Results for “gradient descent algorithm” — Page 3

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 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

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 NTRS1990

30 years of adaptive neural networks - Perceptron, Madaline, and backpropagation

Fundamental developments in feedforward artificial neural networks from the past thirty years are reviewed. The history, origination, operating characteristics, and basic theory of several supervised neural-network training algorithms (including the perceptron rule, the least-mean-square algorithm, three Madaline rules, and the backpropagation technique) are described. The concept underlying these iterative adaptation algorithms is the minimal disturbance principle, which suggests that during training it is advisable to inject new information into a network in a manner that disturbs stored information to the smallest extent possible. The two principal kinds of online rules that have developed for altering the weights of a network are examined for both single-threshold elements and multielement networks. They are error-correction rules, which alter the weights of a network to correct error in the output response to the present input pattern, and gradient rules, which alter the weights of a network during each pattern presentation by gradient descent with the objective of reducing mean-square error (averaged over all training patterns).

Widrow, Bernard↗

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 NTRS1996

Cascade Error Projection: A Learning Algorithm for Hardware Implementation

In this paper, we workout a detailed mathematical analysis for a new learning algorithm termed Cascade Error Projection (CEP) and a general learning frame work. This frame work can be used to obtain the cascade correlation learning algorithm by choosing a particular set of parameters. Furthermore, CEP learning algorithm is operated only on one layer, whereas the other set of weights can be calculated deterministically. In association with the dynamical stepsize change concept to convert the weight update from infinite space into a finite space, the relation between the current stepsize and the previous energy level is also given and the estimation procedure for optimal stepsize is used for validation of our proposed technique. The weight values of zero are used for starting the learning for every layer, and a single hidden unit is applied instead of using a pool of candidate hidden units similar to cascade correlation scheme. Therefore, simplicity in hardware implementation is also obtained. Furthermore, this analysis allows us to select from other methods (such as the conjugate gradient descent or the Newton's second order) one of which will be a good candidate for the learning technique. The choice of learning technique depends on the constraints of the problem (e.g., speed, performance, and hardware implementation); one technique may be more suitable than others. Moreover, for a discrete weight space, the theoretical analysis presents the capability of learning with limited weight quantization. Finally, 5- to 8-bit parity and chaotic time series prediction problems are investigated; the simulation results demonstrate that 4-bit or more weight quantization is sufficient for learning neural network using CEP. In addition, it is demonstrated that this technique is able to compensate for less bit weight resolution by incorporating additional hidden units. However, generation result may suffer somewhat with lower bit weight quantization.

Duong, Tuan A.↗

NASA NTRSDate not supplied

Progress on Inverse Estimation Technique of Non-Linear Pitch Damping Coefficient Curves Using Free-Flight CFD Generated Trajectories

Characterization of entry vehicle pitch damping coefficient curves is crucial to ensure appropriate re-entry and overall mission success. The pitch damping coefficient (C_(m_q )+C_(m_α ̇ )) is used to encapsulate the oscillatory growth or decay of a body during a trajectory. The inverse estimation technique utilizes an existing Free-Flight CFD (FF-CFD) dataset and wraps a reconstruction algorithm in an optimizer. The reconstruction integrates the planar equations of motion derived by Schoenenberger, Queen [1] using Python’s scipy.integrate.solve_ivp. The optimizer’s objective function is the normalized 𝐿2 residual of the angle of attack peaks between the reconstructed trajectory and the original data produced with FF-CFD. Inclusion of the peak times in this residual calculation allows for simultaneous optimization of the pitch moment coefficient, C_(m_α ). This residual equation is shown below in Eq. 1. The optimizer scipy.optimize.minimize was used with the gradient-based Powell method for the analysis presented, however the differential evolution method was investigated as means of comparison, and was found to produce marginally lower residual values with prohibitively longer run times. Further, the pitch damping curve is found by fitting a cubic interpolation function to a set of (α, (C_(m_q )+C_(m_α ̇ ))) control points, where the α points are held constant and the (C_(m_q )+C_(m_α ̇ )) values are the optimized parameters. The pitch moment curve uses a linear interpolation between the minimum and maximum α in the dataset. FF-CFD generated trajectories using the Dragonfly capsule geometry with the Genesis ballistic range model parameters were simulated and used for this analysis. These FF-CFD trajectories simulate planar motion, as restricted by the reconstructing the equations of motion, of three different cases: 1-DoF (free-to-pitch), 2-DoF (free-to-pitch and heave), and 3-DoF (free-to-pitch, heave, and decelerate). Pitch damping coefficient curves generated using this inverse estimation curve technique with FF-CFD 1-DoF Dragonfly data are found in Fig. 1. Preliminary results reconstructing ballistic range shots using these FF-CFD derived predictions of the pitch damping curve (Fig. 1) are shown in Fig. 2. It should be noted that the ballistic range shot used a Genesis model whereas the FF-CFD data used a Dragonfly geometry, however these geometries are similar.

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