Search NASA⌕ Search

SEARCH · Search NASA

Results for “implicit method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Long-term impact of electrification and retrofits of the U.S residential building in diverse locations

The U.S. buildings sector contributes 30% of operational carbon emissions, with residential buildings accounting for 56%. Reducing residential carbon emissions is crucial for achieving net-zero carbon goal. While many studies examine energy efficiency retrofit (EER) and electrification, few explore their long-term impacts across diverse climates and dynamic grid clean energy penetrations, as well as their economic effects on households. Here, this study proposes a method to assess how EER and electrification affect long-term decarbonization and economics across different climates, focusing on carbon emissions, energy burden (the percentage of household income spent on energy), and payback period in four locations: Tampa, San Diego, Denver, and Great Falls. The study also introduces the concept of implicit energy burden by considering investment costs. Results show that while electrification can reduce long-term emissions with increased clean energy penetration, it may not always achieve decarbonization due to mismatches between clean energy availability and demand. In cooling-dominant locations, electrification lowers energy burden and peak demand, but in heating-dominant locations, it increases energy burden to 8.24%, raises peak demand by 632.78%, and shifts it from summer to winter. After integrating investment costs, the implicit energy burden can reach 8.35% in cold climates. For already highly electrified buildings in Denver and Great Falls, the payback period of EER measures can be shortened by up to 48.98%. The study highlights a tradeoff between decarbonization and energy burden alleviation, showing that while EER measures can reduce the energy burden, they only achieve one-quarter of the carbon emission reduction of electrification.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗
DOE OSTI2016

Technical Note: Impact of the geometry dependence of the ion chamber detector response function on a convolution-based method to address the volume averaging effect

Purpose: To investigate the geometry dependence of the detector response function (DRF) of three commonly used scanning ionization chambers and its impact on a convolution-based method to address the volume averaging effect (VAE). Methods: A convolution-based approach has been proposed recently to address the ionization chamber VAE. It simulates the VAE in the treatment planning system (TPS) by iteratively convolving the calculated beam profiles with the DRF while optimizing the beam model. Since the convolved and the measured profiles are subject to the same VAE, the calculated profiles match the implicit “real” ones when the optimization converges. Three DRFs (Gaussian, Lorentzian, and parabolic function) were used for three ionization chambers (CC04, CC13, and SNC125c) in this study. Geometry dependent/independent DRFs were obtained by minimizing the difference between the ionization chamber-measured profiles and the diode-measured profiles convolved with the DRFs. These DRFs were used to obtain eighteen beam models for a commercial TPS. Accuracy of the beam models were evaluated by assessing the 20%–80% penumbra width difference (PWD) between the computed and diode-measured beam profiles. Results: The convolution-based approach was found to be effective for all three ionization chambers with significant improvement for all beam models. Up to 17% geometry dependence of the three DRFs was observed for the studied ionization chambers. With geometry dependent DRFs, the PWD was within 0.80 mm for the parabolic function and CC04 combination and within 0.50 mm for other combinations; with geometry independent DRFs, the PWD was within 1.00 mm for all cases. When using the Gaussian function as the DRF, accounting for geometry dependence led to marginal improvement (PWD < 0.20 mm) for CC04; the improvement ranged from 0.38 to 0.65 mm for CC13; for SNC125c, the improvement was slightly above 0.50 mm. Conclusions: Although all three DRFs were found adequate to represent the response of the studied ionization chambers, the Gaussian function was favored due to its superior overall performance. The geometry dependence of the DRFs can be significant for clinical applications involving small fields such as stereotactic radiotherapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Pressure-stabilized fixed-stress iterative solutions of compositional poromechanics

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the discrete saddle point matrix never appears in the fixed-stress approach. This observation reconciles previous results regarding the pressure stability of the splitting method. Using examples of compositional poromechanics with application to geological CO sequestration, we see that solutions obtained using the fixed-stress scheme with a low order finite element-finite volume discretization which is not inherently inf-sup stable can exhibit the same pressure oscillations obtained with the corresponding fully implicit scheme. Moreover, pressure jump stabilization can effectively remove these spurious oscillations in the fixed-stress setting, while also improving the efficiency of the scheme in terms of the number of iterations required at every time step to reach convergence.

42 ENGINEERING↗
DOE OSTI2026

REV-INR: Regularized Evidential Implicit Neural Representation for Uncertainty-Aware Volume Visualization

Applications of Implicit Neural Representations (INRs) have emerged as a promising deep learning approach for compactly representing large volumetric datasets. These models can act as surrogates for volume data, enabling efficient storage and on-demand reconstruction via model predictions. However, conventional deterministic INRs only provide value predictions without insights into the model’s prediction uncertainty or the impact of inherent noisiness in the data. This limitation can lead to unreliable data interpretation and visualization due to prediction inaccuracies in the reconstructed volume. Identifying erroneous results extracted from model-predicted data may be infeasible, as raw data may be unavailable due to its large size. To address this challenge, we introduce REV-INR, Regularized Evidential Implicit Neural Representation, which learns to predict data values accurately along with the associated coordinate-level data uncertainty and model uncertainty using only a single forward pass of the trained REV-INR during inference. By comprehensively comparing and contrasting REV-INR with existing well-established deep uncertainty estimation methods, we show that REV-INR achieves the best volume reconstruction quality with robust data (aleatoric) and model (epistemic) uncertainty estimates using the fastest inference time. Consequently, we demonstrate that REV-INR facilitates assessment of the reliability and trustworthiness of the extracted isosurfaces and volume visualization results, enabling analyses to be solely driven by model-predicted data.

Saklani, Shanu [Indian Institute of Technology, Ka↗
DOE OSTI2016

A comparison of three approaches to compute the effective Reynolds number of the implicit large-eddy simulations

Here, the implicit large-eddy simulation (ILES) has been utilized as an effective approach for calculating many complex flows at high Reynolds number flows. Richtmyer–Meshkov instability (RMI) induced flow can be viewed as a homogeneous decaying turbulence (HDT) after the passage of the shock. In this article, a critical evaluation of three methods for estimating the effective Reynolds number and the effective kinematic viscosity is undertaken utilizing high-resolution ILES data. Effective Reynolds numbers based on the vorticity and dissipation rate, or the integral and inner-viscous length scales, are found to be the most self-consistent when compared to the expected phenomenology and wind tunnel experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. I. Time-like and Null Geodesics

The numerical integration of particle trajectories in curved spacetimes is fundamental for obtaining realistic models of the particle dynamics around massive compact objects such as black holes and neutron stars. Generalized algorithms capable of handling generic metrics are needed for studies of both standard (Schwarzschild and Kerr metrics) and nonstandard (e.g., Schwarzschild metric plus nonclassical perturbations or multiple black hole metrics) spacetimes. The most commonly employed explicit numerical schemes (e.g., Runge–Kutta) are incapable of producing highly accurate results at critical points, e.g., in the regions close to the event horizon where gravity causes extreme curvature of the spacetime, at an acceptable computational cost. In this work we describe a generalized algorithm for the numerical integration of time-like (massive particles) and null (photons) geodesics in any given 3 + 1 split spacetime. We introduce a new, exactly energy-conserving implicit integration scheme based on the preservation of the underlying Hamiltonian, and we compare its properties with a standard fourth-order Runge–Kutta explicit scheme and an implicit midpoint scheme. We test the numerical performance of the three schemes against analytic solutions of particle and photon orbits in Schwarzschild and Kerr spacetimes. We additionally prove the versatility of our framework in handling more exotic metrics, such as Morris–Thorne wormholes and quantum-perturbed Schwarzschild black holes. The generalized method is also discussed in the perspective of future extensions to more complex particle dynamics, e.g., the addition of the Lorentz force acting on charged particles, which allows for test particle diagnostics in GRMHD simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

NONLINEAR SOIL-STRUCTURE INTERACTION ANALYSIS USING CO-SIMULATION

Nonlinear soil-structure interaction (NLSSI) analysis methods are currently being developed at Idaho National Laboratory. Appendix B in ASCE (2016) includes a framework for performing NLSSI analysis. For NLSSI analysis to be widely implemented in industry, it is important to demonstrate that accurate response in dynamically loaded, nonlinear models can be achieved in an efficient manner. Both explicit and implicit dynamic solvers are applicable to NLSSI. When considering cpu time, an explicit dynamic solver is often desirable for large models with no features (e.g. small elements, stiff elements, or stiffness damping) that can drive the time step unreasonably small. An implicit dynamic solver may be desirable in models not well suited for an explicit solver. A further option is co-simulation where a portion of the model is run with an explicit dynamic solver and the rest of the model is run with an implicit dynamic solver. This study explores NLSSI examples where co-simulation could be the most cpu efficient modelling strategy.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

An Accelerated Clip Algorithm for Unstructured Meshes: A Batch-Driven Approach

The clip technique is a popular method for visualizing complex structures and phenomena within 3D unstructured meshes. Meshes can be clipped by specifying a scalar isovalue to produce an output unstructured mesh with its external surface as the isovalue. Similar to isocontouring, the clipping process relies on scalar data associated with the mesh points, including scalar data generated by implicit functions such as planes, boxes, and spheres, which facilitates the visualization of results interior to the grid. In this paper, we introduce a novel batch-driven parallel algorithm based on a sequential clip algorithm designed for high-quality results in partial volume extraction. Our algorithm comprises five passes, each progressively processing data to generate the resulting clipped unstructured mesh. The novelty lies in the use of fixed-size batches of points and cells, which enable rapid workload trimming and parallel processing, leading to a significantly improved memory footprint and run-time performance compared to the original version. On a 32-core CPU, the proposed batch-driven parallel algorithm demonstrates a run-time speed-up of up to 32.6x and a memory footprint reduction of up to 4.37x compared to the existing sequential algorithm. The software is currently available under an open-source license in the VTK visualization system.

Tsalikis, Spiros↗
DOE OSTI2025

Prediction of Redox Potentials for the Late Actinides Cm to Lr Using Electronic Structure Methods

Our previously developed computational method for calculating the aqueous redox potentials of the early actinides has been extended to the later elements in the actinide series: Cm, Bk, Cf, Es, Fm, Md, No, and Lr in multiple oxidation states. These calculations were performed using density functional theory with small-core pseudopotentials and their associated basis sets. Solvation effects were considered via a supermolecule-continuum approach, with 30 water molecules representing two solvation shells. Both the COSMO and SMD implicit solvation models were utilized. The structural parameters and hydration numbers for Cm(III), Bk(III), Bk(IV), and Cf(III) are in reasonable agreement with the available experimental data. For redox processes involving atomic cations in solution, the B3LYP/COSMO approach predicted redox potentials to within ±0.2 V of experiment for most redox couples, consistent with our prior work. Inclusion of spin-orbit corrections in specific redox pairs, especially those with the later actinides in high oxidation states, yields improved results relative to calculations including only scalar-relativistic corrections. The An +m /An(0) redox potentials were calculated using a Born-Haber cycle incorporating sublimation, ionization, and hydration energies. Due to a lack of experimental data, three sets of ionization energies were used for the Born-Haber cycle. The calculated An(III/0) potentials showed better agreement with experimental data when using the COSMO solvation model and the test set comprising the NIST recommended ionization energies. Furthermore, the Md(II/0) potential was better described with the SMD model, whereas No(II/0) was not well described by all methods. Finally, the computational approach was able to predict redox potentials that for most cases agreed with the current available experimental or estimated data.

Actinides↗
DOE OSTI2021

Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers

We report accurate simulations of flows in stellar interiors are crucial to improving our understanding of stellar structure and evolution. Because the typically slow flows are merely tiny perturbations on top of a close balance between gravity and the pressure gradient, such simulations place heavy demands on numerical hydrodynamics schemes. We demonstrate how discretization errors on grids of reasonable size can lead to spurious flows orders of magnitude faster than the physical flow. Well-balanced numerical schemes can deal with this problem. Three such schemes were applied in the implicit, finite-volume SEVEN-LEAGUE HYDRO code in combination with a low-Mach-number numerical flux function. We compare how the schemes perform in four numerical experiments addressing some of the challenges imposed by typical problems in stellar hydrodynamics. We find that the α-β and deviation well-balancing methods can accurately maintain hydrostatic solutions provided that gravitational potential energy is included in the total energy balance. They accurately conserve minuscule entropy fluctuations advected in an isentropic stratification, which enables the methods to reproduce the expected scaling of convective flow speed with the heating rate. The deviation method also substantially increases accuracy of maintaining stationary orbital motions in a Keplerian disk on long timescales. The Cargo–LeRoux method fares substantially worse in our tests, although its simplicity may still offer some merits in certain situations. Overall, we find the well-balanced treatment of gravity in combination with low Mach number flux functions essential to reproducing correct physical solutions to challenging stellar slow-flow problems on affordable collocated grids.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Learning Constrained Parametric Differentiable Predictive Control Policies With Guarantees

We present differentiable predictive control (DPC), a method for offline learning of constrained neural control policies for nonlinear dynamical systems with performance guarantees. We show that the sensitivities of the parametric optimal control problem can be used to obtain direct policy gradients. Specifically, we employ automatic differentiation (AD) to efficiently compute the sensitivities of the model predictive control (MPC) objective function and constraints penalties. To guarantee safety upon deployment, we derive probabilistic guarantees on closed-loop stability and constraint satisfaction based on indicator functions and Hoeffding’s inequality. We empirically demonstrate that the proposed method can learn neural control policies for various parametric optimal control tasks. In particular, we show that the proposed DPC method can stabilize systems with unstable dynamics, track time-varying references, and satisfy nonlinear state and input constraints. Our DPC method has practical time savings compared to alternative approaches for fast and memory-efficient controller design. Specifically, DPC does not depend on a supervisory controller as opposed to approximate MPC based on imitation learning. We demonstrate that, without losing performance, DPC is scalable with greatly reduced demands on memory and computation compared to implicit and explicit MPC while being more sample efficient than model-free reinforcement learning (RL) algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A Framework for Distributed Approximation of Moments with Higher-Order Derivatives through Automatic Differentiation

We present a framework for the distributed approximation of moments, enabling the evaluation of the uncertainty in a dynamical system. The first and second moment, mean, and variance are computed with up to third-order Taylor series expansion. The required derivatives for the expansion are generated automatically by automatic differentiation and propagated through an implicit time stepper. The computational kernels are the accumulation of the derivatives (Jacobian, Hessian, tensor) and the covariance matrix. We apply distributed parallelism to the Hessian or third-order tensor, and the user merely has to provide a function for the differential equation, thus achieving similar ease of use as Monte Carlo-based methods. We demonstrate our approach using with benchmarks on Theta, a KNL-based system at the Argonne Leadership Computing Facility.

Automatic Differentiation↗
DOE OSTI2025

ESMs Latent Space Exploration for Uncertainty Quantification and Spatiotemporal Downscaling

This final report for DOE Award DE-SC0023044 presents advances in two key areas of climate modeling: (1) representative climate model selection and (2) Earth System Model (ESM) downscaling using hybrid AI methods. The first section introduces a reordered, three-stage workflow to select representative GCM runs that more effectively balance historical skill with ensemble spread, validated across Texas, Bihar, and New York. The second section introduces two novel super-resolution frameworks, ViSIR and ViFOR, that integrate Vision Transformers with sinusoidal and Fourier-based implicit neural representations. These models achieve state-of-the-art reconstruction accuracy for ESM variables including surface temperature and heat fluxes. The report includes detailed methodology, benchmarks, and results, demonstrating significant gains in uncertainty quantification, spatial fidelity, and scalability for climate-impact studies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Implementation of Weighted Delta-Tracking with Scattering in the Serpent 2 Monte Carlo Code

Serpent 2, a continuous-energy Monte Carlo Reactor physics burnup code developed at the VTT Technical Research Centre of Finland, uses a common rejection sampling technique, known as Woodcock delta-tracking. This method improves the efficiency of Monte Carlo in the complicated geometric layout of nuclear reactors and is widely used despite drawbacks that make it inefficient in specific cases, such as in the presence of strong absorbers. At present, Serpent actively uses delta-tracking, falling back to a surface tracking option in situations where delta-tracking is inefficient to partially offset these weaknesses. Morgan and Kotlyar introduced a Weighted Delta Tracking (WDT) routine to address these issues, replacing the rejection sampling of absorption events with an implicit event. In this research, we examine the theoretical basis for rejection sampling and implicit events, and how they relate to WDT. We then discuss implementation of a routine that extends the WDT routine to include scattering events. The routine is implemented and tested within Serpent. We examine various test cases including a Boiling Water Reactor (BWR) pin cell, and homogenous fuel media based on the content of the fuel of the Transient Test Reactor (TREAT) at Idaho National Lab (INL)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2015

Assessing a mini-application as a performance proxy for a finite element method engineering application

The performance of a large-scale, production-quality science and engineering application (‘app’) is often dominated by a small subset of the code. Even within that subset, computational and data access patterns are often repeated, so that an even smaller portion can represent the performance-impacting features. If application developers, parallel computing experts, and computer architects can together identify this representative subset and then develop a small mini-application (‘miniapp’) that can capture these primary performance characteristics, then this miniapp can be used to both improve the performance of the app as well as provide a tool for co-design for the high-performance computing community. However, a critical question is whether a miniapp can effectively capture key performance behavior of an app. This study provides a comparison of an implicit finite element semiconductor device modeling app on unstructured meshes with an implicit finite element miniapp on unstructured meshes. The goal is to assess whether the miniapp is predictive of the performance of the app. Finally, single compute node performance will be compared, as well as scaling up to 16,000 cores. Results indicate that the miniapp can be reasonably predictive of the performance characteristics of the app for a single iteration of the solver on a single compute node.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons

Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C 60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Data-driven operator inference for nonintrusive projection-based model reduction

We presenta a nonintrusive projection-based model reduction method for full models based on time-dependent partial differential equations. Projection-based model reduction constructs the operators of a reduced model by projecting the equations of the full model onto a reduced space. Traditionally, this projection is intrusive, which means that the full-model operators are required either explicitly in an assembled form or implicitly through a routine that returns the action of the operators on a given vector; however, in many situations the full model is given as a black box that computes trajectories of the full-model states and outputs for given initial conditions and inputs, but does not provide the full-model operators. Our nonintrusive operator inference approach infers approximations of the reduced operators from the initial conditions, inputs, trajectories of the states, and outputs of the full model, without requiring the full-model operators. Our operator inference is applicable to full models that are linear in the state or have a low-order polynomial nonlinear term. The inferred operators are the solution of a least-squares problem and converge, with sufficient state trajectory data, in the Frobenius norm to the reduced operators that would be obtained via an intrusive projection of the full-model operators. Our numerical results reflect operator inference on a linear climate model and on a tubular reactor model with a polynomial nonlinear term of third order.

42 ENGINEERING↗