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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Low-Density Parity-Check Stabilizer Codes as Gapped Quantum Phases: Stability under Graph-Local Perturbations

We generalize the proof of stability of topological order, due to Bravyi, Hastings, and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity-check (LDPC) codes without the restriction of geometric locality in Euclidean space. We consider Hamiltonians 𝐻 0 defined by ⟦𝑁,𝐾,𝑑⟧ LDPC codes, which obey certain topological quantum order conditions: (i) code distance 𝑑 ≥ 𝑐⁢log (𝑁), implying local indistinguishability of ground states, and (ii) a mild condition on local and global compatibility of ground states—these include good quantum LDPC codes and the toric code on a hyperbolic lattice, among others. We consider stability under weak perturbations that are quasilocal on the interaction graph defined by 𝐻 0 and that can be represented as sums of bounded-norm terms. As long as the local perturbation strength is smaller than a finite constant, we show that the perturbed Hamiltonian has well-defined spectral bands originating from the 𝑂⁡(1) smallest eigenvalues of 𝐻 0 . The band originating from the smallest eigenvalue has 2 𝐾 states, is separated from the rest of the spectrum by a finite energy gap, and has exponentially narrow bandwidth 𝛿 =𝐶⁢𝑁⁢𝑒 −Θ⁡(𝑑) , which is tighter than the best-known bounds even in the Euclidean case. We also obtain that the new ground-state subspace is related to the initial-code subspace by a quasilocal unitary, allowing one to relate their physical properties. Our proof uses an iterative procedure that performs successive rotations to eliminate non-frustration-free terms in the Hamiltonian. Our results extend to quantum Hamiltonians built from classical LDPC codes, which give rise to stable symmetry-breaking phases. These results show that LDPC codes very generally define stable gapped quantum phases, even in the non-Euclidean setting, initiating a systematic study of such phases of matter.

mathematical physics↗
DOE OSTI2024

Three-dimensional continuum point cloud method for large deformation and its verification

This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Lastly, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.

Compressible neo-Hookean materials↗
DOE OSTI2025

Neural operators for stochastic modeling of nonlinear structural system response to natural hazards

Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on the utilization of deep neural networks to learn operators capable of mapping infinite-dimensional function spaces. Here, in this work, we employ two state-of-the-art neural operators, the deep operator network (DeepONet) and the Fourier neural operator (FNO) for the prediction of the nonlinear time history response of structural systems exposed to natural hazards, such as earthquakes and windstorms. Specifically, we propose two architectures, a self-adaptive FNO and a fast Fourier transform-based DeepONet (DeepFNOnet), where we employ a FNO beyond the DeepONet to learn the discrepancy between the ground truth and the solution predicted by the DeepONet. To demonstrate the efficiency and applicability of the architectures, two problems are considered. In the first, we use the proposed model to predict the seismic nonlinear dynamic response of a six-story shear building subject to stochastic ground motions. In the second problem, we employ the operators to predict the wind-induced nonlinear dynamic response of a high-rise building while explicitly accounting for the stochastic nature of the wind excitation. In both cases, the trained metamodels achieve high accuracy while being orders of magnitude faster than their corresponding high-fidelity models.

DeepONet↗
DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗
DOE OSTI2024

Using Parameter Sweep in WaterTAP to Analyze New Water Treatment Technologies

We describe a powerful and generalized parameter sweep tool in this report that was originally developed to analyze the performance of existing and novel water treatment models being developed in WaterTAP. Since WaterTAP is built upon IDAES and Pyomo, the parameter sweep tool can be used to systematically explore and debug the behavior of most Pyomo and IDAES numerical models. In order to enable meaningful analyses, the parameter sweep tool has been designed with the following features: 1) Model flexibility: The parameter sweep tool does not enforce any restrictions on the types of models that can be used with it. As long as a Pyomo model can be solved and the parameter is active and mutable, the tool only needs functions that describe how to run the model, the sweep parameters, and the output quantities of interest. 2) Flexible sampling: The parameter sweep tool has inbuilt functions to generate samples from a random distribution or a multidimensional Euclidean space. Furthermore, the users have to ability to supply samples generated from a tool of their choice. 3) Multiple sweep types: A user can choose from one of 3 types of parameter sweeps depending on their needs. 4) Detailed outputs: Outputs generated by the parameter sweep tool can be stored in detailed H5 file or user-friendly CSV files for post processing. 5) Parallel computing: The parameter sweep supports shared and distributed memory parallel computing to enable the use of high performance computers (HPC) for large-scale analyses. 6) Modular: The parameter sweep tool is self-contained and can easily be integrated within an outer-loop analysis or as desired by the user. 7) Ease of use: The tool is well documented and a simple sweep can be easily executed by following the online documentation in a few lines of code. We demonstrate the use of the parameter sweep tool on a simple water treatment system from the WaterTAP repository and show its parallel scaling performance on an Apple laptop and NREL's Eagle HPC. The parameter sweep tool is actively being used with models currently being developed within WaterTAP and we expect its use to grow beyond it to other IDAES and Pyomo models.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1968

Boundary Control Systems

Boundary conditions control systems described by partial differential equation in domain of Euclidean space analyzed for optimal controllability

Fattorini, H. O.↗
NASA NTRS1972

Bounded state variables and the calculus of variations

An optimal control problem with bounded state variables is transformed into a Lagrange problem by means of differentiable mappings which take some Euclidean space onto the control and state regions. Whereas all such mappings lead to a Lagrange problem, it is shown that only those which are defined as acceptable pairs of transformations are suitable in the sense that solutions to the transformed Lagrange problem will lead to solutions to the original bounded state problem and vice versa. In particular, an acceptable pair of transformations is exhibited for the case when the control and state regions are right parallelepipeds. Finally, a description of the necessary conditions for the bounded state problem which were obtained by this method is given.

Hanafy, L. M.↗
NASA NTRS1971

A Transformation Approach to Optimal Control Problems with Bounded State Variables

A technique is described and utilized in the study of the solutions to various general problems in optimal control theory, which are converted in to Lagrange problems in the calculus of variations. This is accomplished by mapping certain properties in Euclidean space onto closed control and state regions. Nonlinear control problems with a unit m cube as control region and unit n cube as state region are considered.

Hanafy, Lawrence Hanafy↗
NASA NTRS1971

An approximate theory of imperfect modeling with application to thermal modeling of spacecraft.

Proposal of a new concept of model testing which makes use of imperfect models and is based on the heuristic argument of representing the error states in a multidimensional Euclidean space when the errors in the modeling parameter are sufficiently small. By a separation of these errors into positive and negative groups, and from a consideration of the error paths in the hyperspaces, it is shown that the global effect of these errors may be evaluated with a good degree of approximation. Conditions under which the procedure would yield satisfactory results are discussed. To test the usefulness of the theory a computer experiment was conducted for the prediction of both transient and steady state thermal behavior of a hypothetical spacecraft using perfect, as well as imperfect, models.

Chao, B. T.↗
NASA NTRS1972

Controllability of nonlinear systems.

Discussion of the controllability of nonlinear systems described by the equation dx/dt - F(x,u). Concepts formulated by Chow (1939) and Lobry (1970) are applied to establish criteria for F and its derivatives to obtain qualitative information on sets which can be obtained from x which denotes a variable of state in an arbitrary, real, analytical manifold. It is shown that controllability implies strong accessibility for a large class of manifolds including Euclidean spaces.-

Sussmann, H. J.↗
NASA NTRS1972

Spline smoothing of histograms by linear programming

An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.

Bennett, J. O.↗
NASA NTRS1975

A counter example in linear feature selection theory

The linear feature selection problem in multi-class pattern recognition is described as that of linearly transforming statistical information from n-dimensional (real Euclidean) space into k-dimensional space, while requiring that average interclass divergence in the transformed space decrease as little as possible. Divergence is the expected interclass divergence derived from Hajek two-class divergence; it is known that there always exists a k x n matrix B such that the transformation determined by B maximizes the divergence in k-dimensional space. It is known that, if Q is any k x k invertible matrix, and B is as defined above, then QB again maximizes the divergence in k-space. It is shown that the converse of this result is false: two matrices exist, B sub 1 and B sub 2, each of which maximizes transformed divergence, which are not related in the fashion B sub 2 = QB sub 1 for any k x k matrix Q.

Brown, D. R.↗
NASA NTRS1975

Optimal control of multiplicative control systems arising from cancer therapy

This study deals with ways of curtailing the rapid growth of cancer cell populations. The performance functional that measures the size of the population at the terminal time as well as the control effort is devised. With use of the discrete maximum principle, the Hamiltonian for this problem is determined and the condition for optimal solutions are developed. The optimal strategy is shown to be a bang-bang control. It is shown that the optimal control for this problem must be on the vertices of an N-dimensional cube contained in the N-dimensional Euclidean space. An algorithm for obtaining a local minimum of the performance function in an orderly fashion is developed. Application of the algorithm to the design of antitumor drug and X-irradiation schedule is discussed.

Bahrami, K.↗
NASA NTRS1982

Observer reference triad rotation, magnetic fields, and rotation in Euclidean cosmological models

It is shown that a cosmological model with Euclidean space sections admits fluid flows if a magnetic field is present. Further, if observer reference frames spin in their response to the universe, a vorticity may exist. Limits can be set on any present intergalactic magnetic field of less than 5.38 x 10 to the -10th gauss (for a model with the chosen symmetry and choice of initial field and fluid velocity components).

Fennelly, A. J.↗
NASA NTRS1981

Control of nonlinear time-varying systems

Necessary and sufficient conditions are given for a time-varying nonlinear system of specific form to be transformed into a time-invariant controllable linear system. Since the present work will be in a neighborhood of the origin, it is unnecessary to name specific sets and it is assumed that all assumptions, conditions and results hold in an open set in the appropriate Euclidean space that contains the origin. This theory can be combined with the global inverse function theorems to produce global results.

Hunt, L. R.↗
NASA NTRS1986

Approximate methods for black hole collisions

The head-on collision of two nonrotating black holes, initially falling toward each other with speed of approach equal to escape velocity, is studied. The initial-value problem for the two-black-hole configuration is solved by giving the extrinsic curvature on a Euclidean space slice, with the equal masses of the two holes and their separation as free parameters. An approximating space-time is then constructed by stacking up a whole sequence of initial-value slices with decreasing separation between the black holes. The space-time singularities at the centers of the two black holes collide at some instant of time, and after that time the space-time so constructed is just the Schwarzschild solution with mass equal to the total mass of both black holes. The approximating space-time describes the coalescence of the event horizons, but contains no gravitational waves.

Eardley, D. M.↗