Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stochastic gradient descent”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Risk-Constrained Reinforcement Learning for Inverter-Dominated Power System Controls

Here, this paper develops a risk-aware controller for grid-forming inverters (GFMs) to minimize large frequency oscillations in GFM inverter-dominated power systems. To tackle the high variability from loads/renewables, we incorporate a mean-variance risk constraint into the classical linear quadratic regulator (LQR) formulation for this problem. The risk constraint aims to bound the time-averaged cost of state variability and thus can improve the worst-case performance for large disturbances. The resulting risk-constrained LQR problem is solved through the dual reformulation to a minimax problem, by using a reinforcement learning (RL) method termed as stochastic gradient-descent with max-oracle (SGDmax). In particular, the zero-order policy gradient (ZOPG) approach is used to simplify the gradient estimation using simulated system trajectories. Numerical tests conducted on the IEEE 68-bus system have validated the convergence of our proposed SGDmax for GFM model and corroborate the effectiveness of the risk constraint in improving the worst-case performance while reducing the variability of the overall control cost.

Frequency control↗
DOE OSTI2022

Wavefront shaping with a Hadamard basis for scattering soil imaging

Here, soil is a scattering medium that inhibits imaging of plant-microbial-mineral interactions that are essential to plant health and soil carbon sequestration. However, optical imaging in the complex medium of soil has been stymied by the seemingly intractable problems of scattering and contrast. Here, we develop a wavefront shaping method based on adaptive stochastic parallel gradient descent optimization with a Hadamard basis to focus light through soil mineral samples. Our approach allows a sparse representation of the wavefront with reduced dimensionality for the optimization. We further divide the used Hadamard basis set into subsets and optimize a certain subset at once. Simulation and experimental optimization results demonstrate our method has an approximately seven times higher convergence rate and overall better performance compared to that with optimizing all pixels at once. The proposed method can benefit other high-dimensional optimization problems in adaptive optics and wavefront shaping.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Stabilization of the 81-channel coherent beam combination using machine learning

We develop a rapidly converging algorithm for stabilizing a large channel-count diffractive optical coherent beam combination. An 81-beam combiner is controlled by a novel, machine-learning based, iterative method to correct the optical phases, operating on an experimentally calibrated numerical model. A neural-network is trained to detect phase errors based on interference pattern recognition of uncombined beams adjacent to the combined one. Due to the non-uniqueness of solutions in the full space of possible phases, the network is trained within a limited phase perturbation/error range. This also reduces the number of samples needed for training. Simulations have proven that the network can converge in one step for small phase perturbations. When the trained neural-network is applied to a realistic case of 360 degree full range, an iterative scheme exploits random walking at the beginning, with the accuracy of prediction on phase feedback direction, to allow the neural-network to step into the training range for fast convergence. This neural-network-based iterative method of phase detection works tens of times faster than the commonly used stochastic parallel gradient descent approach (SPGD) using a single-detector and random dither when both are tested with random phase perturbations.

Wang, Dan↗
DOE OSTI2025

Stochastic noise can be helpful for variational quantum algorithms

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided, for example, by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle-points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms. Published by the American Physical Society 2025

Liu, Junyu↗
DOE OSTI2024

Quantum optimization algorithms: Energetic implications

Since the dawn of quantum computing (QC), theoretical developments like Shor's algorithm proved the conceptual superiority of QC over traditional computing. However, such quantum supremacy claims are difficult to achieve in practice because of the technical challenges of realizing noiseless qubits. In the near future, QC applications will need to rely on noisy quantum devices that offload part of their work to classical devices. One way to achieve this is by using parameterized quantum circuits in optimization or even in machine learning tasks. The energy requirements of quantum algorithms have not yet been studied extensively. Here in this article, we explore several optimization algorithms using both theoretical insights and numerical experiments to understand their impact on energy consumption. Specifically, we highlight why and how algorithms like quantum natural gradient descent, simultaneous perturbation stochastic approximations or circuit learning methods, are at least 2x to 4x more energy efficient than their classical counterparts; why feedback-based quantum optimization is energy-inefficient; and how techniques like Rosalin can improve the energy efficiency of other algorithms by a factor of ≥2 0 x. Finally, we use the NchooseK high-level programming model to run optimization problems on both gate-based quantum computers and quantum annealers. Empirical data indicate that these optimization problems run faster, have better success rates, and consume less energy on quantum annealers than on their gate-based counterparts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Correspondence between neuroevolution and gradient descent

Abstract We show analytically that training a neural network by conditioned stochastic mutation or neuroevolution of its weights is equivalent, in the limit of small mutations, to gradient descent on the loss function in the presence of Gaussian white noise. Averaged over independent realizations of the learning process, neuroevolution is equivalent to gradient descent on the loss function. We use numerical simulation to show that this correspondence can be observed for finite mutations, for shallow and deep neural networks. Our results provide a connection between two families of neural-network training methods that are usually considered to be fundamentally different.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗
DOE OSTI2021

Plateau Phenomenon in Gradient Descent Training of RELU Networks: Explanation, Quantification, and Avoidance

The ability of neural networks to provide ‘best in class’ approximation across a wide range of applications is well-documented. Nevertheless, the powerful expressivity of neural networks comes to naught if one is unable to effectively train (choose) the parameters defining the network. In general, neural networks are trained by gradient descent type optimization methods,a stochastic variant thereof. In practice, such methods result in the loss function decreases rapidly at the beginning of training but then, after a relatively small number of steps, significantly slow down. The loss may even appear to stagnate over the period of a large number of epochs, only to then suddenly start to decrease fast again for no apparent reason. This so-called plateau phenomenon manifests itself in many learning tasks. The present work aims to identify and quantify the root causes of plateau phenomenon.analysis is carried out in the setting of univariate ReLU networks. No assumptions are made on the number of neurons relative to the number of training data, and our results hold for both the lazy and adaptive regimes. Here, the main findings are: plateaux correspond to periods during which activation patterns remain constant, where activation pattern refers to the number of data points that activate a given neuron; quantification of convergence of the gradient flow dynamics; and, characterization stationary points in terms solutions of local least squares regression lines over subsets of the training data. Based on these conclusions, we propose a new iterative training method, the Active Neuron Least Squares (ANLS), characterised by the explicit adjustment of the activation pattern at each step, which is designed to enable a quick exit from a plateau. Illustrative numerical examples are included throughout.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An Online Dynamic Amplitude-Correcting Gradient Estimation Technique to Align X-ray Focusing Optics

High-brightness X-ray pulses, as generated at synchrotrons and X-ray free electron lasers (XFELs), are used in a variety of scientific experiments. At these facilities, measurements often require optical equipment, e.g Compound Refractive Lenses (CRLs) to be precisely aligned and focused. The lateral alignment of CRLs to a beamline requires precise positioning along four axes: two translational, and the two rotational. At a synchrotron, alignment is often accomplished manually. However, XFEL beamlines present a beam brightness that fluctuates stochastically, making manual alignment a time-consuming endeavor. Automation using simplex or classic stochastic descent often fails, given the errant gradient estimates. Herein we present a dynamic-amplitude correction to the usual gradient based on the combination of a generalized finite difference stencil and a time-dependent sampling pattern. Intensity is recorded periodically, then used to normalize numerical derivatives against fluctuations. Error expectation is analyzed, and efficacy is demonstrated on classic benchmarks. We provide a proof of concept by laterally aligning optics on a simulated XFEL beamline using data recorded at both synchrotron and XFEL facilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Random coordinate descent: A simple alternative for optimizing parameterized quantum circuits

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the collapse of quantum states after measurements. Thus, gradient estimations constitute a significant overhead in a gradient-based optimization of such quantum circuits. This paper introduces a random coordinate descent algorithm as a practical and easy-to-implement alternative to the full gradient descent algorithm. This algorithm only requires one partial derivative at each iteration. Motivated by the behavior of measurement noise in the practical optimization of parameterized quantum circuits, this paper presents an optimization problem setting that is amenable to analysis. Under this setting, the random coordinate descent algorithm exhibits the same level of stochastic stability as the full gradient approach, making it as resilient to noise. The complexity of the random coordinate descent method is generally no worse than that of the gradient descent and can be much better for various quantum optimization problems with anisotropic Lipschitz constants. Theoretical analysis and extensive numerical experiments validate our findings. Published by the American Physical Society 2024

Ding, Zhiyan (ORCID:000000018863403X)↗
DOE OSTI2023

Stochastic projective splitting

Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

General-Purpose Bayesian Tensor Learning With Automatic Rank Determination and Uncertainty Quantification

A major challenge in many machine learning tasks is that the model expressive power depends on model size. Low-rank tensor methods are an efficient tool for handling the curse of dimensionality in many large-scale machine learning models. The major challenges in training a tensor learning model include how to process the high-volume data, how to determine the tensor rank automatically, and how to estimate the uncertainty of the results. While existing tensor learning focuses on a specific task, this paper proposes a generic Bayesian framework that can be employed to solve a broad class of tensor learning problems such as tensor completion, tensor regression, and tensorized neural networks. We develop a low-rank tensor prior for automatic rank determination in nonlinear problems. Our method is implemented with both stochastic gradient Hamiltonian Monte Carlo (SGHMC) and Stein Variational Gradient Descent (SVGD). We compare the automatic rank determination and uncertainty quantification of these two solvers. We demonstrate that our proposed method can determine the tensor rank automatically and can quantify the uncertainty of the obtained results. We validate our framework on tensor completion tasks and tensorized neural network training tasks.

Bayesian inference↗
DOE OSTI2024

Stochastic Optimization to Find Optimum Beginning-of-Life Core Configuration of Stable Salt Reactor with Online Refueling

A stochastic optimization method has been developed to find an optimum equilibrium cycle core configuration of the waste-burning stable salt reactor, which is a fast-spectrum molten salt reactor with frequent online refueling. An optimum core configuration was determined with the goal of minimizing radial power peaking. Because of the vast number of potential candidate core configurations, stochastic optimization was applied based on simulated annealing and an additional acceleration method, which screened out unpromising core configurations. It has been demonstrated that the developed stochastic optimization method successfully finds the optimal core configuration regardless of the initial guess and outperforms the gradient descent approach. In addition, it has been observed that the use of a so-called out-in core configuration as the initial guess speeds up convergence of the iterative solution more than five times. Based on the searched optimum equilibrium cycle core configuration, new beginning-of-life (BOL) core configurations have been developed. In conclusion, the new BOL core configurations will be used in developing optimum refueling strategies.

Moltex static salt reactor↗
DOE OSTI2024

A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Training neural networks using Metropolis Monte Carlo and an adaptive variant

Abstract We examine the zero-temperature Metropolis Monte Carlo (MC) algorithm as a tool for training a neural network by minimizing a loss function. We find that, as expected on theoretical grounds and shown empirically by other authors, Metropolis MC can train a neural net with an accuracy comparable to that of gradient descent (GD), if not necessarily as quickly. The Metropolis algorithm does not fail automatically when the number of parameters of a neural network is large. It can fail when a neural network’s structure or neuron activations are strongly heterogenous, and we introduce an adaptive Monte Carlo algorithm (aMC) to overcome these limitations. The intrinsic stochasticity and numerical stability of the MC method allow aMC to train deep neural networks and recurrent neural networks in which the gradient is too small or too large to allow training by GD. MC methods offer a complement to gradient-based methods for training neural networks, allowing access to a distinct set of network architectures and principles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Optimality of Gradient-MUSIC for Spectral Estimation

We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is sufficiently small and the signal frequencies are separated by at least 8π/m, where π/m is the standard resolution of this problem. Even though the 1D landscape is nonconvex, we prove a global convergence result for Gradient-MUSIC: coarse scanning provably finds suitable initialization and gradient descent converges at a linear rate. In addition to convergence results, we also upper bound the error between the true signal frequencies and amplitudes with those found by Gradient-MUSIC. For example, if the noise has $\ell^\infty$ norm at most ϵ, then the frequencies and amplitudes are recovered up to error at most Cϵ/m and Cϵ respectively, which are minimax optimal in m and ϵ. Our theory can also handle stochastic noise with performance guarantees under nonstationary independent Gaussian noise. Our main approach is a comprehensive geometric analysis of the landscape, a perspective that has not been explored before.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Stochastic Approximation for Multi-period Simulation Optimization with Streaming Input Data

We consider a continuous-valued simulation optimization (SO) problem, where a simulator is built to optimize an expected performance measure of a real-world system while parameters of the simulator are estimated from streaming data collected periodically from the system. At each period, a new batch of data is combined with the cumulative data and the parameters are re-estimated with higher precision. The system requires the decision variable to be selected in all periods. Therefore, it is sensible for the decision-maker to update the decision variable at each period by solving a more precise SO problem with the updated parameter estimate to reduce the performance loss with respect to the target system. We define this decision-making process as the multi-period SO problem and introduce a multi-period stochastic approximation (SA) framework that generates a sequence of solutions. Two algorithms are proposed: Re-start SA (ReSA) reinitializes the stepsize sequence in each period, whereas Warm-start SA (WaSA) carefully tunes the stepsizes, taking both fewer and shorter gradient-descent steps in later periods as parameter estimates become increasingly more precise. We show that under suitable strong convexity and regularity conditions, ReSA and WaSA achieve the best possible convergence rate in expected sub-optimality either when an unbiased or a simultaneous perturbation gradient estimator is employed, while WaSA accrues significantly lower computational cost as the number of periods increases. In addition, we present the regularized ReSA, which obviates the need to know the strong convexity constant and achieves the same convergence rate at the expense of additional computation.

Computer Science↗