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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.↗

NASA NTRS2008

Sparse Regression as a Sparse Eigenvalue Problem

We extend the l0-norm "subspectral" algorithms for sparse-LDA [5] and sparse-PCA [6] to general quadratic costs such as MSE in linear (kernel) regression. The resulting "Sparse Least Squares" (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem (e.g., binary sparse-LDA [7]). Specifically, for a general quadratic cost we use a highly-efficient technique for direct eigenvalue computation using partitioned matrix inverses which leads to dramatic x103 speed-ups over standard eigenvalue decomposition. This increased efficiency mitigates the O(n4) scaling behaviour that up to now has limited the previous algorithms' utility for high-dimensional learning problems. Moreover, the new computation prioritizes the role of the less-myopic backward elimination stage which becomes more efficient than forward selection. Similarly, branch-and-bound search for Exact Sparse Least Squares (ESLS) also benefits from partitioned matrix inverse techniques. Our Greedy Sparse Least Squares (GSLS) generalizes Natarajan's algorithm [9] also known as Order-Recursive Matching Pursuit (ORMP). Specifically, the forward half of GSLS is exactly equivalent to ORMP but more efficient. By including the backward pass, which only doubles the computation, we can achieve lower MSE than ORMP. Experimental comparisons to the state-of-the-art LARS algorithm [3] show forward-GSLS is faster, more accurate and more flexible in terms of choice of regularization

Exact Sparse Least Squares (ESLS)↗

NASA NTRS2006

Multiple-Flat-Panel System Displays Multidimensional Data

The NASA Ames hyperwall is a display system designed to facilitate the visualization of sets of multivariate and multidimensional data like those generated in complex engineering and scientific computations. The hyperwall includes a 77 matrix of computer-driven flat-panel video display units, each presenting an image of 1,280 1,024 pixels. The term hyperwall reflects the fact that this system is a more capable successor to prior computer-driven multiple-flat-panel display systems known by names that include the generic term powerwall and the trade names PowerWall and Powerwall. Each of the 49 flat-panel displays is driven by a rack-mounted, dual-central-processing- unit, workstation-class personal computer equipped with a hig-hperformance graphical-display circuit card and with a hard-disk drive having a storage capacity of 100 GB. Each such computer is a slave node in a master/ slave computing/data-communication system (see Figure 1). The computer that acts as the master node is similar to the slave-node computers, except that it runs the master portion of the system software and is equipped with a keyboard and mouse for control by a human operator. The system utilizes commercially available master/slave software along with custom software that enables the human controller to interact simultaneously with any number of selected slave nodes. In a powerwall, a single rendering task is spread across multiple processors and then the multiple outputs are tiled into one seamless super-display. It must be noted that the hyperwall concept subsumes the powerwall concept in that a single scene could be rendered as a mosaic image on the hyperwall. However, the hyperwall offers a wider set of capabilities to serve a different purpose: The hyperwall concept is one of (1) simultaneously displaying multiple different but related images, and (2) providing means for composing and controlling such sets of images. In place of elaborate software or hardware crossbar switches, the hyperwall concept substitutes reliance on the human visual system for integration, synthesis, and discrimination of patterns in complex and high-dimensional data spaces represented by the multiple displayed images. The variety of multidimensional data sets that can be displayed on the hyperwall is practically unlimited. For example, Figure 2 shows a hyperwall display of surface pressures and streamlines from a computational simulation of airflow about an aerospacecraft at various Mach numbers and angles of attack. In this display, Mach numbers increase from left to right and angles of attack increase from bottom to top. That is, all images in the same column represent simulations at the same Mach number, while all images in the same row represent simulations at the same angle of attack. The same viewing transformations and the same mapping from surface pressure to colors were used in generating all the images.

Gundo, Daniel↗

NASA NTRS2012

Optimal Force Control of Vibro-Impact Systems for Autonomous Drilling Applications

The need to maintain optimal energy efficiency is critical during the drilling operations performed on future and current planetary rover missions (see figure). Specifically, this innovation seeks to solve the following problem. Given a spring-loaded percussive drill driven by a voice-coil motor, one needs to determine the optimal input voltage waveform (periodic function) and the optimal hammering period that minimizes the dissipated energy, while ensuring that the hammer-to-rock impacts are made with sufficient (user-defined) impact velocity (or impact energy). To solve this problem, it was first observed that when voice-coil-actuated percussive drills are driven at high power, it is of paramount importance to ensure that the electrical current of the device remains in phase with the velocity of the hammer. Otherwise, negative work is performed and the drill experiences a loss of performance (i.e., reduced impact energy) and an increase in Joule heating (i.e., reduction in energy efficiency). This observation has motivated many drilling products to incorporate the standard bang-bang control approach for driving their percussive drills. However, the bang-bang control approach is significantly less efficient than the optimal energy-efficient control approach solved herein. To obtain this solution, the standard tools of classical optimal control theory were applied. It is worth noting that these tools inherently require the solution of a two-point boundary value problem (TPBVP), i.e., a system of differential equations where half the equations have unknown boundary conditions. Typically, the TPBVP is impossible to solve analytically for high-dimensional dynamic systems. However, for the case of the spring-loaded vibro-impactor, this approach yields the exact optimal control solution as the sum of four analytic functions whose coefficients are determined using a simple, easy-to-implement algorithm. Once the optimal control waveform is determined, it can be used optimally in the context of both open-loop and closed-loop control modes (using standard realtime control hardware).

Aldrich, Jack B.↗

NASA NTRS2012

A Localized Ensemble Kalman Smoother

Numerous geophysical inverse problems prove difficult because the available measurements are indirectly related to the underlying unknown dynamic state and the physics governing the system may involve imperfect models or unobserved parameters. Data assimilation addresses these difficulties by combining the measurements and physical knowledge. The main challenge in such problems usually involves their high dimensionality and the standard statistical methods prove computationally intractable. This paper develops and addresses the theoretical convergence of a new high-dimensional Monte-Carlo approach called the localized ensemble Kalman smoother.

recursive estimation↗

NASA NTRS2013

Validating an Air Traffic Management Concept of Operation Using Statistical Modeling

Validating a concept of operation for a complex, safety-critical system (like the National Airspace System) is challenging because of the high dimensionality of the controllable parameters and the infinite number of states of the system. In this paper, we use statistical modeling techniques to explore the behavior of a conflict detection and resolution algorithm designed for the terminal airspace. These techniques predict the robustness of the system simulation to both nominal and off-nominal behaviors within the overall airspace. They also can be used to evaluate the output of the simulation against recorded airspace data. Additionally, the techniques carry with them a mathematical value of the worth of each prediction-a statistical uncertainty for any robustness estimate. Uncertainty Quantification (UQ) is the process of quantitative characterization and ultimately a reduction of uncertainties in complex systems. UQ is important for understanding the influence of uncertainties on the behavior of a system and therefore is valuable for design, analysis, and verification and validation. In this paper, we apply advanced statistical modeling methodologies and techniques on an advanced air traffic management system, namely the Terminal Tactical Separation Assured Flight Environment (T-TSAFE). We show initial results for a parameter analysis and safety boundary (envelope) detection in the high-dimensional parameter space. For our boundary analysis, we developed a new sequential approach based upon the design of computer experiments, allowing us to incorporate knowledge from domain experts into our modeling and to determine the most likely boundary shapes and its parameters. We carried out the analysis on system parameters and describe an initial approach that will allow us to include time-series inputs, such as the radar track data, into the analysis

Statistical emulation↗

NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

CFD↗

NASA NTRS2017

Robonaut 2 and You: Specifying and Executing Complex Operations

Crew time is a precious resource due to the expense of trained human operators in space. Efficient caretaker robots could lessen the manual labor load required by frequent vehicular and life support maintenance tasks, freeing astronaut time for scientific mission objectives. Humanoid robots can fluidly exist alongside human counterparts due to their form, but they are complex and high-dimensional platforms. This paper describes a system that human operators can use to maneuver Robonaut 2 (R2), a dexterous humanoid robot developed by NASA to research co-robotic applications. The system includes a specification of constraints used to describe operations, and the supporting planning framework that solves constrained problems on R2 at interactive speeds. The paper is developed in reference to an illustrative, typical example of an operation R2 performs to highlight the challenges inherent to the problems R2 must face. Finally, the interface and planner is validated through a case-study using the guiding example on the physical robot in a simulated microgravity environment. This work reveals the complexity of employing humanoid caretaker robots and suggest solutions that are broadly applicable.

Baker, William↗

NASA NTRS2016

A Spatiotemporal Indexing Approach for Efficient Processing of Big Array-Based Climate Data with MapReduce

Climate observations and model simulations are producing vast amounts of array-based spatiotemporal data. Efficient processing of these data is essential for assessing global challenges such as climate change, natural disasters, and diseases. This is challenging not only because of the large data volume, but also because of the intrinsic high-dimensional nature of geoscience data. To tackle this challenge, we propose a spatiotemporal indexing approach to efficiently manage and process big climate data with MapReduce in a highly scalable environment. Using this approach, big climate data are directly stored in a Hadoop Distributed File System in its original, native file format. A spatiotemporal index is built to bridge the logical array-based data model and the physical data layout, which enables fast data retrieval when performing spatiotemporal queries. Based on the index, a data-partitioning algorithm is applied to enable MapReduce to achieve high data locality, as well as balancing the workload. The proposed indexing approach is evaluated using the National Aeronautics and Space Administration (NASA) Modern-Era Retrospective Analysis for Research and Applications (MERRA) climate reanalysis dataset. The experimental results show that the index can significantly accelerate querying and processing (10 speedup compared to the baseline test using the same computing cluster), while keeping the index-to-data ratio small (0.0328). The applicability of the indexing approach is demonstrated by a climate anomaly detection deployed on a NASA Hadoop cluster. This approach is also able to support efficient processing of general array-based spatiotemporal data in various geoscience domains without special configuration on a Hadoop cluster.

big data↗

DOE OSTI2024

DeepUQ: Assessing the Aleatoric Uncertainties from two Deep Learning Methods

Assessing the quality of aleatoric uncertainty estimates from uncertainty quantification (UQ) deep learning methods is important in scientific contexts, where uncertainty is physically meaningful and important to characterize and interpret exactly. We systematically compare aleatoric uncertainty measured by two UQ techniques, Deep Ensembles (DE) and Deep Evidential Regression (DER). Our method focuses on both zero-dimensional (0D) and two-dimensional (2D) data, to explore how the UQ methods function for different data dimensionalities. We investigate uncertainty injected on the input and output variables and include a method to propagate uncertainty in the case of input uncertainty so that we can compare the predicted aleatoric uncertainty to the known values. We experiment with three levels of noise. The aleatoric uncertainty predicted across all models and experiments scales with the injected noise level. However, the predicted uncertainty is miscalibrated to $\rm{std}(\sigma_{\rm al})$ with the true uncertainty for half of the DE experiments and almost all of the DER experiments. The predicted uncertainty is the least accurate for both UQ methods for the 2D input uncertainty experiment and the high-noise level. While these results do not apply to more complex data, they highlight that further research on post-facto calibration for these methods would be beneficial, particularly for high-noise and high-dimensional settings.

Nevin, Rebecca↗

DOE OSTI2025

Using machine learning to jointly harness the strength of microscopic, fundamental-science driven and macroscopic, application-driven experiments

The PARADIGM project aims at accelerating progress in science by quantitatively answering the following question: What is the optimal combination of fundamental-science and application driven experiments to maximally reduce pertinent data uncertainties? Hence, we are bridging between microscopic experiments and data, and macroscopic simulations and experiments. Answering this question entails solving a high-dimensional and complex optimization problem which we solve with machine learning techniques.

LANSCE↗

DOE OSTI2026

ZEUS: An Efficient GPU Optimization Method Integrating PSO, BFGS, and Automatic Differentiation

We introduce a novel, efficient computational method, ZEUS, for numerical optimization, and provide an open-source implementation. It has four key ingredients: (1) particle swarm optimization (PSO), (2) the use of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, (3) automatic differentiation (AD), and (4) GPUs. Our approach addresses the computational challenges inherent in high-dimensional, non-convex optimization problems. In the first phase of the algorithm, we get a potentially good set of starting points using PSO. Thereafter, we run BFGS independently in parallel from these starting points. BFGS is one of the best-performing algorithms for numerical optimization. However, it requires the gradient of the function being optimized. ZEUS integrates automatic differentiation into BFGS thus avoiding the need for the user to calculate derivatives explicitly. The use of GPUs allows ZEUS to speed up the calculations substantially. We carry out systematic studies to explore the trade-offs between the number of PSO iterations taken, starting points, and BFGS iteration depth. We show that a handful of iterations of PSO can improve global convergence when combined with BFGS. We also present performance studies using common test functions. The source code can be found at https://github.com/fnal-numerics/global-optimizer-gpu.

Soos, Dominik [Old Dominion U.]↗

DOE OSTI2026

HDSense: An efficient method for ranking observable sensitivity

Identifying which observables most effectively constrain model parameters can be computationally prohibitive when considering full likelihoods of many correlated observables. This is especially important for, e.g., hadronization models, where high precision is required to interpret the results of collider experiments. We introduce the High-Dimensional Sensitivity (HDSense) score, a computationally efficient metric for ranking observable sets using only one-dimensional histograms. Derived by profiling over unknown correlations in the Fisher information framework, the score balances total information content against redundancy between observables. We apply HDSense to rank a set observables in terms of their constraining power with respect to five parameters of the Lund string model of hadronization implemented in Pythia using simulated leptonic collider events at the $Z$ pole. Validation against machine-learning--based full-likelihood approximations demonstrates that HDSense successfully identifies near-optimal observable subsets. The framework naturally handles data from multiple experiments with different acceptances and incorporates detector effects. While demonstrated on hadronization models, the methodology applies broadly to generic parameter estimation problems where correlations are unknown or difficult to model.

Assi, Benoît [Cincinnati U.] (ORCID:00000003092433↗

DOE OSTI2026

Generative models on phase space

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be concentrated on a submanifold of the data embedding space. For high-energy physics data, consisting of collections of relativistic energy-momentum 4-vectors, this submanifold can enforce extremely strong physically-motivated priors, such as energy and momentum conservation. If these constraints are learned only approximately, rather than exactly, this can inhibit the interpretability and reliability of such generative models. To remedy this deficiency, we introduce generative models which are, by construction, confined at every step of their sampling trajectory to the manifold of massless N-particle Lorentz-invariant phase space in the center-of-momentum frame. In the case of diffusion models, the "pure noise" forward process endpoint corresponds to the uniform distribution on phase space, which provides a clear starting point from which to identify how correlations among the particles emerge during the reverse (de-noising) process. We demonstrate that our models are able to learn both few-particle and many-particle distributions with various singularity structures, paving the way for future interpretability studies using generative models trained on simulated jet data.

Bogorad, Zachary [Fermilab]↗

DOE OSTI2026

CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters

High-precision calorimeter simulation at current and future colliders imposes rapidly growing computational demands, motivating the development of machine-learning surrogates for traditional Monte Carlo tools such as Geant4. Flow matching and diffusion-based generative models have become leading approaches for high-dimensional fast simulation because of their sample quality, but typically require ${\cal O}(100)$ function evaluations at inference and often rely on auxiliary networks to constrain global observables, compromising streamlined end-to-end generation. We introduce a unified framework that improves the balance between speed, shower quality, and physics fidelity. The method combines: (i) an average velocity field integrator that enables sampling in one or a few evaluations; (ii) a learned generative prior in shower space, constructed from data rather than random noise; and (iii) physics-guided loss terms that impose inductive biases on key observables during training. These elements are training time regularizers, preserving end-to-end inference with no additional cost. With only one or a few evaluation steps, the model achieves shower quality competitive with state-of-the-art flow and diffusion approaches, tested on several public high granularity calorimeter datasets. The results demonstrate inter-layer shower structure consistent with the underlying physics, providing a strong candidate for future fast simulation workflows.

Jiang, Cheng [Edinburgh U.]↗

DOE OSTI2026

Affine Transformations to Enable Machine Learning for Semi-Quantitative EDS Analysis

Energy Dispersive X-ray Spectroscopy (EDS) is an essential technique for determining elemental concentrations and distributions within microstructures, critical for materials discovery, optimization, and qualification. However, most published EDS data is qualitative because current quantitative EDS analysis methods require extensive calibration and post-processing, limiting their practicality and widespread adoption. This work seeks to establish a framework for accelerated EDS characterization and spectrum analysis that can leverage ML to analyze correlations between various elemental compositions and resulting EDS spectra. The complex physics and data result in a high-dimensional problem that grows exponentially with the number of elements in the system and the complexity of the spectrum analysis. ML provides a way to compute and optimize the results of this highly dimensional problem in a flexible way to tailor it to the user’s specific needs and material system. However, the framework emphasizes transparency through a strictly mathematical affine transformation, so the analysis remains understandable and reviewable to facilitate adoption by the scientific community. While currently implemented methods are simplistic and unvalidated, further development and demonstration of this framework could enable high-throughput, accurate, and accessible EDS characterization.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Affine Transformations to Correlate Experimental and Simulated EDS Spectra for Multi-Element Systems

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Strong Lensing Cosmology with Population-level Calibrated Neural Ratio Estimation

Strong gravitational lensing contains key information about cosmic acceleration. Modern and next-generation galaxy imaging surveys are expected to provide high-quality data on $\mathcal{O}(10^5)$ galaxy-galaxy lensing systems. The plethora and complexity of the data are likely to present computational challenges for parameter inference methods for fitting high-dimensional likelihoods, which are often analytically intractable. Neural Ratio Estimation (NRE) efficiently computes individual likelihood ratios that can be combined into population-level posteriors. We use simulations to study the capacity of NRE to jointly predict the dark energy equation-of-state parameter $w$ and the total matter density $Ω_{m}$ from lensing images and companion spectroscopic information. We also introduce a post hoc posterior coverage calibration procedure that mitigates the model overconfidence that is typically found in neural density estimation applications. Our experiments show that the errors on both parameters decrease with increasing inference population sizes. In particular, for 100 lenses in a standard $Λ$CDM Universe, our calibrated NRE model achieves median fractional uncertainty of $22.8\%$ in $w$ and $2.9\%$ in $Ω_{m}$. This proof of concept demonstrates a potentially scalable approach for efficient cosmological parameter inference with large populations of galaxy-scale lenses observed in future surveys.

Jarugula, Sreevani [Fermilab] (ORCID:0000000253867↗