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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Numerical design considerations for vapor transport deposition of metal-halide perovskite thin films

While metal-halide perovskites (MHPs) offer high efficiency and potential application in single junction and tandem solar cells, challenges remain in translating solution-based methods to commercial-scale production. Vapor transport deposition (VTD) offers advantages such as precise control over film composition and purity, as well as the possibility of achieving high thin film deposition rates for scale-up. In this work, a numerical model is developed to simulate the deposition process, analyzing the impact of parameters including source material temperature, carrier gas and dilution gas flow rates, and chamber pressure to optimize deposition rates and film uniformity. Geometrical parameters, such as throw distance, are also found to significantly affect rate and uniformity. Furthermore, the modeling results presented here offer valuable insight for improving the scalability of VTD for the processing of metal-halide perovskites.

Chemical vapor deposition↗
DOE OSTI2025

Solid solutions limited by grain-boundary solute clustering in ultrafine-grained alloys

Immiscible Ag-Cu alloys exhibit complex behavior due to varying Cu solid solubilities reported under equilibrium and metastable conditions. In ultrafine-grained alloys, these limits are further complicated by a high fraction of grain boundaries, where solute atoms tend to segregate and, in some cases, form clusters. Here, this study investigates the influence of Cu solute segregation and clustering on solid-solution limits in ultrafine-grained Ag-Cu alloys synthesized by magnetron sputtering with varying Cu content. X-ray diffraction peak shifts reveal a solid-solution concentration plateau for Cu contents from 4.9 to 11.7 at %, in contrast to the peak shifts predicted by density-functional theory for Ag-Cu alloys. Scanning transmission electron microscopy further reveals limited solid solubility and the formation of numerous Cu-rich clusters at grain boundaries. Atomistic simulations demonstrate that such limited solubility does not arise from grain boundary segregation alone, but only when strong solute-solute interactions promote the formation of grain-boundary Cu solute clusters.

Density-functional theory↗
DOE OSTI2023

HydroChrono: An Open-Source Hydrodynamics Package for Project Chrono

In this paper we present the development and verification of HydroChrono, a hydrodynamics package for the Project Chrono physics engine. This package includes the implementation of hydrodynamics equations, the added mass for multibody systems, the development of I/O functions as well as a Python API, and comparison against standard reference cases and other existing tools. HydroChrono provides a flexible, fully open-source solution for simulating wave energy converters (WECs), floating offshore wind turbines (FOWTs) platforms, and other hydrodynamic systems. Here we show, via comparisons with existing tools for benchmark verification cases, that HydroChrono accurately models hydrodynamic forces - making it a useful tool for the design and optimization of these systems. Additionally, the integration of HydroChrono with Project Chrono offers access to finite element modeling capabilities and high-fidelity modelling - with Chrono's existing coupling to CFD and SPH codes. This provides numerical modelers with a multifidelity simulation framework for designing and validating these systems. The development of HydroChrono provides a new, open-source solution for simulating hydrodynamic systems. Its compatibility with other simulation tools enables a more streamlined and efficient design process, advancing the field and providing new opportunities for innovation in this area.

BEM↗
DOE OSTI2021

A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries

Herein, we present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodology supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Remote quantification of Cm(III) and HNO 3 by fluorescence spectroscopy and chemometrics

A unique approach to remotely quantify Cm(III) (0–100 µg mL −1 ) in HNO 3 (1–12 M) using steady-state laser fluorescence spectroscopy and multivariate regression models was developed. Photoluminescence is amenable to remote measurements using fiber-optic cables and is sensitive to numerous lanthanide and actinide species. In-line measurements can provide feedback to support complex processing in harsh environments (e.g., hot cells) to help guide and optimize radiochemical separations. In this work, Cm(III) spectra were acquired remotely in a glove box as a function of HNO 3 concentration to better understand spectral characteristics and evaluate the utility of multivariate regression models in this system. Furthermore, the Cm(III) fluorescence peak shape, width, position, and intensity changed significantly as a function of HNO 3 concentration, likely because of the displacement of emission quenching inner-sphere water molecules and complexation with nitrate ions. Despite significant covariance and nonlinearity in the data, a D-optimal design strategy successfully minimized training set sample size and was used to build effective partial least squares regression models for Cm(III) and HNO 3 concentrations without a priori knowledge of solution conditions. Chemometrics for modeling complex fluorescence spectra are promising and may find widespread applicability for online analysis in numerous chemical systems found in the nuclear field.

Actinide↗
DOE OSTI2021

A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physics-informed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LS-ROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers' equations. A speedup of up to 2.6 for 1D Burgers' and a speedup of 11.7 for 2D Burgers' equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Lastly, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Machine learning-enhanced model-based scenario optimization for DIII-D

Abstract Scenario development in tokamaks is an open area of investigation that can be approached in a variety of different ways. Experimental trial and error has been the traditional method, but this required a massive amount of experimental time and resources. As high fidelity predictive models have become available, offline development and testing of proposed scenarios has become an option to reduce the required experimental resources. The use of predictive models also offers the possibility of using a numerical optimization process to find the controllable inputs that most closely achieve the desired plasma state. However, this type of optimization can require as many as hundreds or thousands of predictive simulation cases to converge to a solution; many of the commonly used high fidelity models have high computational burdens, so it is only reasonable to run a handful of predictive simulations. In order to make use of numerical optimization approaches, a compromise needs to be found between model fidelity and computational burden. This compromise can be achieved using neural networks surrogates of high fidelity models that retain nearly the same level of accuracy as the models they are trained to replicate while reducing the computation time by orders of magnitude. In this work, a model-based numerical optimization tool for scenario development is described. The predictive model used by the optimizer includes neural network surrogate models integrated into the fast Control-Oriented Transport simulation framework. This optimization scheme is able to converge to the optimal values of the controllable inputs that produce the target plasma scenario by running thousands of predictive simulations in under an hour without sacrificing too much prediction accuracy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Interpreting strain tensor data to characterize and monitor reservoirs for CO2 storage and other applications

Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and this has opened the door to new opportunities for characterization and monitoring. We have deployed strainmeters and then conducted injection well tests in an underlying reservoir at 530m depth. The resulting data indicated that the horizontal strain at shallow strainmeters (30 to 40m depth) was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 n/d over a few days. The signal at two strainmeters at shallow depth were consistent, although the magnitude of the horizontal strains were different reflecting the different radial directions from the well. The signal at a deep strainmeter deployed at reservoir depth was much different, with tensile vertical strains and compressive horizontal strains. These data can be interpreted by inverting poroelastic forward models developed using numerical and analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. This model is fast and can be inverted to estimate reservoir stiffness and geometry. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. The proxy model is periodically updated and refined using the finite element model to ensure accuracy. This approach significantly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. We have shown that the strain tensor in the caprock is sensitive to pressure in the reservoir, boundaries in the reservoir, and pressure in the caprock caused by leaks. These results indicate that coupling strain tensor data with inversion has the potential to help evaluate reservoirs during initial characterization, and to monitor them during the CO2 injection and storage process.

Murdoch, Larry↗
DOE OSTI2024

Quadrature Based Neural Network Learning of Stochastic Hamiltonian Systems

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadrature-based models according to the integral form of the SHSs’ solutions, where we denoise the loss-by-moment calculations of the solutions. The integral pattern of the models transforms the source of the essential learning error from the discrepancy between the modified Hamiltonian and the true Hamiltonian in the classical HNN models into that between the integrals and their quadrature approximations. This transforms the challenging task of deriving the relation between the modified and the true Hamiltonians from the (stochastic) Hamilton–Jacobi PDEs, into the one that only requires invoking results from the numerical quadrature theory. Meanwhile, denoising via moments calculations gives a simpler data fitting method than, e.g., via probability density fitting, which may imply better generalization ability in certain circumstances. Numerical experiments validate the proposed learning strategy on several concrete Hamiltonian systems. The experimental results show that both the learned Hamiltonian function and the predicted solution of our quadrature-based model are more accurate than that of the corrected symplectic HNN method on a harmonic oscillator, and the three-point Gaussian quadrature-based model produces higher accuracy in long-time prediction than the Kramers–Moyal method and the numerics-informed likelihood method on the stochastic Kubo oscillator as well as other two stochastic systems with non-polynomial Hamiltonian functions. Moreover, the Hamiltonian learning error εH arising from the Gaussian quadrature-based model is lower than that from Simpson’s quadrature-based model. These demonstrate the superiority of our approach in learning accuracy and long-time prediction ability compared to certain existing methods and exhibit its potential to improve learning accuracy via applying precise quadrature formulae.

Mathematics↗
DOE OSTI2021

A new procedure for implementing the modified inherent strain method with improved accuracy in predicting both residual stress and deformation for laser powder bed fusion

As a metal additive manufacturing (AM) process, laser powder bed fusion (L-PBF) has been widely used to produce parts with complex geometries. The large thermal gradient caused by the fast, intense, and repeated laser scanning induces significant residual deformation and stress to the as-built parts, which increase manufacturing difficulty and geometrical inaccuracy as a result. The modified inherent strain (MIS) method exploiting multiscale process simulations was developed to simulate residual deformation accurately and efficiently. However, the existing procedure of implementing the MIS method is found to give inaccurate residual stress prediction. Here in this work, a new implementation procedure for the MIS method is proposed to improve the simulation accuracy of residual stress without degrading the residual deformation prediction. The new procedure concerns the application of inherent strains to the part-scale layer-by-layer finite element model to obtain residual stress and deformation field. While the existing implementation of the part-scale MIS model involves only mechanical properties at ambient temperature, the new procedure adds one more solution step employing mechanical properties at an elevated temperature determined from the inherent strain extraction step. Both numerical and experimental studies are conducted to validate the proposed new implementation procedure. It shows that by using the new procedure, the MIS-based simulation can predict both residual stress and deformation of as-built L-PBF metal parts with good accuracy.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference↗
DOE OSTI2023

The DESC stellarator code suite Part 3: Quasi-symmetry optimization

The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to automatic differentiation, which efficiently provides exact derivative information. A Gauss–Newton trust-region optimization method uses second-order derivative information to take large steps in parameter space and converges rapidly. With just-in-time compilation and GPU portability, high-dimensional stellarator optimization runs take orders of magnitude less computation time with DESC compared to other approaches. This paper presents the theory of the DESC fixed-boundary local optimization algorithm along with demonstrations of how to easily implement it in the code. Example quasi-symmetry optimizations are shown and compared to results from conventional tools. Three different forms of quasi-symmetry objectives are available in DESC, and their relative advantages are discussed in detail. In the examples presented, the triple product formulation yields the best optimization results in terms of minimized computation time and particle transport. This paper concludes with an explanation of how the modular code suite can be extended to accommodate other types of optimization problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Infinite neural network quantum states: entanglement and training dynamics

We study infinite limits of neural network quantum states (∞-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of entanglement entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. The analytic calculations of entanglement entropy bound are tractable because the ensemble statistics are simplified in the Gaussian process limit. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For ∞-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an ∞-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. ∞-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.

quantum state supervised learning↗
DOE OSTI2021

Freedom of the mixer rotation axis improves performance in the quantum approximate optimization algorithm

Variational quantum algorithms such as the quantum approximate optimization algorithm (QAOA) are particularly attractive candidates for implementation on near-term quantum processors. As hardware realities such as error and qubit connectivity will constrain achievable circuit depth in the near future, new ways to achieve high performance at low depth are of great interest. In this work, we present a modification to QAOA that adds additional variational parameters in the form of freedom of the rotation axis in the XY plane of the mixer Hamiltonian. Here, via numerical simulation, we show that this leads to a drastic performance improvement over standard QAOA at finding solutions to the MaxCut problem on graphs of up to seven qubits. Furthermore, we explore the Z-phase error mitigation properties of our modified Ansatz, its performance under a realistic error model for a neutral atom quantum processor, and the class of problems it can solve in a single round.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic Programming

In this report, we study the sensitivity of discrete-time dynamic programs with nonlinear dynamics and objective to perturbations in the initial conditions and reference parameters. Under uniform controllability and boundedness assumptions for the problem data, we prove that the directional derivative of the optimal state and control at time $k$, $x^*_k$, and $u^*_k$, with respect to the reference signal at time $i$, $d_i$, will have exponential decay in terms of $|k-i|$ with a decay rate $\rho$ independent of the temporal horizon length. The key technical step is to prove that a version of the convexification approach proposed by Verschueren et al. can be applied to the KKT conditions and results in a convex quadratic program with uniformly bounded data. In turn, Riccati techniques can be further employed to obtain the sensitivity result, borne from the observation that the directional derivatives are solutions of quadratic programs with structure similar to the KKT conditions themselves. We validate our findings with numerical experiments on a small nonlinear, nonconvex, dynamic program.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Learning Optimal Multigrid Smoothers via Neural Networks

Multigrid methods are one of the most efficient techniques for solving large sparse linear systems arising from partial differential equations (PDEs) and graph Laplacians from machine learning applications. One of the key components of multigrid is smoothing, which aims at reducing high-frequency errors on each grid level. However, finding optimal smoothing algorithms is problem-dependent and can impose challenges for many problems. In this paper, we propose an efficient adaptive framework for learning optimized smoothers from operator stencils in the form of convolutional neural networks (CNNs). Here, the CNNs are trained on small-scale problems from a given type of PDEs based on a supervised loss function derived from multigrid convergence theories and can be applied to large-scale problems of the same class of PDEs. Numerical results on anisotropic rotated Laplacian problems and variable coefficient diffusion problems demonstrate improved convergence rates and solution time compared with classical hand-crafted relaxation methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Nonlinear manifold-based reduced order model

Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov n-width. However, for physical phenomena not of this type, e.g., any advection-dominated flow phenomena such as in traffic flow, atmospheric flows, and air flow over vehicles, a low-dimensional linear subspace poorly approximates the solution. To address cases such as these, we have developed a fast and accurate physicsinformed neural network ROM, namely nonlinear manifold ROM (NM-ROM), which can better approximate high-fidelity model solutions with a smaller latent space dimension than the LSROMs. Our method takes advantage of the existing numerical methods that are used to solve the corresponding full order models. The efficiency is achieved by developing a hyper-reduction technique in the context of the NM-ROM. Numerical results show that neural networks can learn a more efficient latent space representation on advection-dominated data from 1D and 2D Burgers’ equations. A speedup of up to 2.6 for 1D Burgers’ and a speedup of 11.7 for 2D Burgers’ equations are achieved with an appropriate treatment of the nonlinear terms through a hyper-reduction technique. Finally, a posteriori error bounds for the NM-ROMs are derived that take account of the hyper-reduced operators.

97 MATHEMATICS AND COMPUTING↗