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DOE OSTI2026

Efficient derivative computation for unsteady fatigue-constrained nonlinear aero-structural wind turbine blade optimization

Gradient-based optimization offers significant efficiency advantages for wind turbine blade design, but its application has often been limited by the cost and accuracy of finite-difference derivative calculations, especially when fatigue constraints are considered. In this work, we systematically compare and evaluate four differentiation techniques, namely algorithmic differentiation, implicit differentiation, sparsity exploitation, and parallelization, to determine their effectiveness in computing accurate gradients through time-domain aero-structural simulations. By integrating these techniques with unsteady nonlinear aerodynamic and structural models, we develop software designed for accurate gradient computation. We show that combining these techniques addresses memory and runtime challenges associated with long simulations required by design load cases. Specifically, the most effective combination reduces derivative computation wall time by over an order of magnitude compared to finite differencing while maintaining superior accuracy. We demonstrate this approach in a proof-of-concept aero-structural optimization of a wind turbine blade that improves the cost of energy by 12.78 %. This comparative study establishes a viable approach for fatigue-aware blade design that balances computational efficiency with modeling accuracy.

17 WIND ENERGY↗

DOE OSTI2023

Developing an AI-Powered Zero-Trust Cybersecurity Framework for Malware Prevention in Nuclear Power Plants

This study presents the development of an AI-powered Zero-Trust cybersecurity framework for malware prevention in nuclear power plants. The framework aims to enhance the security of critical systems within nuclear power plants by adopting the principles of Zero-Trust and leveraging artificial intelligence (AI) technologies. By assuming no implicit trust in any user or device and continuously authenticating and authorizing access, the framework ensures a robust defense against malware attacks. The integration of AI allows for the detection and prevention of malware through behavioral analytics, endpoint protection, network segmentation, and continuous monitoring. The paper discusses the key considerations, steps, and technologies involved in developing this framework, emphasizing the importance of regular updates, training, compliance, and auditing. The proposed framework serves as a comprehensive approach to safeguarding nuclear power plants from sophisticated malware threats and protecting the integrity and safety of critical infrastructure.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Verification of a fully implicit particle-in-cell method for the  v ∥ -formalism of electromagnetic gyrokinetics in the XGC code

A fully implicit particle-in-cell method for handling the v ∥ -formalism of electromagnetic gyrokinetics has been implemented in XGC. By choosing the v ∥ -formalism, here we avoid introducing the nonphysical skin terms in Ampère's law, which are responsible for the well-known “cancellation problem” in the p ∥ -formalism. The v ∥ -formalism, however, is known to suffer from a numerical instability when explicit time integration schemes are used due to the appearance of a time derivative in the particle equations of motion from the inductive component of the electric field. Here, using the conventional δf scheme, we demonstrate that our implicitly discretized algorithm can provide numerically stable simulation results with accurate dispersive properties. We verify the algorithm using a test case for shear Alfvén wave propagation in addition to a case demonstrating the ion temperature gradient-kinetic ballooning mode (ITG-KBM) transition. The ITG-KBM transition case is compared to results obtained from other δf gyrokinetic codes/schemes, whose verification has already been archived in the literature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks

Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges since these systems enable ever-increasing size and complexity. In recent years, there has been renewed interest in developing multirate methods as a means to handle the large range of time scales, as these methods may afford greater accuracy and efficiency than more traditional approaches of using implicit-explicit (IMEX) and low-order operator splitting schemes. However, to date there have been few performance studies that compare different classes of multirate integrators on complex application problems. In this work, we study the performance of several newly developed multirate infinitesimal (MRI) methods, implemented in the SUNDIALS solver package, on two reacting flow model problems built on structured mesh frameworks. The first model revisits prior work on a compressible reacting flow problem with complex chemistry that is implemented using BoxLib but where we now include comparisons between a new explicit MRI scheme with the multirate spectral deferred correction (SDC) methods in the original paper. The second problem uses the same complex chemistry as the first problem, combined with a simplified flow model, but runs at a large spatial scale where explicit methods become infeasible due to stability constraints. Two recently developed IMEX MRI multirate methods are tested. These methods rely on advanced features of the AMReX framework on which the model is built, such as multilevel grids and multilevel preconditioners. The results from these two problems show that MRI multirate methods can offer significant performance benefits on complex multiphysics application problems and that these methods may be combined with advanced spatial discretization to compound the advantages of both.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

An assessment of the utility of multirate time integration for the modeling of laser powder bed fusion

Finite element simulation of the laser powder bed fusion process is made challenging by the inherently multiscale nature of the process. When using the typical global time stepping techniques, slowly-evolving regions of the domain receive the same numerical treatment as the regions with the highest temperature rates. The current work details the implementation and evaluation of an implicit multirate method which is able to advance different regions of the domain with distinct time steps, depending on their current solution rate. Previous work indicates that this representation of the temporal scales of the problem can lead to significant reductions in wall clock run time, and it is shown herein that multirate time integration, when used with a uniform process-scale mesh, can result in speedups of approximately 19, 42, and 87 times, for domains with edge lengths of approximately 1 mm, 2 mm, and 5 mm, respectively. When used in conjunction with $\ h$-refinement (limited to two levels of refinement), the resulting speedups (taken relative to the uniform mesh) are around 28, 85, and 665 times. The method is demonstrated to converge as indicated by the literature, and its use with an AM-Bench domain is demonstrated.

42 ENGINEERING↗

DOE OSTI2022

Data-driven linear time advance operators for the acceleration of plasma physics simulation

In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

(U) A Theoretical Study of Asay Foil Trajectories (V.02)

We consider the trajectory of a generic Asay foil ejecta momentum diagnostic sensor, for scenarios where ejecta are produced at a planar surface and fly ballistically through a perfect vacuum to the sensor. To do so, we build upon a previously established mathematical formalism derived for the analytic study of stationary sensors (i.e., piezopins). First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source areal mass function (“source model”). This defines an integro-differential equation (IDE) for the foil trajectory. When ejecta production is instantaneous - as is generally assumed in momentum diagnostic data analyses - the IDE leads to an implicit and easily calculable closed-form solution for the foil trajectory in a perfect system, as long as the ejecta particle velocity distribution is twice-integrable. General properties of the instant-production trajectory solution indicate the existence of a boundary condition the particle velocity distribution must satisfy in order for the analytically predicted foil trajectories to be compatible with certain features commonly observed in foil data. This boundary condition is identical to one derived previously from a consideration of piezopin data. Armed with the analytic solution for instant production, we also consider various techniques used to extract time-dependent cumulative ejecta masses from foil trajectories, and derive an expression for the error imposed by using an approximated equation of motion. This analytic trajectory solution furthermore makes it possible to examine the common practice of presenting inferred cumulative ejecta masses as a function of a normalized implied velocity; we derive conditions under which this methodology is and is not meaningful. We also propose a strategy for extending the instant-production trajectory solution to time-dependent source functions.

42 ENGINEERING↗

DOE OSTI2020

Capabilities of multivariate Bayesian inference toward seismic hazard assessment

Multivariate Bayesian analysis can bring significant benefits to seismic hazard analysis: Its multivariate feature enables computing scalar and vector hazard without making any approximations; Correlations between intensity measures are implicitly modeled, permitting direct simulation of ground motion selection tools such as the conditional mean spectrum and the generalized conditioning intensity measure; and Its updating feature enables a seamless integration of new ground motion data into the hazard results. Here, we first develop a multivariate Bayesian ground motion model through the NGA-West2 database. The model functional form considers fault-type, magnitude, and distance dependencies, and also the linear and the rock intensity dependent site response. We use a hybrid Markov Chain Monte Carlo sampling to perform Bayesian inference consisting of Gibbs step and a multilevel Metropolis-Hastings step. We then perform several checks on the model and note that its performance is satisfactory. Finally, we illustrate the merits of this multivariate Bayesian analysis, which include: ground motion model updating with ground motion data recorded in the last four years not part of the NGA-West2 database; computation of scalar and vector seismic hazard using the un-updated and updated ground motion models for Los Angeles, CA; and simulation of the conditional mean spectrum under scalar and vector IM conditioning while accounting for different sources of aleatoric and epistemic uncertainties.

58 GEOSCIENCES↗

DOE OSTI2019

The Bloch equation for spin dynamics in electron storage rings: Computational and theoretical aspects

In this paper, we describe our work on spin polarization in high-energy electron storage rings which we base on the Full Bloch equation (FBE) for the polarization density and which aims towards the [Formula: see text] option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The FBE takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov–Ternov effect with its Baier–Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev–Kondratenko formulas. For our numerical and analytical studies of the FBE, we develop an approximation to the latter to obtain an effective FBE. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations (SDEs) underlying the FBE and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective FBE. This discretizes the phase space using spectral methods and discretizes time via the additive Runge–Kutta (ARK) method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.

Physics↗

DOE OSTI2024

Simulation of Multiphase Flow and Poromechanical Effects Around Injection Wells in CO 2 Storage Sites

In geological CO 2 storage operations, wellbore deformations and leakage pathways formations can occur around injection and abandoned wells subjected to high rates and long-term CO 2 injection. To guide engineering design and prevent CO 2 leakage risks, a full understanding of the underlying physics and robust numerical models is necessary to evaluate the response of underground formations in the near wellbore region and in the reservoir. In this study, a multi-scale and multi-physics open-source simulator (GEOS) is used to simulate multiphase flow and poromechanical deformations over time in three dimensions. The governing equations for mechanical deformations of the rock body and multiphase compositional fluid flow within the rock matrix are solved with a fully coupled finite element and finite volume approach. The Drucker–Prager model with friction hardening is applied to simulate elastoplastic deformation and a multiphase fluid model with power-law correlations for relative permeability is used to model the migration of CO 2 plume, which are coupled with numerical implicit scheme. Simulation results are verified against multiple analytical solutions for multiphase flow and wellbore problems, thus demonstrating the accuracy of this advanced simulator. In two engineering applications, here we highlight the impact of elastoplastic deformation and coupled modeling for assessing induced displacements and stress perturbations, which are more pronounced in the near wellbore regions. This work focuses on short-term processes in the vicinity of injection wells where stress evolutions, rock deformations and multiphase compositional flow and transport are simulated jointly to ensure wellbore stability and prevent damage. This fully coupled geomechanical model can simulate multiphase flow and any associated poromechanical effects within the CO 2 storage site and in the surrounding formations. Such a large-scale, long-term, multi-physics simulation model is useful in many ways: it can guide operational decisions for CO 2 injection, assess the containment potential and risks of a site, and analyze the wellbore stability and integrity during and after CO 2 injection.

58 GEOSCIENCES↗

DOE OSTI2022

The role of surface forces in environment-enhanced cracking of brittle solids

Fracture initiation and propagation in brittle materials is promoted in surface-reactive (sorptive) environments, a phenomenon known as subcritical crack growth (SCG). Laboratory measured crack-propagation velocity vs. stress intensity factor relationships typically exhibit highly nonlinear, multi-stage characteristics that are sensitive to environmental factors such as adsorbate concentration and temperature. For practical purposes, empirical relationships (e.g., a power law) have been used to describe this complex phenomenon. However, how the overall SCG behavior emerges from the underlying fundamental processes near the crack tip, such as the interaction of the crack surfaces separated by only a few nanometers and mass transport within the nano-confined space, is still not well understood. This paper develops a mechanistic, surface-force-based fracture theory (SFFT) which integrates surface force models, fluid transport models, and linear elastic fracture mechanics to quantitatively explain the multi-stage characteristics of SCG in brittle solids. A numerical model is developed based on SFFT and solved through an implicit partitioned scheme for efficiency and modularity. The results are validated by Wiederhorn's data on crack propagation in soda-lime glasses at a wide range of relative humidity levels. We show that, for the first time, the entire range of an SCG curve can be captured by a single physics-based model. The predicted SCG curves reveal that the development of repulsive disjoining pressure behind the crack tip can be responsible for the reduced apparent fracture toughness in a sorptive environment. In conclusion, the shape of the SCG curve, and its changes with respect to the environment, is found to critically depend on the assumed transport models.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Correction to “Ruthenium Dye Excitations and Relaxations in Natural Sunlight”

An error in computing the optical rate coefficients for dye RuP was discovered in Table S4 of the Supporting Information Section S8 Model S? for this article, published in J. Phys. Chem. A, 2021, 125, 4365-4372, 10.1021/acs.jpca.1c02386. The optical rate coefficients include absorption, stimulated emission, and ground-state bleach associated with the ground state and the singlet and triplet excited states as well as for the excited-state absorption between the excited states and implicit higher-energy excited states. The optical rate coefficients for continuous solar irradiance were computed using eq 3 of the main text in which the product of the individual signal components and the solar spectrum are integrated and multiplied by the fundamental optical rate coefficient. We determined the incorrect signal components were used for RuP in the published Supporting Information Table S4. The corrected Table S4 column for RuP is presented with the reported values from the original paper in the corrected Supporting Information. New simulations have been performed using the corrected values, and the results were used to update Figures 5 and 6 and also Figure S9 in the corrected Supporting Information. The published conclusions are unchanged. The populations of RuP excited states, Figure 5, are only marginally smaller, which should be expected with minor changes to the optical rate coefficients. There is not a significant change in the results for the number of radiative and nonradiative interactions per dye per second (the optical transitions and nonradiative transitions increased, respectively, by approximately 2% and 10%, Figure 6A). The occurrence of excited-state absorption (ESA) and excited-state emission (ESE) events, Figure 6C, both decreased from the original simulation results by 20% and 33%. The most notable difference is exhibited in Figure 6B; the fraction of population moving from the lowest-energy singlet state (i.e., intersystem crossing or ultrafast nonradiative relaxation) and nonradiative relaxation from the triplet state have decreased from ~0.45 to ~0.4 and increased from ~0.35 to ~0.4, respectively..

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Improving the Performance of NEML2 with Modern Graph Compilation Backends

NEML2 vectorizes constitutive-model evaluation for large-scale multiphysics simulation, using PyTorch as its tensor backend so that a batch of material-point updates runs on CPU or GPU through a single implementation. In the two prior reports in this series it was a C++-native library, deployed through TorchScript tracing and just-in-time (JIT) compilation; it has since been rewritten from the ground up into a Python-native library deployed through Ahead-of-Time Inductor (AOTInductor), a modern PyTorch graph-compilation backend. The rewrite is driven by a persistent tension, not a language preference: NEML2 composes constitutive models at runtime from a registry of small, independently-authored pieces, and that flexibility is difficult to reconcile with the compile-time knowledge an efficient GPU kernel needs. This report documents the rewrite and the investment that accompanied it: the AOTInductor export pipeline that turns a Python-authored model into a portable, Python-free compiled artifact loadable from pure C++; the eager and compiled runtimes and the new implicit solver layer built on them; a head-to-head benchmark of legacy JIT against AOTInductor; the physics-model catalog and its worked examples; the developer tooling; and the corresponding overhaul of MOOSE’s NEML2 integration that lets MOOSE consume it. A central objective is to examine whether modern PyTorch graph-compilation backends are effective for MOOSE GPU integration. The benchmark answers directly: AOTInductor outperforms legacy JIT on every GPU scenario measured, by 1.0–4.5×. Modern graph-compilation backends are effective for MOOSE GPU integration, and AOTInductor specifically – not compilation in the abstract – is why.

Hu, Gary (Tianchen) [Argonne National Laboratory (↗

DOE OSTI2020

RELAP-7 Application and Enhancement for FLEX Strategies and ATF Behavior under Extended Loss of AC Power Conditions

This report summarizes the results of a three-year research project sponsored by the U.S. Department of Energy (DOE) Nuclear Energy University Program (NEUP) to enhance and apply the RELAP-7 code by adding and improving several important components (e.g., a mechanistic Reactor Core Isolation Cooling (RCIC) system model) for thermal hydraulic studies of LWRs under ELAP conditions and evaluating the time available for transition to portable FLEX equipment. The project team included University of Massachusetts–Lowell, The Ohio State University, Texas A&M University, Idaho National Laboratory and Oak Ridge National Laboratory. In the Fukushima accident, it was found that the RCIC system played a crucial role in delaying core meltdown by almost three days in Fukushima Daiichi Unit 2, because of self-regulated operation of the steam driven RCIC turbine-pump injection system. Steam flow in the convergent-divergent nozzles of the RCIC Terry turbine is two-phase non-equilibrium transonic flow with homogenous nucleation condensation. To more accurately predict the dynamic process and behavior of the transonic compressible steam flow, a one-dimensional transient two-phase analytical model is presented. A simplified four-fluid model was employed in the present work with the consideration of four separate fluid fields: vapor, liquid film, entrained droplets and condensed droplets. The mass, momentum and energy interactions between the fluids were considered and modeled. An extended seven-equation non-equilibrium critical flow model was developed to obtain the critical pressure and velocities of each phase at the nozzle throat. To predict the wetness in the divergent section, a mechanistic nucleation condensation model was integrated in the nozzle analysis model, considering the generation and consequent growth of droplets. The governing differential equations on a staggered grid were discretized using the second-order Lax-Wendroff scheme with a flux limiter, and the Semi-Implicit Method for Pressure-Linked Equation (SIMPLE) algorithm was employed to solve the discrete linear system. To demonstrate the predictability and reliability of the physical models and the numerical method proposed in the present work, three representative nozzles were modeled and simulated. The results show good agreement with the available experimental data, even for condensation shock. Then, the 1D nozzle model was employed to obtain nozzle flow tables of the Terry turbine nozzle for different working pressures which can cover the operation pressure range of the RCIC system. A mechanistic RCIC turbine-pump system model was developed and implemented in the system code TRACE to simulate dynamic responses of the RCIC system under Beyond Design Basis Accident (BDBA) conditions. The turbine-pump governing equations are based on the control volume approach of the angular momentum balance. The physics based mechanistic RCIC model was developed using the TRACE control system components (i.e., signal variables, control blocks, and tables), and incorporated into a TRACE boiling water reactor (BWR) model. The TRACE model in this report has a detailed nodalization of the reactor pressure vessel (RPV), and all of the major flow paths and system components, including the safety relief valves (SRVs) and the containment suppression pool and drywell. Based on the nozzle flow tables generated from the 1D nozzle model developed, the turbine drive torque can be calculated from table lookup. Since the detailed specifications of the RCIC pump are unavailable, the homologous curves for a Bingham pump were used in the current pump component. A station black-out (SBO) accident test problem was selected to demonstrate the TRACE RCIC model. The short-term SBO simulations were performed for two cladding materials: Zircaloy and FeCrAl, to demonstrate the effect of the accident tolerant fuel cladding on fuel heat-up under BDBA accident conditions. The wetwell plays a vital safety role in SBO and other BWR accident scenarios in that it can reduce containment pressure and supply additional core make-up water. The suppression pool temperature distribution has a very large impact on both RPV and containment pressure. Thus, another novel contribution of the project comes mainly from an improved, systems-level wetwell model which can capture buoyancy-induced thermal stratification effects due to steam injection and condensation. A two-zone stratified wetwell model has been implemented in RELAP-7 and some results from that model are presented. This wetwell model is capable of simulating thermal stratification due to a low steam mass injection rate. With a low mass flow rate, the model assumes that all the steam condenses within the pipe and the resulting plume can be approximated with a purely buoyant, heat-source driven model. The wetwell model developed with these assumptions is adequate to simulate slow transients such as extended SBO transients.

42 ENGINEERING↗

DOE OSTI2021

Impact of Integration Scheme on Performance of Anisotropic Plasticity Models

Given the prevalent role of metals in a variety of industries, schemes to integrate corresponding constitutive models in finite element applications have long been studied. A number of formulations have been developed to accomplish this task; each with their own advantages and costs. Often the focus has been on ensuring the accuracy and numerical stability of these algorithms to enable robust integration. While important, emphasis on these performance metrics may often come at the cost of computational expense potentially neglecting the needs of individual problems. In the current work, the performance of two of the most common integration methods for anisotropic plasticity -- the convex cutting plane (CCP) and closest point projection (CPP) -- across a variety of metrics is assessed; including accuracy and cost. A variety of problems are considered ranging from single elements to large representative simulations including both implicit quasistatic and explicit transient dynamic type responses. The relative performance of each scheme in the different instances is presented with an eye towards guidance on when the different algorithms may be beneficial.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Error Estimates for the Optimal Control of a Parabolic Fractional PDE

In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Deep learning approaches for instantaneous laser absorptance prediction in additive manufacturing

Abstract The quantification of absorbed light is essential for understanding laser-material interactions and melt pool dynamics in order to minimize defects in additively manufactured metal components. The geometry of a vapor depression formed during laser melting is closely related to laser energy absorption. This relationship has been observed by the state-of-the-art in situ high-speed synchrotron X-ray visualization and integrating sphere radiometry. These two techniques create a temporally resolved dataset consisting of vapor depression images and corresponding laser absorptance. In this work, we propose two different approaches to predict instantaneous laser absorptance. The end-to-end approach uses deep convolutional neural networks to learn implicit features of X-ray images automatically and predict the laser energy absorptance. The two-stage approach uses a semantic segmentation model to engineer geometric features and predict absorptance using classical regression models. While having distinct advantages, both approaches achieved a consistently low mean absolute error of less than 3.3%.

Chemistry↗