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 289 records · Page 16

Fuzzy Modeling and Parallel Distributed Compensation for Aircraft Flight Control from Simulated Flight Data

A method is described that combines fuzzy system identification techniques with Parallel Distributed Compensation (PDC) to develop nonlinear control methods for aircraft using minimal a priori knowledge, as part of NASA’s Learn-to-Fly initiative. A fuzzy model was generated with simulated flight data, and consisted of a weighted average of multiple linear time invariant state-space cells having parameters estimated using the equation-error approach and a least-squares estimator. A compensator was designed for each subsystem using Linear Matrix Inequalities (LMI) to guarantee closed-loop stability and performance requirements. This approach is demonstrated using simulated flight data to automatically develop a fuzzy model and design control laws for a simplified longitudinal approximation of the F-16 nonlinear flight dynamics simulation. Results include a comparison of flight data with the estimated fuzzy models and simulations that illustrate the feasibility and utility of the combined fuzzy modeling and control approach.

Weinstein, Rose↗

Active learning emulators for nuclear two-body scattering in momentum space

In this work we extend the active learning emulators for two-body scattering in coordinate space with error estimation, recently developed by Maldonado et al. [Phys. Rev. C 112, 024002], to coupled-channel scattering in momentum space. Our full-order model (FOM) solver is based on the Lippmann-Schwinger integral equation for the scattering t-matrix as opposed to the radial Schrödinger equation. We use (Petrov-)Galerkin projections and high-fidelity calculations at a few snapshots across the parameter space of the interaction to construct efficient reduced-order models (ROMs), trained by a greedy algorithm for locally optimal snapshot selection. Both the FOM solver and the corresponding ROMs are implemented efficiently in Python using Google's JAX library. We present results for emulating scattering phase shifts in coupled and uncoupled channels and cross sections, and assess the accuracy of the developed ROMs and their computational speedup factors. We also develop emulator error estimation for both the t-matrix and the total cross section. The software framework for reproducing and extending our results is publicly available. Together with our recent advances in developing active-learning emulators for three-body scattering, these emulator frameworks set the stage for full Bayesian calibrations of chiral nuclear interactions and optical models against scattering data with quantified emulator errors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Development and assessment of hierarchical multi-reward reinforcement learning based potential for silicene with state-of-the-art models

We develop a new interatomic force field for Silicene, a 2D material with a buckled hexagonal lattice structure with high polymorphism. We introduce new parameterizations of a Tersoff model using a hierarchical multi-reward reinforcement learning (RL) methodology coupled with a continuous Monte Carlo Tree Search optimization. Our model significantly outperforms existing methods by enhancing the accuracy of predictions for the structural and thermodynamic properties of seven silicene polymorphs-including structure, energy, equation of state, elasticity, and phonon dispersion-when compared to established models. We further make a comprehensive comparison of the various models in predicting the mechanical and thermal properties of silicene. We trace the origin of the improved performance to the description of the angular dependence in the bond-order term, suggesting that modifying the angular terms in short-range models is essential to capture the structural diversity in low dimensional systems.

2D materials↗

Metrics and extrapolation of resonant magnetic perturbation thresholds for ELM suppression

This large database study of resonant magnetic perturbation (RMP) edge localized mode (ELM) suppression thresholds in the AUG, DIII-D, EAST, and KSTAR tokamaks details the key strengths and weaknesses of RMP metrics. The RMP ELM suppression database used for this work contains plasma information at the time of transition from ELMing to ELM suppressed states where a clear experimental threshold is identified. The experimental threshold distributions are compared for five metrics: (1) the island overlap width, (2) pedestal top Chirikov overlap, (3) peeling edge displacement, (4) pedestal top resonant drive, and (5) edge dominant mode overlap. The distributions, the regularity of the dependence on RMP coil currents, and the sensitivities of a given metric to equilibrium reconstruction details are compared. The overlap metric proves to be a good compromise between including the appropriate plasma response physics and maintaining a numerical robustness. This quantity does not exhibit clear power-law scalings for projection, but machine learning can assist in predicting thresholds within the existing parameter ranges and providing uncertainty quantification of those predictions. Two new first-principles models, one utilizing a threshold from the non-linear Modified Rutherford equation evaluated at the pedestal top and one utilizing the SLAYER code to calculate the linear tearing threshold from torque balance, offer possible paths to extrapolation beyond the existing database parameter space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Grey-Box System Identification of Grid-Forming Inverters

This paper demonstrates the use of grey-box system identification methods for simplifying and understanding the nonlinear power dynamics of grid-forming inverters (GFMs). The power and frequency outputs of complex high-order GFM models are fed into system identification software in order to fit them to a predetermined LTI system and learn system parameters such as (synthetic) inertia and droop constants. The same process is then run for a high-order synchronous generator model, and the outputs are fit to the same set of LTI equations. Simulation of a network of GFM inverters with diverse control architecture is also performed for the same process. The intent is threefold: first, to demonstrate the appropriateness of unified LTI models for describing the power and frequency dynamics of individual resources and connected networks, in order to facilitate analysis of larger heterogeneous networked systems; second, to discover the relationship between internal control parameters of GFMs and their externally observed values; and third, to validate that grey-box data-driven system identification techniques can be a valuable tool to discover the values of important parameters in the absence of explicit vendor models.

analytical models↗

Some Aspects of Bifurcation Structure of Laminar Flow in Curved Ducts

A bifurcation study is made of laminar flow in curved ducts. The problem is formulated in a curvilinear coordinate system, and the governing equations, after orthogonal mapping is applied, are solved numerically by an iterative finite-difference method. Many computer runs were made with various duct cross-sections ranging from a circle to a square, to learn the transition of bifurcation structure with this change in cross-section and to reconcile the differences between them. In addition, a simpler technique is proposed to generate symmetric four-cell solutions in a circular pipe and a means is put forward to stabilize four-vortex structures in a complete cross-section.

Kao, Hsiao C.↗

Working With the Wave Equation in Aeroacoustics: The Pleasures of Generalized Functions

The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun.

Farassat, F.↗

Recurrent convolutional neural networks for modeling nonadiabatic dynamics of quantum-classical systems

Recurrent neural networks (RNNs) have recently been extensively applied to model the time evolution in fluid dynamics, weather predictions, and even chaotic systems due to their ability to capture temporal dependencies and sequential patterns in data. Here we present an RNN model based on convolutional neural networks for modeling the nonlinear nonadiabatic dynamics of hybrid quantum-classical systems. The dynamical evolution of the hybrid systems is governed by equations of motion for classical degrees of freedom and von Neumann equation for electrons. The Physics-Aware Recurrent Convolution (PARC) neural network structure incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. Here, we apply our RNN approach to learn the space-time evolution of a one-dimensional semiclassical Holstein model after an interaction quench. For shallow quenches (small changes in electron-lattice coupling), the deterministic dynamics can be accurately captured using a single-CNN-based recurrent network. In contrast, deep quenches induce chaotic evolution, making long-term trajectory prediction significantly more challenging. Nonetheless, we demonstrate that the PARC-CNN architecture can effectively learn the statistical climate of the Holstein model under deep-quench conditions.

Holstein model↗

Automated Knowledge Discovery From Simulators

A computational method, SimLearn, has been devised to facilitate efficient knowledge discovery from simulators. Simulators are complex computer programs used in science and engineering to model diverse phenomena such as fluid flow, gravitational interactions, coupled mechanical systems, and nuclear, chemical, and biological processes. SimLearn uses active-learning techniques to efficiently address the "landscape characterization problem." In particular, SimLearn tries to determine which regions in "input space" lead to a given output from the simulator, where "input space" refers to an abstraction of all the variables going into the simulator, e.g., initial conditions, parameters, and interaction equations. Landscape characterization can be viewed as an attempt to invert the forward mapping of the simulator and recover the inputs that produce a particular output. Given that a single simulation run can take days or weeks to complete even on a large computing cluster, SimLearn attempts to reduce costs by reducing the number of simulations needed to effect discoveries. Unlike conventional data-mining methods that are applied to static predefined datasets, SimLearn involves an iterative process in which a most informative dataset is constructed dynamically by using the simulator as an oracle. On each iteration, the algorithm models the knowledge it has gained through previous simulation trials and then chooses which simulation trials to run next. Running these trials through the simulator produces new data in the form of input-output pairs. The overall process is embodied in an algorithm that combines support vector machines (SVMs) with active learning. SVMs use learning from examples (the examples are the input-output pairs generated by running the simulator) and a principle called maximum margin to derive predictors that generalize well to new inputs. In SimLearn, the SVM plays the role of modeling the knowledge that has been gained through previous simulation trials. Active learning is used to determine which new input points would be most informative if their output were known. The selected input points are run through the simulator to generate new information that can be used to refine the SVM. The process is then repeated. SimLearn carefully balances exploration (semi-randomly searching around the input space) versus exploitation (using the current state of knowledge to conduct a tightly focused search). During each iteration, SimLearn uses not one, but an ensemble of SVMs. Each SVM in the ensemble is characterized by different hyper-parameters that control various aspects of the learned predictor - for example, whether the predictor is constrained to be very smooth (nearby points in input space lead to similar output predictions) or whether the predictor is allowed to be "bumpy." The various SVMs will have different preferences about which input points they would like to run through the simulator next. SimLearn includes a formal mechanism for balancing the ensemble SVM preferences so that a single choice can be made for the next set of trials.

Burl, Michael↗

AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks

We propose the artificial intelligence velocimetry-thermometry (AIVT) method to reconstruct a continuous and differentiable representation of the temperature and velocity in turbulent convection from measured three-dimensional (3D) velocity data. AIVT is based on physics-informed Kolmogorov-Arnold networks and trained by optimizing a loss function that minimizes residuals of the velocity data, boundary conditions, and governing equations. We apply AIVT to a set of simultaneously measured 3D temperature and velocity data of Rayleigh-Bénard convection, obtained by combining particle image thermometry and Lagrangian particle tracking. This enables us to directly compare machine learning results to true volumetric, simultaneous temperature and velocity measurements. We demonstrate that AIVT can reconstruct and infer continuous, instantaneous velocity and temperature fields and their gradients from sparse experimental data at a high resolution, providing an additional approach for understanding thermal turbulence.

Science & Technology - Other Topics↗

An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.

42 ENGINEERING↗

Designing a quantum-accurate machine-learning potential to enable large-scale simulations of deuterium under shock

Large-scale molecular dynamics of deuterium under shock can elucidate kinetic processes vital to the target design in inertial confinement fusion and high-energy-density experiments. However, modeling the complex evolution of this material from an insulating molecular state at ambient pressure to an ionized, atomic fluid under strong shock is beyond the capability of simple pair and even bond order potentials. We thus train a quantum-accurate and broadly transferable machine-learning interatomic potential for deuterium using the Chebyshev Interaction Model for Efficient Simulations framework. We show that due to an improved description of the molecular-to-atomic transition, our model is able to better reproduce the ab initio equation of state, radial distribution functions, and principal Hugoniot than bond order potentials. This represents an important step toward large-scale quantum-accurate and nonequilibrium simulations of complicated systems under dynamic changes including phase transitions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NLML: A Deep Neural Network Emulator for the Exact Nonlinear Interactions in a Wind Wave Model

Nonlinear wave interactions describe the resonant energy transfer between wave components, playing a fundamental role in the evolution of ocean wave spectra. Nonlinear wave interactions significantly influence wave growth and development, making them essential for accurate wave modeling. However, resolving the full six-dimensional Boltzmann integral of the exact nonlinear wave interactions (Webb-Resio-Tracy method, WRT) is computationally expensive, limiting its application in real-time operational wave forecasting and for research purposes. Current approximations, such as the Discrete Interaction Approximation (DIA), prioritize computational speed over accuracy, resulting in significant errors in wave mean parameters. Here, we introduce NLML, a machine learning (ML) emulator designed to approximate the exact nonlinear wave interactions within WAVEWATCH III (WW3), with the goal of achieving the accuracy of WRT while maintaining the stability and computational speed of DIA. By leveraging GPU capabilities such as half precision inference, we achieved substantial speedups, up to 136x mathematical equation faster than the WRT and only a modest 1.04x mathematical equation slowdown relative to DIA, while achieving 2x mathematical equation the accuracy of DIA in global wave spectral energy and mean wave parameters, with up to 7x mathematical equation higher accuracy in some regions. Unlike previous ML approaches, NLML maintained inherent stability throughout model integration in a standalone, year-long WW3 simulation, without requiring additional constraints. Our new ML parameterization bridges the gap between accuracy and efficiency, offering a promising alternative for improving wave modeling in operational settings and research purposes.

16 TIDAL AND WAVE POWER↗

Real-time dynamics of the Schwinger model as an open quantum system with Neural Density Operators

Ab-initio simulations of multiple heavy quarks propagating in a Quark-Gluon Plasma are computationally difficult to perform due to the large dimension of the space of density matrices. This work develops machine learning algorithms to overcome this difficulty by approximating exact quantum states with neural network parametrisations, specifically Neural Density Operators. As a proof of principle demonstration in a QCD-like theory, the approach is applied to solve the Lindblad master equation in the 1 + 1d lattice Schwinger Model as an open quantum system. Neural Density Operators enable the study of in-medium dynamics on large lattice volumes, where multiple-string interactions and their effects on string-breaking and recombination phenomena can be studied. Thermal properties of the system at equilibrium can also be probed with these methods by variationally constructing the steady state of the Lindblad master equation. Scaling of this approach with system size is studied, and numerical demonstrations on up to 32 spatial lattice sites and with up to 3 interacting strings are performed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Predicting U.S. federal fleet electric vehicle charging patterns using internal combustion engine vehicle fueling transaction statistics

Utilizing fueling transactions from internal combustion engine vehicles (ICEVs), the authors estimated how frequently midday public charging would be required for U.S. federal fleet battery electric vehicles (BEVs). Fueling transaction summary statistics are more widely available than trip-level telematics data, making this methodology more accessible and transferable to other researchers and fleet managers considering BEV replacements. For example, readers can easily apply a linear model using only the count of back-to-back fueling events at gas stations over 57 straight-line miles apart to predict days exceeding range. This linear regression predicted binned days exceeding 250 miles at 80% accuracy on a hold-out test set from the same fleet as the training data and 66 % accuracy on a new fleet displaying different driving behaviors. The authors additionally provide linear equations for days exceeding 200 and 300 miles as alternative range estimates to account for differences in BEV range and temperature impacts. Beyond the single-feature linear models which readers can apply, the authors tuned and trained other machine learning models on a variety of fueling transaction statistics including consecutive transaction distances, transaction distance from garage, estimated miles traveled from fuel economy and fuel quantity, and transaction periodicity. Utilizing a subset of 1678 light-duty federal fleet vehicles which contained daily vehicle miles traveled (VMT) in addition to fueling statistics, the authors determined which fueling transaction statistics were most relevant in predicting driving days exceeding 250 miles (an approximation of BEV rated driving range). In support of the U.S. federal fleet transition to zero-emission vehicles (ZEVs), the authors used these statistics and machine learning models to predict the frequency of BEV midday charging. After training models on the subset with VMT, the authors predicted days exceeding rated range for 112,902 light-duty vehicles operating in similar circumstances in the federal fleet using a Support Vector Regressor (SVR). In conclusion, they then used the projections as part of the ZEV Planning and Charging (ZPAC) tool to identify optimal candidates for BEVs for the federal fleet. An anonymized version of ZPAC is included in the supplementary materials.

25 ENERGY STORAGE↗

Effective many-body interactions in reduced-dimensionality spaces through neural network models

Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head on. Therefore, developing reduced-dimensionality representations that encapsulate complex correlation effects in many-body systems is crucial to advance the understanding of these complicated problems. However, a numerical evaluation of these predictive models can still be associated with a significant computational overhead. To address this challenge, in this paper we discuss a combined framework that integrates recent advances in the development of active-space representations of coupled cluster (CC) downfolded Hamiltonians with neural network approaches. The primary objective of this effort is to train neural networks to eliminate the computationally expensive steps required for evaluating hundreds or thousands of Hugenholtz diagrams, which correspond to multidimensional tensor contractions necessary for evaluating a many-body form of downfolded effective Hamiltonians. Using small molecular systems (the H 2 O and HF molecules) as examples, we demonstrate that training neural networks employing effective Hamiltonians for a few nuclear geometries of molecules can accurately interpolate or extrapolate their forms to other geometrical configurations characterized by different intensities of correlation effects. We also discuss differences between effective interactions that define CC downfolded Hamiltonians with those of bare Hamiltonians defined by Coulomb interactions in the active spaces. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗

Air Separation Using Hollow Fiber Membranes

The NASA Glenn Research Center in partnership with the Ohio Aerospace Institute provides internship programs for high school and college students in the areas of science, engineering, professional administrative, and other technical areas. During the summer of 2004, I worked with Dr. Clarence T. Chang at NASA Glenn Research Center s combustion branch on air separation using hollow fiber membrane technology. . In light of the accident of Trans World Airline s flight 800, FAA has mandated that a suitable solution be created to prevent the ignition of fuel tanks in aircrafts. In order for any type of fuel to ignite, three important things are needed: fuel vapor, oxygen, and an energy source. Two different ways to make fuel tanks less likely to ignite are reformulating the fuel to obtain a lower vapor pressure for the fuel and or using an On Board Inert Gas Generating System (OBIGGS) to inert the Central Wing Tank. goal is to accomplish the mission, which means that the Air Separation Module (ASM) tends to be bulky and heavy. The primary goal for commercial aviation companies is to transport as much as they can with the least amount of cost and fuel per person, therefore the ASM must be compact and light as possible. The plan is to take bleed air from the aircraft s engines to pass air through a filter first to remove particulates and then pass the air through the ASM containing hollow fiber membranes. In the lab, there will be a heating element provided to simulate the temperature of the bleed air that will be entering the ASM and analysis of the separated air will be analyzed by a Gas Chromatograph/Mass Spectrometer (GC/MS). The GUMS will separate the different compounds in the exit streams of the ASM and provide information on the performance of hollow fiber membranes. Hopefully I can develop ways to improve efficiency of the ASM. different types of jet fuel were analyzed and data was well represented on SAE Paper 982485. Data consisted of the concentrations of over 300 different hydrocarbons commonly found in JP- 8, Jet A, and JP-5 fuels. I researched the major hydrocarbons that has a concentration of greater than 50 parts per million and found the vapor pressure data coefficients for a specific temperature range. The coefficients were applied to Antoine s Equation and Riedel's Equation to calculate the vapor pressures for that specific hydrocarbon in the specific temperature range. With the vapor pressure data scientists can formulate a fuel composition that has a lower vapor pressure profile, therefore making jet fuels less flammable. work, learn how to operate and examine the data from Gas Chromatograph and Mass Spectrometer, and develop new ways in applying hollow fiber membrane technology to other areas of environmental engineering. The United States military currently uses air separation technology and their primary The other side of making air travel safer is to reformulate the fuel. Analyses of three My goal this summer is to learn about hollow fiber membrane technologies and how they

Huang, Stephen E.↗