Search NASA⌕ Search

SEARCH · Search NASA

Results for “Equation learning”

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

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

At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Optimal control of the electron temperature profile in DIII-D using machine learning surrogate models

The viability of the tokamak as a potential fusion reactor depends on the ability to keep the plasma in a stable regime while achieving temperatures, densities, and confinement times that are as high as possible. Tokamak scenario development attempts to find plasma regimes that achieve all of these conditions and are accessible with a given set of hardware constraints. This requires the ability to control plasma properties such as the normalized beta, the internal inductance, safety factor, rotation, etc. One property that has received less attention than some of the others, but is no less critical to achieving high performance, is the electron temperature (T e ) profile. In this work, Linear Quadratic Integral (LQI) control is used to develop a controller for the electron temperature profile in DIII-D. The controller is based on a linearized model derived from the transport equation that describes the evolution of the electron temperature, and includes contributions from the neural network surrogate models NubeamNet and MMMnet. Furthermore, the controller is tested in simulation using COTSIM, and is proven capable of tracking a target T e profile.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1993

Determination of the mass properties of a manipulator

Space applications for telerobotics requires a manipulator that is robust to the large payload variations that occur in a zero-g environment. One approach to provide the required performance for this large payload variation is to provide inertial decoupling to the controller. The equations to generate the required joint torques can be obtained in several manners but the independent parameters required to perform the calculations are difficult to obtain. This presentation consists of an overview of the inertial decoupling control system and discusses how to reduce the inertial parameter set to a minimum and obtain the required parameter set to a minimum and obtain the required parameter vector using sensed joint positions and torques. In addition, as telerobotic technology becomes more prevalent in the space environments the ability to emulate the effect of zero-g in a one-g environment is critical in learning how to perform tasks in space. To emulate the zero-g environment it is necessary to remove the effect of gravity on the manipulator by determining the feedforward joint torques. A subset of the algorithm developed to obtain the decoupling parameters is used to obtain the gravity offload parameters. These parameters are used to eliminate the effect of gravity. The algorithm is validated on Martin Marietta/NASA Langley's, 7 Degrees-Of-Freedom (DOF) Flight Telerobotic Servicer Hydraulic Manipulator Test Bed. A video portraying actual results of the algorithm is provided.

Goldenberg, Stewart↗
DOE OSTI2024

Efficient learning of accurate surrogates for simulations of complex systems

Machine learning methods are increasingly deployed to construct surrogate models for complex physical systems at a reduced computational cost. However, the predictive capability of these surrogates degrades in the presence of noisy, sparse or dynamic data. Here, we introduce an online learning method empowered by optimizer-driven sampling that has two advantages over current approaches: it ensures that all local extrema (including endpoints) of the model response surface are included in the training data, and it employs a continuous validation and update process in which surrogates undergo retraining when their performance falls below a validity threshold. We find, using benchmark functions, that optimizer-directed sampling generally outperforms traditional sampling methods in terms of accuracy around local extrema even when the scoring metric is biased towards assessing overall accuracy. Finally, the application to dense nuclear matter demonstrates that highly accurate surrogates for a nuclear equation-of-state model can be reliably autogenerated from expensive calculations using few model evaluations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Extended Galerkin Neural Network Approximation of Singular Variational Problems with Error Control

We present extended Galerkin neural networks, a variational framework for approximating general boundary value problems (BVPs) with error control. The main contributions of this work are (1) a rigorous theory guiding the construction of new weighted least squares variational formulations suitable for use in neural network approximation of general BVPs, and (2) an “extended” feedforward network architecture which incorporates and is even capable of learning singular solution structures, thus greatly improving approximability of singular solutions. Furthermore, numerical results are presented for several problems, including steady Stokes flow around reentrant corners and in convex corners with Moffatt eddies in order to demonstrate efficacy of the method.

a posteriori error estimate↗
NASA NTRS1994

A workstation based simulator for teaching compressible aerodynamics

A workstation-based interactive flow simulator has been developed to aid in the teaching of undergraduate compressible aerodynamics. By solving the equations found in NACA 1135, the simulator models three basic fluids problems encountered in supersonic flow: flow past a compression corner, flow past two wedges in series, and flow past two opposed wedges. The study can vary the geometry or flow conditions through a graphical user interface and the new conditions are calculated immediately. Various graphical formats present the results of the flow calculations to the student. The simulator includes interactive questions and answers to aid in both the use of the tool and to develop an understanding of some of the complexities of compressible aerodynamics. A series of help screens make the simulator easy to learn and use.

Benson, Thomas J.↗
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 NTRSDate not supplied

Recent Developments to the Porous Microstructure Analysis (PuMA) Software

Introduction The Porous Microstructure Analysis (PuMA) software is an open source framework for image-based simulation, primarily used to determine effective properties based on material microstructure. PuMA was originally developed for the study of NASA thermal protection materials; however, many of the solvers in PuMA have applicability to a broad range of materials science applications. PuMA version 3.2 computes material surface area, pore diameters, effective thermal conductivity, continuum and rarefied tortuosity, and permeability. For anisotropic materials, PuMA can estimate material orientation and compute anisotropic thermal conductivity and elasticity. In this talk, a brief overview of the PuMA software and underlying methods will be presented, as well as some recent and ongoing developments, including the use of immersed boundary methods for image-based simulation and the development of a new weave segmentation tool, called TomoSAM. Cut-Cell method for heat and mass transfer For simulations on complex microstructures, traditional unstructured meshing techniques often prove to be difficult and time-intensive. Voxel-based solvers, which represent the surface as a staircase structure, are relatively simple to implement but can lose accuracy when feature resolution is poor. In this work, we present a novel 3D cut-cell method for solving the variable coefficient Poisson equation on complex microstructures, suitable for the determination of effective thermal conductivity or tortuosity of a material. The method uses a Marching Cubes/Marching Squares surface reconstruction to create cut-cells and determine geometric quantities. A flux-correction method is extended to 3D, with least squares gradient reconstruction, to solve for the boundary fluxes in the cut-cells. Verification cases show the solver achieves globally 2nd order accuracy on complex microstructures. TomoSAM TomoSAM, a module of the PuMA software, has been developed as a plugin for 3D Slicer, a software platform used for 3D image processing and visualization. It utilizes the Segment Anything Model (SAM), a deep learning model capable of identifying objects and generating image masks based on minimal user input. This feature enables efficient segmentation of complex 3D datasets, particularly of woven materials, from tomography or similar imaging methods, reducing the need for manual segmentation.

Tomography↗
NASA NTRSDate not supplied

Recent Developments to the Porous Microstructure Analysis (PuMA) Software

The Porous Microstructure Analysis (PuMA) software is an open source framework for image-based simulation, primarily used to determine effective properties based on material microstructure. PuMA was originally developed for the study of NASA thermal protection materials; however, many of the solvers in PuMA have applicability to a broad range of materials science applications. PuMA version 3.2 computes material surface area, pore diameters, effective thermal conductivity, continuum and rarefied tortuosity, and permeability. For anisotropic materials, PuMA can estimate material orientation and compute anisotropic thermal conductivity and elasticity. In this talk, a brief overview of the PuMA software and underlying methods will be presented, as well as some recent and ongoing developments, including the use of immersed boundary methods for image-based simulation and the development of a new weave segmentation tool, called TomoSAM. Cut-Cell method for heat and mass transfer For simulations on complex microstructures, traditional unstructured meshing techniques often prove to be difficult and time-intensive. Voxel-based solvers, which represent the surface as a staircase structure, are relatively simple to implement but can lose accuracy when feature resolution is poor. In this work, we present a novel 3D cut-cell method for solving the variable coefficient Poisson equation on complex microstructures, suitable for the determination of effective thermal conductivity or tortuosity of a material. The method uses a Marching Cubes/Marching Squares surface reconstruction to create cut-cells and determine geometric quantities. A flux-correction method is extended to 3D, with least squares gradient reconstruction, to solve for the boundary fluxes in the cut-cells. Verification cases show the solver achieves globally 2nd order accuracy on complex microstructures. TomoSAM TomoSAM, a module of the PuMA software, has been developed as a plugin for 3D Slicer, a software platform used for 3D image processing and visualization. It utilizes the Segment Anything Model (SAM), a deep learning model capable of identifying objects and generating image masks based on minimal user input. This feature enables efficient segmentation of complex 3D datasets, particularly of woven materials, from tomography or similar imaging methods, reducing the need for manual segmentation.

Tomography↗
NASA NTRS2016

Unique Results and Lessons Learned from the TSS Missions

In 1924, Irvin Langmuir and H. M. Mott-Smith published a theoretical model for the complex plasma sheath phenomenon in which they identified some very special cases which greatly simplified the sheath and allowed a closed solution to the problem. The most widely used application is for an electrostatic, or "Langmuir," probe in laboratory plasma. Although the Langmuir probe is physically simple (a biased wire) the theory describing its functional behavior and its current-voltage characteristic is extremely complex and, accordingly, a number of assumptions and approximations are used in the LMS model. These simplifications, correspondingly, place limits on the model's range of application. Adapting the LMS model to real-life conditions is the subject of numerous papers and dissertations. The Orbit-Motion Limited (OML) model that is widely used today is one of these adaptions that is a convenient means of calculating sheath effects. The OML equation for electron current collection by a positively biased body is simply: I is approximately equal to A x j(sub eo) x 2/√𝜋(phi)(exp ½) where A is the area of the body and phi is the electric potential on the body with respect to the plasma. Since the Langmuir probe is a simple biased wire immersed in plasma, it is particularly tempting to use the OML equation in calculating the characteristics of the long, highly biased wires of an Electric Sail in the solar wind plasma. However, in order to arrive at the OML equation, a number of additional simplifying assumptions and approximations (beyond those made by Langmuir-Mott-Smith) are necessary. The OML equation is a good approximation when all conditions are met, but it would appear that the Electric Sail problem lies outside of the limits of applicability.

Stone, Nobie H.↗
DOE OSTI2024

Uncertainty quantification of graph convolution neural network models of evolving processes

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural networks have proved to be adept at modeling processes with spatial–temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial–temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar pushed forward uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance. As a result, projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Data-based filtered dissipation rate modelling for multi-modal turbulent combustion: evaluating a priori model generalizability

Manifold-based models offer a computationally efficient alternative to directly transporting the thermochemical state in computational simulations of turbulent reacting flows, projecting the high-dimensional thermochemical state-space onto a low-dimensional manifold. Recent efforts have yielded a manifold-based model applicable to multi-modal combustion, enabling reconstruction of the thermochemical state from solutions to two-dimensional manifold equations in mixture fraction and generalized progress variable that are parameterised by three scalar dissipation rates. In coarse-grained simulations such as Large Eddy Simulation (LES), closure of the multi-modal manifold equations and subfilter variances/covariance requires closure of three filtered scalar dissipation rates. Here, the present work adopts a data-based approach, providing closure for the three filtered scalar dissipation rates via deep neural networks (DNNs). High-fidelity datasets corresponding to an autoigniting n-dodecane jet flame and a bluff body swirl-stabilized confined lifted spray flame of two aviation fuels (Jet-A and C1) with different ignition propensities are leveraged to generate training data that spans a diverse range of thermodynamic conditions and combustion modes, including low- and high-temperature ignition regimes in addition to premixed and nonpremixed behaviour. A final DNN model is trained to enforce inherent physical constraints by learning nonlinear functional transformations of the three filtered scalar dissipation rates. The generalizability of this constrained DNN model is demonstrated a priori via conditional statistics evaluated on the lifted spray flame with C1–a configuration that had not been included in the training data. Excellent DNN agreement with conditional DNS statistics is observed, and integrated gradients are computed to identify the most sensitive input variables. The similarity of the marginal PDFs of the most informative input variables and outputs across configurations are quantified via the Wasserstein metric, demonstrating that data-based models may successfully generalize to unseen parametric conditions so long as the most informative input variables share similar distributions across training and testing datasets.

Data-based modelling↗
NASA NTRS1998

Expert System Architecture for Rocket Engine Numerical Simulators: A Vision

Simulation of any complex physical system like rocket engines involves modeling the behavior of their different components using mostly numerical equations. Typically a simulation package would contain a set of subroutines for these modeling purposes and some other ones for supporting jobs. A user would create an input file configuring a system (part or whole of a rocket engine to be simulated) in appropriate format understandable by the package and run it to create an executable module corresponding to the simulated system. This module would then be run on a given set of input parameters in another file. Simulation jobs are mostly done for performance measurements of a designed system, but could be utilized for failure analysis or a design job such as inverse problems. In order to use any such package the user needs to understand and learn a lot about the software architecture of the package, apart from being knowledgeable in the target domain. We are currently involved in a project in designing an intelligent executive module for the rocket engine simulation packages, which would free any user from this burden of acquiring knowledge on a particular software system. The extended abstract presented here will describe the vision, methodology and the problems encountered in the project. We are employing object-oriented technology in designing the executive module. The problem is connected to the areas like the reverse engineering of any simulation software, and the intelligent systems for simulation.

Mitra, D.↗
DOE OSTI2024

Non-Intrusive Parallel-in-Time Solvers for Partial Differential Equations (Final Report)

Many time-dependent problems and simulations are often modeled using Partial Differential Equations. Traditional modeling approaches that use sequential time-stepping are reaching a bottleneck in optimizing efficiency. The Center of Applied Science and Computing at Lawrence Livermore National Laboratory extensively works on parallelizing these algorithms to leverage the increasing computational power from the growing number of processors in computer hardware. In particular, they aim to design non-intrusive algorithms that can generalize to a variety of problems and sizes without requiring additional information from or modifications on the original problems. Multigrid Reduction in Time (MGRIT) is a parallel-in-time algorithm that is designed to be non-intrusive. This project focuses on increasing the efficiency of MGRIT by approximating the coarse-grid operator using machine learning approaches as a means to find the most non-intrusive, or general, solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak

The linear response of a plasma to perturbations of arbitrary frequency and wavelength is derived for any axisymmetric magnetized toroidal plasma. An explicit transformation to action-angle coordinates is achieved using orthogonal magnetic coordinates and the Littlejohn Lagrangian, establishing the validity of this result to arbitrary order in normalized Larmor radius. The global resonance condition for compressional modes is clarified in more detail than in previous works, confirming that the poloidal orbit-average of the cyclotron frequency gives the desired result at lowest order in Larmor radius. The global plasma response to the perturbation at each resonance is captured by a poloidal and gyroaverage of the perturbing potential. A “global gyroaveraging” of the potential is a natural by-product of this analysis which takes into account the changing of the magnetic field over an orbit. The resonance condition depends on two arbitrary integers which completely separately capture the effects poloidal non-uniformity and finite Larmor radius in generating sidebands. We learn that poloidal sidebands generated for compressional modes are dominated by the change in gyrofrequency over the orbit, which is very different to shear modes where the gyrofrequency only contributes via a finite Larmor radius effect. This increases the number of bounce harmonics required to compute the linear drive, giving a more complicated resonance map. An example calculation is given comparing resonance of shear and compressional modes in a published DIII-D case.

Compressional↗
DOE OSTI2026

A Statistician’s Overview of Physics-Informed Neural Networks for Spatio-Temporal Data

The recent success of deep neural network models with physical constraints (so-called, Physics-Informed Neural Networks, PINNs) has led to renewed interest in the incorporation of mechanistic information in predictive models. Statisticians and others have long been interested in this problem, which has led to several practical and innovative solutions dating back decades. In this overview, we focus on the problem of data-driven prediction and inference of dynamic spatio-temporal processes that include mechanistic information, such as would be available from partial differential equations, with a strong focus on the quantification of uncertainty associated with data, process, and parameters. Here, we give a brief review of several paradigms and focus our attention on Bayesian implementations given they naturally accommodate uncertainty quantification. We then show that it is straight-forward to include the Bayesian PINN (B-PINN) within the Bayesian hierarchical model (BHM) framework that has long been considered for modeling dynamic spatio-temporal processes. Such a BHM-PINN is illustrated via a simulation study in which a latent nonlinear Burgers’ equation PDE governs the dynamics of Poisson distributed spatio-temporal data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Bayesian↗
DOE OSTI2025

Surrogate modeling of Cellular-Potts agent-based models as a segmentation task using the U-Net neural network architecture

The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 562 times compared to single-core CPM code execution on CPU. Over short timescales of up to 3 recursive evaluations, or 300 MCS, our model captures the emergent behaviors demonstrated by the original Cellular-Potts model such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as a step toward efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM simulations of biological processes.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2013

Analyses Made to Order: Using Transformation to Rapidly Configure a Multidisciplinary Environment

Aerospace problems are highly multidisciplinary. Four or more major disciplines are involved in analyzing any particular vehicle. Moreover, the choice of implementation technology of various subsystems can lead to a change of leading domain or reformation of the driving equations. An excellent example is the change of expertise required to consider aircraft built from composite or metallic structures, or those propelled by chemical or electrical thrusters. Another example is in the major reconfiguration of handling and stability equations with different control surface configuration (e.g., canards, t-tail v four-post tail). Combinatorial problems are also commonplace anytime that a major system is to be designed. If there are only 5 attributes of a design to consider with 4 different options, this is already 1024 options. Adding just 5 more dimensions to the study explodes the space to over one million. Even generous assumptions like the idea that only 10% of the combinations are physically feasible can only contain the problem for so long. To make matters worse, the simple number of combinations is only the beginning. Combining the issue of trade space size with the need to reformulate the design problem for many of the possibilities makes life exponentially more difficult. Advances in software modeling approaches have led to the development of model-driven architecture. This approach uses the transformation of models into inferred models (e.g. inferred execution traces from state machines) or the skeletons for code generation. When the emphasis on transformation is applied to aerospace, it becomes possible to exploit redundancy in the information specified in multiple domain models into a unified system model. F1urther, it becomes possible to overcome the combinatorial nature of specifying integrated system behavior by manually combining the equations governing a given component technology. Transformations from a system specification combined with a system-analysis mapping specification enable one-click combination of domain analyses. This is a flexibility that has been missing from many engineering codes, which often entangle design specification and physical examination much more than is required to conduct the analysis. This capability has been investigated and cultivated within the DARPA F6 program by a team of JPL and Phoenix Integration engineers building the Adapatable Systems Design and Analysis (ASDA) framework. By embracing system modeling with SysML and the Query-View-Transformation (QVT) language, the ASDA team has been able to build a flexible, easily reconfigurable framework for building up and solving large tradespaces. Examples of application and lessons learned in building the framework will be described in this paper. In addition, the motivation will be laid for various tool vendors to develop open model description standards while being able to maintain competitive advantage through proprietary algorithms and approaches. These standards will also be compared to the underpinnings of model-driven architecture and the OMG standards of the Meta-Object Facility (MOF), SysML, and QVT.

Cole, Bjorn↗
NASA NTRS1989

Optimal selection of space transportation fleet to meet multi-mission space program needs

A space program that spans several decades will be comprised of a collection of missions such as low earth orbital space station, a polar platform, geosynchronous space station, lunar base, Mars astronaut mission, and Mars base. The optimal selection of a fleet of several recoverable and expendable launch vehicles, upper stages, and interplanetary spacecraft necessary to logistically establish and support these space missions can be examined by means of a linear integer programming optimization model. Such a selection must be made because the economies of scale which comes from producing large quantities of a few standard vehicle types, rather than many, will be needed to provide learning curve effects to reduce the overall cost of space transportation if these future missions are to be affordable. Optimization model inputs come from data and from vehicle designs. Each launch vehicle currently in existence has a launch history, giving rise to statistical estimates of launch reliability. For future, not-yet-developed launch vehicles, theoretical reliabilities corresponding to the maturity of the launch vehicles' technology and the degree of design redundancy must be estimated. Also, each such launch vehicle has a certain historical or estimated development cost, tooling cost, and a variable cost. The cost of a launch used in this paper includes the variable cost plus an amortized portion of the fixed and development costs. The integer linear programming model will have several constraint equations based on assumptions of mission mass requirements, volume requirements, and number of astronauts needed. The model will minimize launch vehicle logistic support cost and will select the most desirable launch vehicle fleet.

Morgenthaler, George W.↗