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DOE OSTI2025

Faster solutions to the interdiction defense problem using suboptimal solutions

The interdiction defense (ID) problem solves a defender-attacker-defender model where the defender and attacker share the same set of components to harden and target. Here, we build upon the best response intersection (BRI) algorithm by developing the BRI with suboptimal solutions (BRI-SS) algorithm to solve the ID problem. The BRI-SS algorithm utilizes off-the-shelf optimization solvers that return suboptimal solutions at no additional computation cost. We derive novel cuts from suboptimal solutions, reducing the number of iterations required for the algorithm to converge while maintaining optimality guarantees. We also present a heuristic that utilizes all obtained suboptimal solutions to select the next defense to evaluate at each iteration. We perform computational experiments applied to power grid interdiction on standard test cases. Our results demonstrate that the BRI-SS algorithm consistently outperforms the BRI algorithm across all test cases.

Computer science↗

NASA NTRS2019

Development and Analysis of the Automated Object Reentry Survival Analysis Tool Parametric Study Wrapper

The NASA Orbital Debris Program Office (ODPO) studies all aspects of spacecraft end-of-life and orbital debris measurement, modeling, and mitigation. The reentry safety group within the ODPO uses the Object Reentry Survival Analysis Tool (ORSAT) to calculate the casualty risk due to reentry of spacecraft and other types of orbital debris. ORSAT models spacecraft as a collection of fragments that break apart from the parent object at a pre-defined “breakup altitude.” It then calculates the trajectory and aero-heating of these fragments to determine which fragments are completely destroyed and which survive to the ground and pose a risk to human population. Because of the historically high computational cost of these calculations, many simplifying assumptions have been made in the traditional calculation and analysis process used by the ODPO, some of which have been shown by recent research by the ODPO and others to be incorrect. Improvements to the ORSAT code and advancements in computer technology have vastly decreased the program’s processing time, and have allowed the ODPO to develop a capability for large-scale parametric studies and Monte Carlo reentry simulations that can aid in both the initial spacecraft design and provide more detailed and accurate risk analysis to spacecraft operators.

Smith, Andrew N.↗

DOE OSTI2026

Gradient-informed Hamiltonian Monte Carlo for multicomponent CALPHAD model optimization and uncertainty quantification

CALPHAD model parameter optimization is inherently challenging due to non-smooth objective functions, high-dimensional parameter spaces, and the need for uncertainty quantification (UQ). Traditional weighted nonlinear least squares approaches are computationally efficient but local, whereas black-box global optimizers and ensemble Markov Chain Monte Carlo (MCMC) methods provide broader exploration at substantial computational cost. The objective of this work is to combine the global exploration capability of gradient-informed Hamiltonian Monte Carlo – specifically the No-U-Turn Sampler (NUTS) – with local deterministic refinement using BFGS to efficiently optimize multicomponent CALPHAD models with minimal manual intervention. Analytic gradients are computed via the Jansson derivative framework. The methodology is demonstrated on the Cr—Fe binary system and extended to the Cr—Fe—Ni ternary system with 32 degrees of freedom. For Cr—Fe, NUTS achieves comparable or superior optimality relative to ensemble MCMC while requiring over an order-of-magnitude fewer likelihood evaluations. Parameter uncertainties are quantified through NUTS sampling and propagated to thermodynamic observables using local expansion, demonstrating a novel modular approach that combines binary and ternary parameter subsets without requiring global relaxation. These results establish gradient-informed exploration as a scalable strategy for multicomponent CALPHAD optimization and provide a practical route towards efficient higher-order database development with quantified uncertainty.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Modeling cross-beam energy transfer with sector ray tracing

Ray-based cross-beam energy transfer (CBET) models are an essential feature of the radiation-hydrodynamic codes used to simulate inertial confinement fusion implosions, but full 3D ray-based CBET calculations can have a prohibitively high computational cost. Sector ray tracing can be used to reduce the cost by orders of magnitude in cases where the coronal plasma and laser drive can be approximated as spherically symmetric. An extension of sector ray tracing (section ray tracing) can be used to relax the assumption of a spherically symmetric drive while still retaining most of the computational savings of a sector ray trace. We discuss the foundations of sector and section ray tracing and compare them to full ray tracing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Enabling Dynamic Probabilistic Risk Assessment of Physical Security Using EMRALD and MAAP

The optimization of physical security in nuclear power plants requires sophisticated methodologies that integrate operator actions and plant behavior through advanced simulation tools. To address this, Idaho National Laboratory [JL2.1]has developed the Modeling and Analysis for Safety and Security using the Dynamic EMRALD Framework (MASS-DEF) methodology, an approach that integrates force-on-force simulations, dynamic probabilistic risk assessment, and thermal-hydraulics modeling [JL3.1]to enhance security planning while reducing costs. We developed a tool that produces reduced order models using thermal hydraulic simulations from the Modular Accident Analysis Program (MAAP) [1]. These models can quickly evaluate reactor core behavior during attack simulations, and in so doing, address two barriers of traditional methods: (1) MAAP simulations are computationally intensive, and (2) attack scenarios must be run in a secure environment, which complicates analysis and validation. By precomputing scenario outcomes for a small number of modified parameters, the reduced order model significantly decreases the computational cost and enables offsite review of the results.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1993

Comparison of symbolic and numerical integration methods for an assumed-stress hybrid shell element

Hybrid shell elements have long been regarded with reserve by the commercial finite element developers despite the high degree of reliability and accuracy associated with such formulations. The fundamental reason is the inherent higher computational cost of the hybrid approach as compared to the displacement-based formulations. However, a noteworthy factor in favor of hybrid elements is that numerical integration to generate element matrices can be entirely avoided by the use of symbolic integration. In this paper, the use of the symbolic computational approach is presented for an assumed-stress hybrid shell element with drilling degrees of freedom and the significant time savings achieved is demonstrated through an example.

Rengarajan, Govind↗

NASA NTRS1993

Strategies and methodologies to develop techniques for computer-assisted analysis of gas phase formation during altitude decompression

It would be of operational significance if one possessed a device that would indicate the presence of gas phase formation in the body during hypobaric decompression. Automated analysis of Doppler gas bubble signals has been attempted for 2 decades but with generally unfavorable results, except with surgically implanted transducers. Recently, efforts have intensified with the introduction of low-cost computer programs. Current NASA work is directed towards the development of a computer-assisted method specifically targeted to EVA, and we are most interested in Spencer Grade 4. We note that Spencer Doppler Grades 1 to 3 have increased in the FFT sonogram and spectrogram in the amplitude domain, and the frequency domain is sometimes increased over that created by the normal blood flow envelope. The amplitude perturbations are of very short duration, in both systole and diastole and at random temporal positions. Grade 4 is characteristic in the amplitude domain but with modest increases in the FFT sonogram and spectral frequency power from 2K to 4K over all of the cardiac cycle. Heart valve motion appears to characteristic display signals: (1) the demodulated Doppler signal amplitude is considerably above the Doppler-shifted blow flow signal (even Grade 4); and (2) demodulated Doppler frequency shifts are considerably greater (often several kHz) than the upper edge of the blood flow envelope. Knowledge of these facts will aid in the construction of a real-time, computer-assisted discriminator to eliminate cardiac motion artifacts. There could also exist perturbations in the following: (1) modifications of the pattern of blood flow in accordance with Poiseuille's Law, (2) flow changes with a change in the Reynolds number, (3) an increase in the pulsatility index, and/or (4) diminished diastolic flow or 'runoff.' Doppler ultrasound devices have been constructed with a three-transducer array and a pulsed frequency generator.

Powell, Michael R.↗

NASA NTRS1981

Computation of separated flows by a vortex-tracing algorithm

Numerical solutions for two-dimensional, time-dependent, separated flows around bodies are obtained, using a new version of the vortex method. This method provides an efficient representation of flows involving large regions of separation. The modifications incorporated in the new version, which improve its accuracy, versatility, and computing speed, are described. The computer cost is only of the order of the 3/2 power on N, instead of N-squared, for each step with N vortices. Arbitrary shapes can be treated; a conformal mapping is not required. Special attention is paid to the viscous character of the solution and to the accurate computation of the pressure distribution at the body surface. The vortex solution for the outer flow is coupled to an inner solution for the attached part of the boundary layer. Numerical results are presented for several bluff bodies exhibiting dependence on Reynolds number, for stationary airfoils under steady or transient conditions and for oscillating airfoils, including dynamic stalls. These results are compared with other available results, analytical or experimental, and demonstrate the enhanced reliability and accuracy of the improved method.

Spalart, P. R.↗

NASA NTRS1996

Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that this basic methodology could be ported to distributed memory parallel computing architectures. In this paper, our concern will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

Reuther, James↗

NASA NTRS2010

A Computational Approach for Probabilistic Analysis of LS-DYNA Water Impact Simulations

NASA s development of new concepts for the Crew Exploration Vehicle Orion presents many similar challenges to those worked in the sixties during the Apollo program. However, with improved modeling capabilities, new challenges arise. For example, the use of the commercial code LS-DYNA, although widely used and accepted in the technical community, often involves high-dimensional, time consuming, and computationally intensive simulations. Because of the computational cost, these tools are often used to evaluate specific conditions and rarely used for statistical analysis. The challenge is to capture what is learned from a limited number of LS-DYNA simulations to develop models that allow users to conduct interpolation of solutions at a fraction of the computational time. For this problem, response surface models are used to predict the system time responses to a water landing as a function of capsule speed, direction, attitude, water speed, and water direction. Furthermore, these models can also be used to ascertain the adequacy of the design in terms of probability measures. This paper presents a description of the LS-DYNA model, a brief summary of the response surface techniques, the analysis of variance approach used in the sensitivity studies, equations used to estimate impact parameters, results showing conditions that might cause injuries, and concluding remarks.

Horta, Lucas G.↗

DOE OSTI2025

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Machine learning for seismic low-frequency extrapolation

The cycle-skipping problem that plagues full waveform inversion (FWI) can be at least partially mitigated if low frequencies (which encode the kinematics of wave propagation in seismic data) are recorded. However, seismic sources and receivers are band-limited, so seismic data does not generally include signals down to 0 Hz. To improve our ability to solve the seismic inverse problem, one can synthesize this missing low-frequency (LF) content from the recorded high-frequency (HF) data using machine learning (ML) models. Deep learning models such as convolutional neural networks (CNNs) demonstrate impressive ability to perform low frequency extrapolation. However, such models require powerful hardware (GPU machines) and careful training. We assess the extrapolation capabilities of three different ML models that do not require GPU machines, namely, random forest, Gaussian process regression and gradient boosting, on both synthetic and real data. Experimental results on two synthetic data sets (generated from a low velocity lens embedded in a homogeneous medium, and the Marmousi model) demonstrate that FWI applied to the extrapolated data consistently improves inversion accuracy relative to FWI applied to the original data sets that do not contain low frequencies. Application of low-frequency extrapolation to real data from the Northwest Shelf of Australia demonstrates that tree-based ML models such as gradient boosting can outperform CNNs in terms of both accuracy and computational cost on non-GPU architectures.

58 GEOSCIENCES↗

DOE OSTI2026

Parametric reduced order models for graded lattice structures

Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. Here, to address these challenges, this paper introduces a novel Efficient Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to efficiently manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be efficiently assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method's modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to biomedical engineering.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Accelerating high-order continuum kinetic plasma simulations using multiple GPUs

Kinetic plasma simulations solve the Vlasov-Poisson or Vlasov-Maxwell equations to evolve scalar-variable distribution functions in position-velocity phase space and vector-variable electromagnetic fields in configuration space. The immense computational cost of evolving high-dimensional variables, and their large number of degrees of freedom, often limits the utility of continuum kinetic simulations and presents a challenge when it comes to accurately simulating real-world physical phenomena. To address this challenge, we present techniques that accelerate and minimize the computational work required for a scalable Vlasov-Poisson solver. We show theoretical hardware compute and communication bounds for solving a fourth-order finite-volume Vlasov-Poisson system. These bounds are then used to inform and evaluate the design of performance portable algorithms for a multiple graphics processing unit (GPU) accelerated version of the Vlasov-Poisson solver VCK-CPU [1]. We demonstrate that the multi-GPU Vlasov solver implementation, VCK-GPU, simultaneously minimizes required inter-process data transfer while also being bounded by the machine network performance limits. This results in an overall strong scaling speedup per timestep of up to 40x in three-dimensional phase space (one position, two velocity coordinates) and 54x in four dimensional phase space (two position, two velocity coordinates) and a 341x increase in simulation throughput of the GPU accelerated code over the existing CPU code. The GPU code is also able to weak scale up to 256 compute nodes and 1024 GPUs. In conclusion, we demonstrate that the improved compute performance enables exploring configurations which were previously computationally infeasible, including resolving fine-scale distribution function filamentation and multi-species dynamics with realistic electron-proton mass ratios.

Continuum kinetics↗

NASA NTRSDate not supplied

Fast and Precise Trajectory Simulation for Entry, Descent, and Landing Using A Multi-Model Monte Carlo Approach

Predicting landing radius and other quantities of interest (QoI) for entry, descent, and landing (EDL) applications requires a viable uncertainty propagation method for quantifying the impact of uncertainties in wind pattern variations, atmospheric uncertainties, etc. While standard MC simulation is the defacto standard for providing robust and unbiased predictions,it is often infeasible for expensive, high-fidelity EDL models. Low-fidelity models are commonly constructed to replace the high-fidelity model in MC simulation for computational speedup,but at the expense of accuracy and unbiasedness. Emerging multi-model MC methods are bridging this gap by combining predictions from two or more models of varying fidelity and computational cost for efficient and unbiased uncertainty propagation. This work explores the use of multi-model MC for increasing the speed and precision of trajectory simulation for EDL. It is shown that combining a high-fidelity EDL model with low-fidelity models (e.g,data-driven, reduced physics) yields substantial computational speedup versus standard MCwith only the high-fidelity model. Moreover, the unbiasedness of multi-model MC predictions is highlighted by showing increased accuracy versus an approach that leverages a low-fidelity surrogate model alone.

James E. Warner↗

NASA NTRS1996

Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods (13, 12, 44, 38). The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method (19, 20, 21, 23, 39, 25, 40, 41, 42, 43, 9) was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations (39, 25). In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that the basic methodology could be ported to distributed memory parallel computing architectures [241. In this paper, our concem will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

Reuther, James↗

NASA NTRS2006

Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry

Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper.

Nemec, Marian↗

NASA NTRS2019

Computational Modeling for Non-Equilibrium Shock Tube Flows

Time accurate simulation of non-equilibrium flows inside shock tube facilities presents several challenges from both physical and mathematical aspects. Furthermore, the large computational cost makes it impractical to support a real-time experimental test campaign. In this work, we explore other methods for modeling the shock tube problem with the main focus on the post-shock region and the absolute radiation emanating from it. The proposed alternative approach is several orders of magnitude less computationally expensive while still accurate enough with regards to the quantities of interest. Excellent agreement is found with the established stagnation-line approach. Comparison with time-accurate simulations shows good agreement close to the peak values and disagreement of the temperatures relaxation and radiance profiles toward equilibrium.

Bensassi, Khalil↗