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Results for “Mathematical Computing”

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.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Recent trends in digital human modeling and the concurrent issues that face human modeling approach

Tremendous strides have been made in the recent years to digitally represent human beings in computer simulation models ranging from assembly plant maintenance operations to occupants getting in and out of vehicles to action movie scenarios. While some of these tools are being actively pursued by the engineering communities, there is still a lot of work that remains to be done for the newly planned planetary exploration missions. For example, certain unique and several common challenges are seen in developing computer generated suited human models for designing the next generation space vehicle. The purpose of this presentation is to discuss NASA s potential needs for better human models and to show also many of the inherent yet not too obvious pitfalls that still are left unresolved in this new arena of digital human modeling. As part of NASA s Habitability and Human Factors Branch, the Anthropometry and Biomechanics Facility has been engaged in studying the various facets of computer generated human physical performance models; for instance, it has been engaged in utilizing three-dimensional laser scan data along with three dimensional video based motion and reach data to gather suited anthropometric and shape and size information that are not available yet in the form of computer mannequins. Our goal is to bring in new approaches to deal with heavily clothed humans (such as, suited astronauts) and to overcome the current limitations of wrongly identifying humans (either real or virtual) as univariate percentiles. We are looking at whole-body posture based anthropometric models as a means to identify humans of significantly different shapes and sizes to arrive at mathematically sound computer models for analytical purposes.

Rajulu, Sudhakar↗
DOE OSTI2025

Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.

Autoencoders↗
DOE OSTI2024

Transforming Energy Through Computational Excellence: NREL's Computational Science Center

Computational methods underpin advancing the science and engineering of energy efficiency, sustainable transportation, renewable power technologies, and developing a knowledge base to optimize energy systems. NREL's Computational Science Center (CSC) proudly focuses on providing the service of computing, advancing the science of computing, and enabling NREL's clean energy mission.

applied mathematics↗
NASA NTRS1989

Assessment of autonomic response by broad-band respiration

We present a technique for introducing broad-band respiratory perturbations so that the response characteristics of the autonomic nervous system can be determined noninvasively over a wide range of physiologically relevant frequencies. A subject's respiratory bandwidth was broadened by breathing on cue to a sequence of audible tones spaced by Poisson intervals. The transfer function between the respiratory input and the resulting instantaneous heart rate was then computed using spectral analysis techniques. Results using this method are comparable to those found using traditional techniques, but are obtained with an economy of data collection.

NASA Discipline Cardiopulmonary↗
DOE OSTI2025

Solving sparse finite element problems on neuromorphic hardware

The finite element method (FEM) is one of the most important and ubiquitous numerical methods for solving partial differential equations (PDEs) on computers for scientific and engineering discovery. Applying the FEM to larger and more detailed scientific models has driven advances in high-performance computing for decades. Here we demonstrate that scalable spiking neuromorphic hardware can directly implement the FEM by constructing a spiking neural network that solves the large, sparse, linear systems of equations at the core of the FEM. We show that for the Poisson equation, a fundamental PDE in science and engineering, our neural circuit achieves meaningful levels of numerical accuracy and close to ideal scaling on modern, inherently parallel and energy-efficient neuromorphic hardware, specifically Intel’s Loihi 2 neuromorphic platform. We illustrate extensions to irregular mesh geometries in both two and three dimensions as well as other PDEs such as linear elasticity. Our spiking neural network is constructed from a recurrent network model of the brain’s motor cortex and, in contrast to black-box deep artificial neural network-based methods for PDEs, directly translates the well-understood and trusted mathematics of the FEM to a natively spiking neuromorphic algorithm.

Applied mathematics↗
NASA NTRS2004

Dynamic visual acuity using "far" and "near" targets

CONCLUSIONS: DVA may be useful for assessing the functional consequences of an impaired gaze stabilization mechanism or for testing the effectiveness of a rehabilitation paradigm. Because target distance influences the relative contributions of canal and otolith inputs, the ability to measure DVA at near and far viewing distances may also lead to tests that will independently assess canal and otolith function. OBJECTIVE: To present and test a methodology that uses dynamic visual acuity (DVA) to assess the efficacy of compensatory gaze mechanisms during a functionally relevant activity that differentially measures canal and otolith function. MATERIAL AND METHODS: The effect of treadmill walking at a velocity of 1.79 m/s on subjects' visual acuity was assessed at each of two viewing distances. A custom-written threshold determination program was used to display Landolt C optotypes on a laptop computer screen during a "far" (4 m) target condition and on a micro-display for a "near" (50 cm) target condition. The walking acuity scores for each target distance were normalized by subtracting a corresponding acuity measure obtained while standing still on the treadmill belt. RESULTS: As predicted by subjective reports of relative target motion, the decrease in visual acuity was significantly greater (p < 0.00001) for the near compared to the far condition.

Pattern Recognition, Visual/physiology↗
NASA NTRS2004

Formalization of the Integral Calculus in the PVS Theorem Prover

The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.

Butler, Ricky W.↗
NASA NTRS2026

Development of a One-Domain Volume-Averaged Navier–Stokes Solver

The interaction between a high-enthalpy flow and a thermal protection material is inherently multiscale and multiphysics. In conventional aerothermal analyses, the external flow and material response are generally modeled using separate computational domains coupled through boundary conditions at the material surface. Although this approach has supported many practical applications, it requires assumptions about the location and behavior of the interface and may become difficult to apply when material decomposition, internal reactions, and surface recession substantially alter the porous structure. This report presents the development of a one-domain formulation in which the free-fluid and porous-material regions are represented within a single computational domain. The formulation is based on the volume-averaged Navier–Stokes (VANS) equations, derived from the governing equations for reacting, compressible flow and condensed material. Volume averaging transfers the influence of the unresolved material microstructure to the macroscale equations through effective transport properties, interfacial source terms, and dispersion fluxes. Particular attention is given to regions in which porosity and permeability vary rapidly, including the diffuse transition between a porous material and the surrounding fluid. The resulting equations are implemented in the Porous-material Analysis Toolbox based on OpenFOAM (PATO). The report describes the pressure–velocity coupling strategy used by the solver, examines spatial filtering techniques for deriving effective properties, and evaluates the influence of a smoothly varying interface permeability. Numerical demonstrations include canonical porous-flow configurations, a flow-tube configuration representative of FiberForm® permeability experiments, and the oxidation of a porous carbon material. The purpose of this work is to establish a mathematical and computational foundation for a unified treatment of flow and thermal protection material response. The present formulation is intended to support the progressive inclusion of additional physical processes, including multicomponent transport, finite-rate gas–surface chemistry, pyrolysis, internal oxidation, and material recession. It also provides a framework for connecting pore-scale simulations and microstructural characterization with macroscale aerothermal-response calculations. This report is intended for researchers and engineers working in computational fluid dynamics, porous-media transport, material response, and thermal protection system modeling. It documents both the theoretical development and the initial numerical assessment of the one-domain approach, while identifying the closure of effective and dispersion terms as an important subject for continued investigation.

Ablation↗
NASA NTRS2003

Application of a data-mining method based on Bayesian networks to lesion-deficit analysis

Although lesion-deficit analysis (LDA) has provided extensive information about structure-function associations in the human brain, LDA has suffered from the difficulties inherent to the analysis of spatial data, i.e., there are many more variables than subjects, and data may be difficult to model using standard distributions, such as the normal distribution. We herein describe a Bayesian method for LDA; this method is based on data-mining techniques that employ Bayesian networks to represent structure-function associations. These methods are computationally tractable, and can represent complex, nonlinear structure-function associations. When applied to the evaluation of data obtained from a study of the psychiatric sequelae of traumatic brain injury in children, this method generates a Bayesian network that demonstrates complex, nonlinear associations among lesions in the left caudate, right globus pallidus, right side of the corpus callosum, right caudate, and left thalamus, and subsequent development of attention-deficit hyperactivity disorder, confirming and extending our previous statistical analysis of these data. Furthermore, analysis of simulated data indicates that methods based on Bayesian networks may be more sensitive and specific for detecting associations among categorical variables than methods based on chi-square and Fisher exact statistics.

NASA Discipline Neuroscience↗
DOE OSTI2025

Data imbalance in drug response prediction: multi-objective optimization approach in deep learning setting

Abstract Drug response prediction (DRP) methods tackle the complex task of associating the effectiveness of small molecules with the specific genetic makeup of the patient. Anti-cancer DRP is a particularly challenging task requiring costly experiments as underlying pathogenic mechanisms are broad and associated with multiple genomic pathways. The scientific community has exerted significant efforts to generate public drug screening datasets, giving a path to various machine learning models that attempt to reason over complex data space of small compounds and biological characteristics of tumors. However, the data depth is still lacking compared to application domains like computer vision or natural language processing domains, limiting current learning capabilities. To combat this issue and improves the generalizability of the DRP models, we are exploring strategies that explicitly address the imbalance in the DRP datasets. We reframe the problem as a multi-objective optimization across multiple drugs to maximize deep learning model performance. We implement this approach by constructing Multi-Objective Optimization Regularized by Loss Entropy loss function and plugging it into a Deep Learning model. We demonstrate the utility of proposed drug discovery methods and make suggestions for further potential application of the work to achieve desirable outcomes in the healthcare field.

Biochemistry & Molecular Biology↗
DOE OSTI2025

Competition and cooperation: The plasticity of bacterial interactions across environments

Bacteria live in diverse communities, forming complex networks of interacting species. A central question in bacterial ecology is whether species engage in cooperative or competitive interactions. But this question often neglects the role of the environment. Here, we use genome-scale metabolic networks from two different open-access collections (AGORA and CarveMe) to assess pairwise interactions of different microbes in varying environmental conditions (provision of different environmental compounds). By computationally simulating thousands of environments for 10,000 pairs of bacteria from each collection, we found that most pairs were able to both compete and cooperate depending on the availability of environmental resources. This modeling approach allowed us to determine commonalities between environments that could facilitate the potential for cooperation or competition between a pair of species. Namely, cooperative interactions, especially obligate, were most common in less diverse environments. Further, as compounds were removed from the environment, we found interactions tended to degrade towards obligacy. However, we also found that on average at least one compound could be removed from an environment to switch the interaction from competition to facultative cooperation or vice versa. Together our approach indicates a high degree of plasticity in microbial interactions in response to the availability of environmental resources.

Biochemistry & Molecular Biology↗
DOE OSTI2025

Chromatin structures from integrated AI and polymer physics model

The physical organization of the genome in three-dimensional space regulates many biological processes, including gene expression and cell differentiation. Three-dimensional characterization of genome structure is critical to understanding these biological processes. Direct experimental measurements of genome structure are challenging; computational models of chromatin structure are therefore necessary. We develop an approach that combines a particle-based chromatin polymer model, molecular simulation, and machine learning to efficiently and accurately estimate chromatin structure fromindirectmeasures of genome structure. More specifically, we introduce a new approach where the interaction parameters of the polymer model are extracted from experimental Hi-C data using a graph neural network (GNN). We train the GNN on simulated data from the underlying polymer model, avoiding the need for large quantities of experimental data. The resulting approach accurately estimates chromatin structures across all chromosomes and across several experimental cell lines despite being trained almost exclusively on simulated data. The proposed approach can be viewed as a general framework for combining physical modeling with machine learning, and it could be extended to integrate additional biological data modalities. Ultimately, we achieve accurate and high-throughput estimations of chromatin structure from Hi-C data, which will be necessary as experimental methodologies, such as single-cell Hi-C, improve.

Biochemistry & Molecular Biology↗
DOE OSTI2025

The role of chromatin state in intron retention: A case study in leveraging large scale deep learning models

Complex deep learning models trained on very large datasets have become key enabling tools for current research in natural language processing and computer vision. By providing pre-trained models that can be fine-tuned for specific applications, they enable researchers to create accurate models with minimal effort and computational resources. Large scale genomics deep learning models come in two flavors: the first are large language models of DNA sequences trained in a self-supervised fashion, similar to the corresponding natural language models; the second are supervised learning models that leverage large scale genomics datasets from ENCODE and other sources. We argue that these models are the equivalent of foundation models in natural language processing in their utility, as they encode within them chromatin state in its different aspects, providing useful representations that allow quick deployment of accurate models of gene regulation. We demonstrate this premise by leveraging the recently created Sei model to develop simple, interpretable models of intron retention, and demonstrate their advantage over models based on the DNA language model DNABERT-2. Our work also demonstrates the impact of chromatin state on the regulation of intron retention. Using representations learned by Sei, our model is able to discover the involvement of transcription factors and chromatin marks in regulating intron retention, providing better accuracy than a recently published custom model developed for this purpose.

Biochemistry & Molecular Biology↗
DOE OSTI2025

Towards large-scale quantum optimization solvers with few qubits

Quantum computers hold the promise of more efficient combinatorial optimization solvers, which could be game-changing for a broad range of applications. However, a bottleneck for materializing such advantages is that, in order to challenge classical algorithms in practice, mainstream approaches require a number of qubits prohibitively large for near-term hardware. Here we introduce a variational solver for MaxCut problems over $m={{\mathcal{O}}}({n}^{k})$ binary variables using only n qubits, with tunable k > 1. The number of parameters and circuit depth display mild linear and sublinear scalings in m , respectively. Moreover, we analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature. Altogether, this leads to high quantum-solver performances. For instance, for m = 7000, numerical simulations produce solutions competitive in quality with state-of-the-art classical solvers. In turn, for m = 2000, experiments with n = 17 trapped-ion qubits feature MaxCut approximation ratios estimated to be beyond the hardness threshold 0.941. Our findings offer an interesting heuristics for quantum-inspired solvers as well as a promising route towards solving commercially-relevant problems on near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Improving the five-point bootstrap

We present a new algorithm for the numerical evaluation of five-point conformal blocks in d-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the 〈σσϵσσ〉 correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff ∆ ⩽ ∆cutoff. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Assessment of Extinction‐, Satellite‐, and Model‐Based Vertical Cloud Condensation Nuclei (CCN) Retrieval Methods Using Airborne CCN Measurements Over the Southern Great Plains

Abstract Accurate estimates of the vertical profile of cloud condensation nuclei (CCN) concentration are crucial to better quantify aerosol‐cloud interactions. We assessed the correlation between the vertical CCN concentrations obtained from extinction‐, satellite‐, and model‐based retrieval methods and airborne CCN concentrations collected at 0.24% supersaturation within the 3, 9, 27, and 81 km regions centered over the U.S. Department of Energy's Atmospheric Radiation Measurement User Facility Southern Great Plains (SGP) site during the spring and summer of 2016. The extinction profiles at a wavelength 355 nm were provided by the ground‐based Raman lidar. Our analysis showed moderate correlation between dry‐corrected extinction and airborne CCN data. We found the retrieved number concentration of CCN (RNCCN) method showed regression best‐fit slopes close to unity and consistent prediction errors for the majority of the data. The Lenhardt et al. (2023, https://doi.org/10.5194/amt‐16‐2037‐2023 ) method showed similar conclusions but only during spring, whereas the Mamouri and Ansmann (2016, https://doi.org/10.5194/acp‐16‐5905‐2016 ) method showed poor correlation. The Shinozuka et al. (2015, https://doi.org/10.5194/acp‐15‐7585‐2015 ) satellite‐based method exhibited reasonable agreement during summer but poor correlation during periods where both high (∼1,400 #/cm 3 ) and low (∼50 #/cm 3 ) airborne CCN concentrations were observed. The Copernicus Atmosphere Monitoring Service reanalysis modeled 3‐D CCN data set showed a moderate to weak positive correlation but performed poorly at high airborne CCN concentrations. Our analysis suggests the extinction‐based RNCCN method performed better than other methods across most observation periods under the diverse meteorological conditions observed at the SGP site.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

A quantum eigenvalue solver based on tensor networks

Electronic ground states are of central importance in chemical simulations, but have remained beyond the reach of efficient classical algorithms except in cases of weak electron correlation or one-dimensional spatial geometry. We introduce a hybrid quantum-classical eigenvalue solver that constructs a wavefunction ansatz from a linear combination of matrix product states in rotated orbital bases, enabling the characterization of strongly correlated ground states with arbitrary spatial geometry. The energy is converged via a gradient-free generalized sweep algorithm based on quantum subspace diagonalization, with a potentially exponential speedup in the off-diagonal matrix element contractions upon translation into compact quantum circuits of linear depth in the number of qubits. Chemical accuracy is attained in numerical experiments for both a stretched water molecule and an octahedral arrangement of hydrogen atoms, achieving substantially better correlation energies compared to a unitary coupled-cluster benchmark, with orders of magnitude reductions in quantum resource estimates and a surprisingly high tolerance to shot noise. This proof-of-concept study suggests a promising new avenue for scaling up simulations of strongly correlated chemical systems on near-term quantum hardware.

chemistry↗