Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “neural ordinary differential equations”

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.

Neural network error correction for solving coupled ordinary differential equations

A neural network is presented to learn errors generated by a numerical algorithm for solving coupled nonlinear differential equations. The method is based on using a neural network to correctly learn the error generated by, for example, Runge-Kutta on a model molecular dynamics (MD) problem. The neural network programs used in this study were developed by NASA. Comparisons are made for training the neural network using backpropagation and a new method which was found to converge with fewer iterations. The neural net programs, the MD model and the calculations are discussed.

Shelton, R. O.↗

Optimization with artificial neural network systems - A mapping principle and a comparison to gradient based methods

General formulae for mapping optimization problems into systems of ordinary differential equations associated with artificial neural networks are presented. A comparison is made to optimization using gradient-search methods. The performance measure is the settling time from an initial state to a target state. A simple analytical example illustrates a situation where dynamical systems representing artificial neural network methods would settle faster than those representing gradient-search. Settling time was investigated for a more complicated optimization problem using computer simulations. The problem was a simplified version of a problem in medical imaging: determining loci of cerebral activity from electromagnetic measurements at the scalp. The simulations showed that gradient based systems typically settled 50 to 100 times faster than systems based on current neural network optimization methods.

Leong, Harrison Monfook↗

Numerical solution of differential equations by artificial neural networks

Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks (ANN's) are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed by the author to mate the adaptability of the ANN with the speed and precision of the digital computer. This method has been successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

Meade, Andrew J., Jr.↗

Development of programmable artificial neural networks

Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed to mate the adaptability of the ANN with the speed and precision of the digital computer. This method was successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

Meade, Andrew J.↗

Uncertainty Quantification using Deep Ensembles for Decision Making in Cyber-Physical-Human Systems

In this paper and its companion, Differential Equation Approximation Using Gradient-Boosted Quantile Regression, Robison et al., we examine an approach to quantifying model uncertainty with the aim of increasing the trustworthiness of computational models in human-machine interactions. In Differential Equation Approximation Using Gradient-Boosted Quantile Regression, we focus on gradient-boosted decision trees, while in this one, we give more details about deep ensembles. Uncertainty quantification is crucial for building trustworthy autonomous decision-making agents in human-machine teams. There are two types of uncertainties: aleatoric and epistemic. The former is related to the inherent stochasticity (noise) of the process, whereas the latter is associated with the lack of knowledge or representation capability of models, such as neural networks. By lack of knowledge, we mean the model’s inability to accurately predict outputs for all possible inputs. The aleatory uncertainty can be estimated fairly easily with, for example, filters, whereas epistemic uncertainty is challenging to compute. This paper uses deep ensembles to quantify both aleatory and epistemic uncertainty. It can act as an uncertainty-aware surrogate transition model for decision-making frameworks. "Uncertainty-aware" means that the surrogate transition model should make predictions along with confidence in those predictions. In the context of decision-making, the transition models are ordinary differential equations (ODEs). Since ODEs can be simulated to make one-step or multi-step predictions, a good surrogate model for them should perform reasonably well in both modes. In a multi-step approach, the trajectory sampling method TS∞ was used to propagate uncertainty over multiple steps. The cartpole dynamical system was selected to demonstrate the ability of deep ensembles as good surrogate transition models for decision-making frameworks. The deep ensembles modeled the dynamics of cartpole ODEs and made uncertainty-aware predictions in single-step and multi-step transition modes.

CPH systems↗

Machine Learning based Aircraft Performance Model Estimation for Trajectory Prediction

The accurate prediction of aircraft trajectory by ground-based decision support tools is a critical component of air traffic management in the US National Airspace System (NAS). Accurate predictions of where the aircraft will be in the future or when they will arrive at specific locations (e.g., fixes) is a key enabler for sequencing and efficient arrival management of flights. Traditional physics based aircraft trajectory prediction relies on a simplified point-mass total energy model whose parameters are referred to as Aircraft Performance Model (APM) parameters. Even though the performance coefficients and weight of an aircraft are a vital part of the aircraft performance model’s predictions and accuracy, these coefficients are proprietary in nature and therefore, unavailable to decision-support tools. Current approaches freeze some coefficients to default base of aircraft data (BADA) values and optimize others. However, the APM parameters are highly coupled by the flight dynamics and prioritizing one parameter over others leads to bias and skewed predictions. To alleviate this problem, we provide a combined optimization framework to predict all the critical (thrust, drag and weight) APM parameters. This paper is focused on training Machine Learning (ML) models that map historical flights to optimized APM parameters that provide the best fit (in terms of prediction error). Our dataset obtained from NASA’s Sherlock data warehouse is comprised of thousands of historical flights and includes weather and track data collected from 2019. Using different subsets of relevant features (e.g., aircraft type), we trained several ML models to estimate the aircraft’s take off weight, drag polar coefficients (both parasitic and lift induced), and thrust settings (multiplier applied to the maximum engine thrust). The chosen flights are from three of the most common aircraft types (B738, B737, and A320) arriving at four airports (LAX, DEN, MSP, and DFW). Our ML approach is comprised of two different solutions: 1- using a subset of features that are known prior to the flight departure and do not change during flight (such as engine type, current temperature at departure & destination airports, aircraft type) and 2 - using a subset of temporal features of the flight trajectory (such as cruise altitude, Mach, airspeed, and rate of climb) in addition to the pre-departure features from the first solution. The labels or target variables are the APM parameters that were obtained by an optimized ordinary differential equations (ODE) fitting process (applied to individual flights). The ODE-fitting is very time intensive and is therefore performed offline. Thus, training an ML model to learn the relationship between the flight features and ODE-generated labels enables faster estimation of the APM parameters and is therefore amenable to real-time prediction. Various ML models including linear regression, random forest, XGBoost, and neural network were trained, and the results are compared. After model validation and hyperparameter-tuning, we observed that the Random Forest model outperformed the other three models by the overall mean square error (MSE) of 2% for the first solution and 1.5% for the second solution. Finally, the ML-derived parameters are compared against default BADA APM parameters using NASA’s Autonomy Development toolkit (ADK) simulation software. The simulation results for one of each aircraft type is shown and discussed.

Aida Sharif Rohani↗

Intelligent failure-tolerant control

An overview of failure-tolerant control is presented, focusing on the control of continuous-time dynamic systems (or plants) whose motions can be represented by integrals of nonlinear ordinary differential equations. Failure tolerance may be called upon to improve system reliability, maintainability, and survivability, and the issues attached to achieving these goals are examined. Robustness, which is required in some degree by all failure-tolerant systems, is discussed. The use of parallel redundancy is examined. Analytical redundancy, the principal functions of which are failure detection, failure identification, and control-system reconfiguration, is also considered. The use of expert systems and neural networks is discussed.

Stengel, Robert F.↗