Results for “gradient descent” — Page 5

NASA NTRS2006

Multiclass Reduced-Set Support Vector Machines

There are well-established methods for reducing the number of support vectors in a trained binary support vector machine, often with minimal impact on accuracy. We show how reduced-set methods can be applied to multiclass SVMs made up of several binary SVMs, with significantly better results than reducing each binary SVM independently. Our approach is based on Burges' approach that constructs each reduced-set vector as the pre-image of a vector in kernel space, but we extend this by recomputing the SVM weights and bias optimally using the original SVM objective function. This leads to greater accuracy for a binary reduced-set SVM, and also allows vectors to be 'shared' between multiple binary SVMs for greater multiclass accuracy with fewer reduced-set vectors. We also propose computing pre-images using differential evolution, which we have found to be more robust than gradient descent alone. We show experimental results on a variety of problems and find that this new approach is consistently better than previous multiclass reduced-set methods, sometimes with a dramatic difference.

reduced set methods↗

NASA NTRS2007

Space Invariant Independent Component Analysis and ENose for Detection of Selective Chemicals in an Unknown Environment

In this paper, we present a space invariant architecture to enable the Independent Component Analysis (ICA) to solve chemical detection from two unknown mixing chemical sources. The two sets of unknown paired mixture sources are collected via JPL 16-ENose sensor array in the unknown environment with, at most, 12 samples data collected. Our space invariant architecture along with the maximum entropy information technique by Bell and Sejnowski and natural gradient descent by Amari has demonstrated that it is effective to separate the two mixing unknown chemical sources with unknown mixing levels to the array of two original sources under insufficient sampled data. From separated sources, they can be identified by projecting them on the 11 known chemical sources to find the best match for detection. We also present the results of our simulations. These simulations have shown that 100% correct detection could be achieved under the two cases: a) under-completed case where the number of input (mixtures) is larger than number of original chemical sources; and b) regular case where the number of input is as the same as the number of sources while the time invariant architecture approach may face the obstacles: overcomplete case, insufficient data and cumbersome architecture.

ENose↗

NASA NTRS2005

Kurtosis Approach Nonlinear Blind Source Separation

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation Keywords: Independent Component Analysis, Kurtosis, Higher order statistics.

Duong, Vu A.↗

NASA NTRS2005

Kurtosis Approach for Nonlinear Blind Source Separation

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation.

kurtosis↗

NASA NTRS2012

Preliminary Exploration of Adaptive State Predictor Based Human Operator Modeling

Control-theoretic modeling of the human operator dynamic behavior in manual control tasks has a long and rich history. In the last two decades, there has been a renewed interest in modeling the human operator. There has also been significant work on techniques used to identify the pilot model of a given structure. The purpose of this research is to attempt to go beyond pilot identification based on collected experimental data and to develop a predictor of pilot behavior. An experiment was conducted to quantify the effects of changing aircraft dynamics on an operator s ability to track a signal in order to eventually model a pilot adapting to changing aircraft dynamics. A gradient descent estimator and a least squares estimator with exponential forgetting used these data to predict pilot stick input. The results indicate that individual pilot characteristics and vehicle dynamics did not affect the accuracy of either estimator method to estimate pilot stick input. These methods also were able to predict pilot stick input during changing aircraft dynamics and they may have the capability to detect a change in a subject due to workload, engagement, etc., or the effects of changes in vehicle dynamics on the pilot.

Trujillo, Anna C.↗

NASA NTRS2015

Adaptive State Predictor Based Human Operator Modeling on Longitudinal and Lateral Control

Control-theoretic modeling of the human operator dynamic behavior in manual control tasks has a long and rich history. In the last two decades, there has been a renewed interest in modeling the human operator. There has also been significant work on techniques used to identify the pilot model of a given structure. The purpose of this research is to attempt to go beyond pilot identification based on collected experimental data and to develop a predictor of pilot behavior. An experiment was conducted to categorize these interactions of the pilot with an adaptive controller compensating during control surface failures. A general linear in-parameter model structure is used to represent a pilot. Three different estimation methods are explored. A gradient descent estimator (GDE), a least squares estimator with exponential forgetting (LSEEF), and a least squares estimator with bounded gain forgetting (LSEBGF) used the experiment data to predict pilot stick input. Previous results have found that the GDE and LSEEF methods are fairly accurate in predicting longitudinal stick input from commanded pitch. This paper discusses the accuracy of each of the three methods - GDE, LSEEF, and LSEBGF - to predict both pilot longitudinal and lateral stick input from the flight director's commanded pitch and bank attitudes.

Trujillo, Anna C.↗

NASA NTRS2009

Sequential Principal Component Analysis -An Optimal and Hardware-Implementable Transform for Image Compression

This paper presents the JPL-developed Sequential Principal Component Analysis (SPCA) algorithm for feature extraction / image compression, based on "dominant-term selection" unsupervised learning technique that requires an order-of-magnitude lesser computation and has simpler architecture compared to the state of the art gradient-descent techniques. This algorithm is inherently amenable to a compact, low power and high speed VLSI hardware embodiment. The paper compares the lossless image compression performance of the JPL's SPCA algorithm with the state of the art JPEG2000, widely used due to its simplified hardware implementability. JPEG2000 is not an optimal data compression technique because of its fixed transform characteristics, regardless of its data structure. On the other hand, conventional Principal Component Analysis based transform (PCA-transform) is a data-dependent-structure transform. However, it is not easy to implement the PCA in compact VLSI hardware, due to its highly computational and architectural complexity. In contrast, the JPL's "dominant-term selection" SPCA algorithm allows, for the first time, a compact, low-power hardware implementation of the powerful PCA algorithm. This paper presents a direct comparison of the JPL's SPCA versus JPEG2000, incorporating the Huffman and arithmetic coding for completeness of the data compression operation. The simulation results show that JPL's SPCA algorithm is superior as an optimal data-dependent-transform over the state of the art JPEG2000. When implemented in hardware, this technique is projected to be ideally suited to future NASA missions for autonomous on-board image data processing to improve the bandwidth of communication.

Duong, Tuan A.↗

NASA NTRS2012

A Robust Initialization Scheme for a Lateral Trajectory Optimization Problem with Time of Arrival Windows

We present a robust initialization scheme that estimates parameter values for the numerical solution of a two-point boundary value problem. The two-point boundary value problem formulation stems from the optimization of a cost functional subject to the dynamics of a simplified lateral aircraft model and other constraints. Leveraging regular perturbation methods, initial parameter estimates are analytically determined and used to initialize a gradient descent optimization routine which is shown to rapidly converge over a range of initial aircraft positions and heading angles. Additionally, the velocity of the aircraft is optimized to ensure the trajectory of the aircraft terminates within a desired region in both time and space.

lateral trajectory optimization↗

NASA NTRSDate not supplied

MULTI-OBJECTIVE REINFORCEMENT LEARNING FOR LOW-THRUST TRANSFER DESIGN BETWEEN LIBRATION POINT ORBITS

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective reinforcement learning algorithm used to construct low-thrust transfers between periodic orbits in multi-body systems. Previous implementations of MRPPO have relied on a predefined reference transfer to successfully train each policy. In this paper, an algorithmic modification labeled the ‘moving reference’, is introduced to autonomously construct these reference trajectories during training. With this modification, MRPPO is used to recover various low-thrust transfers between two periodic orbits in the Earth-Moon circular restricted three-body problem to solve a multi-objective optimization problem. These results are then compared with the solutions recovered via a gradient descent optimization scheme to validate the performance of MRPPO with the moving reference modification.

Christopher J. Sullivan↗

NASA NTRSDate not supplied

MULTI-OBJECTIVE REINFORCEMENT LEARNING FOR LOW-THRUST TRANSFER DESIGN BETWEEN LIBRATION POINT ORBITS

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective reinforcement learning algorithm used to construct low-thrust transfers between periodic orbits in multi-body systems. Previous implementations of MRPPO have relied on a predefined reference transfer to successfully train each policy. In this paper, an algorithmic modification labeled the ‘moving reference’, is introduced to autonomously construct these reference trajectories during training. With this modification, MRPPO is used to recover various low-thrust transfers between two periodic orbits in the Earth-Moon circular restricted three-body problem to solve a multi-objective optimization problem. These results are then compared with the solutions recovered via a gradient descent optimization scheme to validate the performance of MRPPO with the moving reference modification

Christopher John Sullivan↗

NASA NTRS2021

AIRS Point Spread Function Reconstruction using AIRS and MODIS Data

The purpose of this work is to use data from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) to refine our knowledge of post-launch AIRS point spread functions (PSFs), including suspected changes over the mission. We develop methodology, by deriving mathematical optimization formulation based on variational principles and Sobolev gradient descent, for reconstruction of AIRS spatial response functions. We use the data over the ocean, collected for the duration of a day, to reconstruct a single PSF. We examine the repeatability of our reconstructions by computing PSFs based on data collected during two consecutive days, and also investigating the change in the reconstructions by comparing the reconstructed PSF based on data collected in the beginning and the middle of the mission. We also quantify uncertainties in our reconstruction results.

Vese, Luminita↗

NASA NTRS2021

Multi-objective Reinforcement Learning for Low-thrust Transfer Design Between Libration Point Orbits

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective rein- forcement learning algorithm used to construct low-thrust transfers between pe- riodic orbits in multi-body systems. Previous implementations of MRPPO have relied on a predefined reference transfer to successfully train each policy. In this paper, an algorithmic modification labeled the ‘moving reference’, is introduced to autonomously construct these reference trajectories during training. With this modification, MRPPO is used to recover various low-thrust transfers between two periodic orbits in the Earth-Moon circular restricted three-body problem to solve a multi-objective optimization problem. These results are then compared with the solutions recovered via a gradient descent optimization scheme to validate the performance of MRPPO with the moving reference modification.

Anderson, Rodney L.↗

NASA NTRS2021

Multi-objective Reinforcement Learning for Low-thrust Transfer Design Between Libration Point Orbits

Multi-Reward Proximal Policy Optimization (MRPPO) is a multi-objective rein- forcement learning algorithm used to construct low-thrust transfers between pe- riodic orbits in multi-body systems. Previous implementations of MRPPO have relied on a predefined reference transfer to successfully train each policy. In this paper, an algorithmic modification labeled the ‘moving reference’, is introduced to autonomously construct these reference trajectories during training. With this modification, MRPPO is used to recover various low-thrust transfers between two periodic orbits in the Earth-Moon circular restricted three-body problem to solve a multi-objective optimization problem. These results are then compared with the solutions recovered via a gradient descent optimization scheme to validate the performance of MRPPO with the moving reference modification.

Anderson, Rodney L↗

NASA NTRSDate not supplied

Multi-Agent Search and Rescue Applied to a Swarm of Ground Vehicles

This paper presents an algorithm for efficient search and rescue using a multi-agent system of vehicles. The algorithm uses an artificial potential field combined with a time-varying reward function for visiting various points within the search area. The reward function is used as a weight for the attractiveness of these points in the potential field. The reward value increases while the point is not being observed, and decreases while the point is observed. Collision avoidance terms are used to repel vehicles from each other, which has the additional effect of reducing duplication of searching efforts. Gradient descent of the potential field results in persistent surveillance of the search area. The algorithm generates position commands in real-time based on communication with the other vehicles. This framework allows vehicles to react in a dynamic environment, which is a significant advantage to simply following a-priori defined trajectories. The algorithm is applied to a swarm of ground robots, and experimental data is presented showing that the swarm effectively searches the entire area and self-allocates search regions to individual vehicles.

multi-agent↗

NASA NTRS2024

Accelerating Continuous Variable Coherent Ising Machines Via Momentum

The Coherent Ising Machine (CIM) is a non-conventional architecture that takes inspiration from physical annealing processes to solve Ising problems heuristically. Its dynamics are naturally continuous and described by a set of ordinary differential equations that have been proven to be useful for the optimization of continuous variables nonconvex quadratic optimization problems. The dynamics of such Continuous Variable CIMs (CV-CIM) encourage optimization via optical pulses whose amplitudes are determined by the negative gradient of the objective; however, standard gradient descent is known to be trapped by local minima and hampered by poor problem conditioning. In this work, we propose to modify the CV-CIM dynamics using more sophisticated pulse injections based on tried-and-true optimization techniques such as momentum and Adam. Through numerical experiments, we show that the momentum and Adam updates can significantly speed up the CV-CIM’s convergence and improve sample diversity over the original CV-CIM dynamics. We also find that the Adam-CV-CIM’s performance is more stable as a function of feedback strength, especially on poorly conditioned instances, resulting in an algorithm that is more robust, reliable, and easily tunable. More broadly, we identify the CIM dynamical framework as a fertile opportunity for exploring the intersection of classical optimization and modern analog computing.

Ising Model↗

NASA NTRSDate not supplied

Flight Dynamics Modeling for a Rapid Conceptual Development Environment

This paper presents the integration of flight dynamics modeling (FDM) within an aircraft conceptual development framework. Within this framework, FDM and simulation are used for the preliminary analysis of the takeoff, landing, and critical loss of thrust performance of early-stage aircraft concepts. The aerodynamic and propulsive models are built using the XML-based DAVE-ML model exchange. Automated integration of these models is achieved using the Simulink® model generation available through the DAVEtools Java package in addition to Simulink®-based flight simulation blocks. Results demonstrating the established methods are presented for the analysis of a twin-engine light transport example aircraft. This work establishes methods that will be used to perform trade studies of aircraft designed for Regional Air Mobility operations. These aircraft will require short takeoff and landing distances in addition to steep climb and descent gradients, each of which can be estimated and applied as design space constraints using the current methods.

Flight Dynamics↗

DOE OSTI2025

Accelerating iterative ptychography with an integrated neural network

Electron ptychography is a powerful and versatile tool for high-resolution and dose-efficient imaging. Iterative reconstruction algorithms are powerful but also computationally expensive due to their relative complexity and the many hyperparameters that must be optimised. Gradient descent-based iterative ptychography is a popular method, but it may converge slowly when reconstructing low spatial frequencies. Here, in this work, we present a method for accelerating a gradient descent-based iterative reconstruction algorithm by training a neural network (NN) that is applied in the reconstruction loop. The NN works in Fourier space and selectively boosts low spatial frequencies, thus enabling faster convergence in a manner similar to accelerated gradient descent algorithms. We discuss the difficulties that arise when incorporating a NN into an iterative reconstruction algorithm and show how they can be overcome with iterative training. We apply our method to simulated and experimental data of gold nanoparticles on amorphous carbon and show that we can significantly speed up ptychographic reconstruction of the nanoparticles.

4DSTEM↗

DOE OSTI2024

Convergence of variational Monte Carlo simulation and scale-invariant pre-training

We provide theoretical convergence bounds for the variational Monte Carlo (VMC) method as applied to optimize neural network wave functions for the electronic structure problem. Here, we study both the energy minimization phase and the supervised pre-training phase that is commonly used prior to energy minimization. For the energy minimization phase, the standard algorithm is scale-invariant by design, and we provide a proof of convergence for this algorithm without modifications. The pre-training stage typically does not feature such scale-invariance. We propose using a scale-invariant loss for the pretraining phase and demonstrate empirically that it leads to faster pre-training.

97 MATHEMATICS AND COMPUTING↗