Experimental results across TIDEs from a wide range of scientific and engineering domains demonstrate that DS-TIDE achieves ~10^3× speedup, ~10^5× energy savings, and competitive or superior accuracy compared to state-of-the-art numerical and ML-based solvers.

Liu, Chuan↗

DOE OSTI2024

Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Differentiable vertex fitting for jet flavor tagging

This work explores the use of differentiable programming to integrate domain knowledge, in the form of domain specific software, into neural networks to develop scientific machine learning systems. We propose a differentiable vertex fitting algorithm that estimates the crossing point of multiple curves. In the high energy physics setting, these curves are defined by particle equations of motion and the crossing point represents the origin of particle production. This differentiable vertex fitting algorithm can be seamlessly integrated into neural networks, and we show its utility and efficacy in the high energy physics application of the classification of jets, i.e., collimated streams of particles in particle detectors whose originating parent particle we aim to classify. We demonstrate how differentiable vertex fitting can be integrated into larger transformer-based models for jet flavor tagging and show improvements in heavy flavor jet classification when compared to baseline models. Published by the American Physical Society 2024

Smith, Rachel E. C. (ORCID:0000000335851262)↗

DOE OSTI2024

Creation Synthetic Data to Train a Digital Twin to Predict Reactor Operations

Understanding techniques to strengthen the nuclear safeguards regime is crucial in preventing nuclear proliferation due to recent advancements in the nuclear energy industry such as Generation IV reactors and microreactors. Prior to the construction of a nuclear power plant, it is necessary to understand the proliferation potential of the plant's reactor. Digital twins serve as a unique solution to recognizing reactor behavior indicative of nuclear proliferation. A digital twin is defined as a virtual model that works in unison to represent a physical asset, with a transference of data between the virtual and physical assets [1]. This work serves as validation for training a digital twin on synthetic data fabricated via means of Serpent reactor physics and point kinetics equations simulations. In this case this work is based on parameters of Idaho State University's AGN-201 reactor. The synthetic data can then be utilized to train machine learning models in the future to further investigate the utility of these methods. The accuracy of the predicted data is measured against real operational data to verify the reliability of the synthetic data creation methods and decide whether these methods should be used in the future to inform inspectors of a reactor's proliferation potential.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

NASA NTRSDate not supplied

Open-source Numerical Modeling of Solidification Cracking Susceptibility: Application to Refractory Alloy Systems

Introduction. Alloys such as aluminum, nickel-base, and austenitic stainless steels are susceptible to solidification cracking during welding and 3D printing. Compositional optimization is one method used to effectively mitigate solidification cracking of those alloy systems. With the surge in hypersonic and in-space propulsion activities, refractory metals (Nb, Mo, Ta, W, and Re) and their alloy derivatives are increasing in importance due to their extreme high melting point and retention of high-temperature strength; however, their chemistry was most typically optimized to promote ductility during mechanical operations such as drawing and forming. Welding of such alloys has been a challenge due to a number of issues including solidification cracking, atmospheric contamination (O, C, and N), as well as a shift in ductile-to-brittle transition to higher temperature following grain growth induced by welding. Compositional optimization of refractory alloys for solidification cracking resistance in particular is desirable as their usage increases with the advent of advanced manufacturing methods such as 3D printing. This work evaluates the effect of compositional variation in refractory metal systems on the solidification cracking susceptibility with the goals of optimizing existing alloys and joining process techniques, and formulating new alloys with increased solidification cracking resistance. Experimental Procedures. A python code was developed in a Jupyter notebook environment (Michael and Sowards, 2023) to facilitate the calculation of crack susceptibility index proposed by Kou (2015). Composition is entered as a single point, or as a 1-D or 2-D array. The notebook calls pycalphad (Otis and Liu, 2017 and Bocklund et al, 2020) to calculate the evolution of fraction solid as a function of temperature (under either Scheil or equilibrium assumptions) and then evaluates steepness of the fraction solid curve near the terminal stage of solidification to predict solidification cracking resistance. Open source thermodynamic databases available at online repositories are used (van de Walle). The process is setup in an automated fashion to generate plots that show variation in solidification cracking susceptibility according to composition on 1-D line plots or 2-D contour plots. The Jupyter notebook and crack susceptibility algorithm was also integrated with a widely used commercial CALPHAD code for validation and alloy exploration. Results and Discussion. The crack susceptibility model was first validated against a series of refractory alloy compositions evaluated in past work which utilized a specialized Varestraint test built inside a vacuum chamber environment (Lessman and Gold, 1971). The alloys tested in the Varestraint apparatus included T-111 (Ta-8W-2Hf), ASTAR-811C (Ta-8W-1Re-0.7Hf-0.025C), FS-85 (Nb-27Ta-10W-1Zr), T-222 (Ta-9.6W-2.4Hf-0.01C), Ta-10W, B-66 (Nb-5Mo-5V-1Zr), and SCb-291 (Nb-10W-10Ta). The initial test of the model showed a strong correlation with empirical Varestraint data, i.e., a Spearman rank correlation between model predictions and hot cracking measurements was observed to be greater than 0.8. Following the validation, a set of refractory metal binary mixtures was investigated to evaluate sensitivity of Nb, Mo, W, and Ta to C, N, and O content. A series of plots were produced that suggest ppmw ranges of C, N, and O where solidification cracking increases significantly and reaches a maximum. Also comparative ranking of each primary refractory metal to each interstitial was produced. For example C produces greater cracking response in Mo whereas O produces greater cracking response in Ta and Nb. Such compositional values have utility in setting limits on pickup of these interstitial elements during welding and printing rather than using a one-size-fits-all approach. Furthermore, the results have use in determining additive powder recycling requirements, which is especially pertinent for refractory metal powders due to their high cost compared to conventional alloys. Another application created thousands of hypothetical alloys within the nominal specified composition range of two widely used refractory alloys C103 (Nb-10Hf-1Ti) and TZM (Mo-0.5Ti-0.1Zr). The cracking index was calculated for the alloys and results were fed into machine learning regression techniques including Multiple Linear Regression, Ridge Regression, and Lasso Regression to determine relative potency each alloying element had on computed solidification cracking index. A series of linear equations were produced that relate composition of C103 and TZM to solidification cracking index. The crack susceptibility of C103 for example is described by an equation of the form: cracking index ~ O + 0.667*C + 0.635*N + 0.00037*Ta – 0.0008*Hf (in wt.%) From that equation, it is clear that O has strong propensity to induce solidification cracking. Interestingly, Hf is shown to reduce calculated cracking response. Finally, realizing the potential of this method to discover new refractory alloy formulations across the period table that have low solidification cracking sensitivity, the code was applied to new untested alloy systems including W-Zr-C, W-Ta-C, and others. Conclusions. In summary, an open source numerical method has been developed using Python code to calculate Kou’s crack susceptibility index. The method was applied to refractory metals which are inherently difficult to study from a weldability testing standpoint since inert shielding gas is not sufficient and welding is typically done in vacuum, especially in light of findings presented here where oxygen has profound influence on solidification cracking. This work revealed the effect of compositional variations on a series of refractory metals and showed the framework defined here will be useful in 1) the development of new alloys that have improved weldability and 3D printability, 2) placing compositional limits on existing alloys, and 3) ensuring adequate controls of manufacturing processes such as 3D printing where powder reuse is critical. Keywords. pycalphad; Python; refractory metals; solidification cracking. References. B. Bocklund et. al. (2020) http://doi.org/10.5281/zenodo.3630657. S. Kou. (2015) https://doi.org/10.1016/j.actamat.2015.01.034. G.G. Lessmann and R.E. Gold. Welding Journal, issue 1, pp. 1-s – 8-s (1971). F.N. Michael and J.W. Sowards. NASA/TM-20230002218 (2023). R. Otis and Z.-K. Liu. (2017) http://doi.org/10.5334/jors.140. A. Van de Wallle et. al. (2018) https://doi.org/10.1016/j.calphad.2018.04.003.

pycalphad↗

DOE OSTI2025

Kinetic Deep Learning v0.1

Here, we present a method that uses protein levels to predict times series of metabolite concentrations. Understanding this type of pathway dynamics is important in order to predict the behavior of the pathway and, more pragmatically, to be able to design biological systems (such as strains bioengineered to produce chemical products) reliably. Typically, for this purpose, kinetic models consisting of differential equations based on the Michaelis-Menten dynamics have been used in the past. However, these methods can rarely produce good fits to measured data time series. Possibly, this happens because the kinetic constants are unknown or are different from the ones measured in vivo, or perhaps because Michaelis-Menten dynamics is not a satisfactory description. In order to improve the predictive nature of these kinetic models we have eliminated the Michaelis-Menten description of pathway dynamics and we have substituted it by algorithms that automatically learn these dynamics from previously obtained metabolomics and proteomics data using machine learning approaches. Specifically, kinetic deep learning uses deep learning to map proteomics time series to metabolite concentration time series, instead of learning the first metabolite derivative and integrating in (as in the first version of kinetic learning). This approach is shown to provide good to excellent results with a data set specifically collected for this purpose.

Garcia Martin, Hector [Joint BioEnergy Institute (↗