Search NASA⌕ Search

SEARCH · Search NASA

Results for “gradient descent optimization”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Preparation of the SU(3) lattice Yang-Mills vacuum with variational quantum methods

Studying QCD and other gauge theories on quantum hardware requires the preparation of physically interesting states. The variational quantum eigensolver provides a way of performing vacuum state preparation on quantum hardware. Here in this work, variational quantum eigensolver is applied to pure SU(3) lattice Yang-Mills on a single plaquette and one dimensional plaquette chains. Bayesian optimization and gradient descent were investigated for performing the classical optimization. Ansatz states for plaquette chains are constructed in a scalable manner from smaller systems using domain decomposition and a stitching procedure analogous to the density matrix renormalization group. Small examples are performed on IBM’s superconducting Manila processor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Crossing The Gap Using Variational Quantum Eigensolver: A Comparative Study

Within the evolving domain of quantum computational chemistry, the Variational Quantum Eigensolver (VQE) has been developed to explore not only the ground state but also the excited states of molecules. In this study, we compare the performance of Variational Quantum Deflation (VQD) and Subspace-Search Variational Quantum Eigensolver (SSVQE) methods in determining the low-lying excited states of $LiH$. Our investigation reveals that while VQD exhibits a slight advantage in accuracy, SSVQE stands out for its efficiency, allowing the determination of all low-lying excited states through a single parameter optimization procedure. We further evaluate the effectiveness of optimizers, including Gradient Descent (GD), Quantum Natural Gradient (QNG), and Adam optimizer, in obtaining $LiH$'s first excited state, with the Adam optimizer demonstrating superior efficiency in requiring the fewest iterations. Moreover, we propose a novel approach combining Folded Spectrum VQE (FS-VQE) with either VQD or SSVQE, enabling the exploration of highly excited states. We test the new approaches for finding all three $H_4$'s excited states. Folded Spectrum SSVQE (FS-SSVQE) can find all three highly excited states near $-1.0$ Ha with only one optimizing procedure, but the procedure converges slowly. In contrast, although Folded spectrum VQD (FS-VQD) gets highly excited states with individual optimizing procedures, the optimizing procedure converges faster.

Chen, I-Chi↗
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 OSTI2023

Optimization Stability in Excited-State-Specific Variational Monte Carlo

Here, we investigate the issue of optimization stability in variance-based state-specific variational Monte Carlo, discussing the roles of the objective function, the complexity of wave function ansatz, the amount of sampling effort, and the choice of minimization algorithm. Using a small cyanine dye molecule as a test case, we systematically perform minimizations using variants of the linear method as both a standalone algorithm and in a hybrid combination with accelerated descent. We demonstrate that adaptive step control is crucial for maintaining the linear method's stability when optimizing complicated wave functions and that the hybrid method enjoys both greater stability and minimization performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Large gradients via correlation in random parameterized quantum circuits

Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in cost function landscapes is an obstacle to optimization by gradient descent methods. In this work, we prove that reducing the dimensionality of the parameter space by utilizing circuit modules containing spatially or temporally correlated gate layers can allow one to circumvent the vanishing gradient phenomenon. Here, examples are drawn from random separable circuits and asymptotically optimal variational versions of Grover's algorithm based on the quantum alternating operator ansatz. In the latter scenario, our bounds on cost function variation imply a transition between vanishing gradients and efficient trainability as the number of layers is increased toward $\mathcal{O}\left({2}^{n/2}\right)$, the optimal oracle complexity of quantum unstructured search.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Mode connectivity in the loss landscape of parameterized quantum circuits

Variational training of parameterized quantum circuits (PQCs) underpins many workflows employed on near-term noisy intermediate scale quantum (NISQ) devices. It is a hybrid quantum-classical approach that minimizes an associated cost function in order to train a parameterized ansatz. In this work we adapt the qualitative loss landscape characterization for neural networks introduced in Goodfellow et al. (2014); Li et al. (2017) and tests for connectivity used in Draxler et al. (2018) to study the loss landscape features in PQC training. We present results for PQCs trained on a simple regression task, using the bilayer circuit ansatz, which consists of alternating layers of parameterized rotation gates and entangling gates. Multiple circuits are trained with 3 different batch gradient optimizers: stochastic gradient descent, the quantum natural gradient, and Adam. We identify large features in the landscape that can lead to faster convergence in training workflows.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2025

Efficient Training of Deep Neural Operator Networks via Randomized Sampling

Neural operators (NOs) employ deep neural networks to learn the mappings between infinitedimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. While constructing the loss function, DeepONet training traditionally considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing the memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework’s performance in modeling complex physical systems.

Karumuri, Sharmila [Department of Civil & Systems ↗
DOE OSTI2020

Parallel-in-Time Simulation of Lindblad's Equation

Constructing fast quantum logic gates is critical to building a scalable quantum computer. We consider a qudit, a quantum version of a bit that can take an arbitrary number of states, coupled with a cavity. In this project, we wish to force the qudit to reach the 0-state, for any possible initial state. The coupled system changes in time according to Lindblad’s equation, an ordinary differential equation on the density matrix of the quantum system. Lindblad’s equation contains some parameters that we can control, so-called control functions. We seek control functions which force the qudit to the 0-state within 2 microseconds, which is much faster than what is currently done in practice. The search method is gradient descent, a numerical optimization method that uses gradient information to iteratively improve the control parameters. My contribution to this project is an attempt to speed up the computation of the gradient. It currently takes about 40 seconds to compute the gradient which involves solving a set of ODEs sequentially. Current supercomputers have thousands of cores, but sequential computations can only make use of 1 core at a time. We wish to divide up the work better, so that we can use many more cores at once. To this end, we have implemented the Multigrid Reduction in Time (MGRIT) algorithm. We perform a systematic parameter search on how to best apply this algorithm. Results indicate a 25 percent speed up for solving Lindblad’s equation and determining how close the final state is the 0-state.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Scalable and Energy-Efficient Methods for Interactive Exploration of Scientific Data

The main scientific contributions of this project are the following novel concepts for multidimensional arrays: shape-based similarity join (SIGMOD 2016), incremental view maintenance (SIGMOD 2017), user-defined stencil functions (HPDC 2017), and distributed caching for in-situ processing (SSDBM 2018). Building on our collaboration with the astrophysics group at LBNL, we applied these techniques to the data generated in the Palomar Transient Factory (PTF) astronomical survey. They played a pivotal role in the first-ever observation of a neutron star merger, which produces gravitational waves and turns out to be the origin of heavy elements, including gold. This has lead to a Science magazine article that has received extensive media coverage on ACM TechNews, Slashdot, FiveThirtyEight, and Quanta Magazine, among others. Additionally, two other articles detailing related aspects of the same discovery have been published in the Astrophysical Journal Letters journal. These publications have more than 3,000 citations according to Google Scholar (as of February 2022). This cross-disciplinary collaboration provided very good opportunities to apply database techniques to real-life scientific problems. The fact that they facilitated major discoveries in astrophysics proves the importance of our research. In addition to the work on multidimensional array databases, this project has also developed stochastic gradient descent (SGD) optimization algorithms for training large scale machine learning models, methods for querying in-situ data, and a database query optimizer based on sketch synopses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Gradient-Informed Design Optimization of Select Nuclear Systems

In this work, we present a gradient-informed design optimization of nuclear reactor core components based on neutronics objectives with both continuous and discrete materials. The main argument in favor of using gradient-informed design optimization is that it scales well with increasing dimensionality of the design space. First, a challenge problem with 121 free parameters is solved with a gradient-informed method and then with a genetic algorithm. Then, a challenge problem to optimize the flux profile of a simplified assembly with eight axial zones is solved. Both challenge problems are solved using directly calculated derivatives from Tools for Sensitivity and Uncertainty Analysis Methodology Implementation (TSUNAMI) in the SCALE package. Furthermore, we demonstrate how a discrete optimization problem—selection of materials for 121 voxels—can be lifted into a continuous problem with mixed materials. In the continuous space, adjoint-based gradients are well-defined, and gradient descent is applicable. Then, a forcing function is introduced that with the selection of an appropriately sized hyperparameter can be used to guide the optimized continuous solution back into a discrete solution. This paper presents an account of the challenges that were faced when applying a gradient-informed optimization algorithm using a Monte Carlo calculation to estimate the gradient information and compares a gradient descent optimization method to a genetic algorithm optimization of the same geometry. Overall, this work demonstrates the potential use of adjoint-based gradient calculations in design optimization of nuclear systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

End-to-End Differentiable Modeling and Management of the Environment

Focal Area: (2) Data acquisition and assimilation enabled by machine learning, AI, and advanced methods including experimental/network design/optimization. We emphasize the importance of leveraging optimization techniques from AI/machine learning (ML) to solve challenging problems in Earth system modeling. Science Challenge: Automatic differentiation has had a transformative effect on ML by allowing the calculation of gradients of arbitrary functions in an incredibly large class of models. We can potentially realize similar improvements in parameter estimation and control for Earth system models (ESMs) by reimplementing them in computational frameworks from ML. Practitioners working with large (>10 7 parameters) models in ML and AI can obtain good predictive performance in a range of spatiotemporal tasks by making use of optimization via stochastic gradient descent and incorporating prior knowledge at multiple levels. We propose writing ESMs in open-source computational frameworks such as Torch, Tensorflow, and JAX to greatly expand the scope of environmental forecasting and management challenges, which can be addressed by leveraging automatic differentiation and gradient descent-like algorithms. We do not call for a wholesale replacement of physical models with data-driven surrogates, but rather advocate for interleaving physical and empirical equations in a manner that is most faithful to the extent of our scientific knowledge and observational data. Central to this topic is the merging of differentiable physical simulations with differentiable optimization layers, which are now both beginning to come to the forefront.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Distributed and communication-efficient solutions to linear equations with special sparse structure

In this paper we report two distributed and communication-efficient algorithms based on the multi-agent system are proposed to solve a system of linear equations with the Laplacian sparse system matrix. One algorithm is based on the gradient descent method in optimization. In this algorithm, the agents only share partial information instead of all of their collective state vectors to save significant communication. The other algorithm is obtained by approximating Newton’s method for a faster convergence rate. Although it requires twice as much communication as the first one, it is still communication-efficient given the low dimension of the information shared among agents. The convergence at a linear rate is proved for both algorithms, and a comprehensive comparison of their convergence rate, communication burden, and computation costs is also performed. The proposed algorithms can be applied to various systems to solve those problems that can be modeled as a system of linear equations with a Laplacian sparse system matrix. Simulation results with the electric power system illustrate their effectiveness.

42 ENGINEERING↗
DOE OSTI2022

GIGA-Lens: Fast Bayesian Inference for Strong Gravitational Lens Modeling

We present GIGA-Lens: a gradient-informed, GPU-accelerated Bayesian framework for modeling strong gravitational lensing systems, implemented in TensorFlow and JAX. The three components, optimization using multistart gradient descent, posterior covariance estimation with variational inference, and sampling via Hamiltonian Monte Carlo, all take advantage of gradient information through automatic differentiation and massive parallelization on graphics processing units (GPUs). We test our pipeline on a large set of simulated systems and demonstrate in detail its high level of performance. The average time to model a single system on four Nvidia A100 GPUs is 105 s. The robustness, speed, and scalability offered by this framework make it possible to model the large number of strong lenses found in current surveys and present a very promising prospect for the modeling of ${ \mathcal O }({10}^{5})$ lensing systems expected to be discovered in the era of the Vera C. Rubin Observatory, Euclid, and the Nancy Grace Roman Space Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

HGQ: High Granularity Quantization for Real-time Neural Networks on FPGAs

Neural networks with sub-microsecond inference latency are required by many critical applications. Targeting such applications deployed on FPGAs, we present High Granularity Quantization (HGQ), a quantization-aware training framework that optimizes parameter bit-widths through gradient descent. Unlike conventional methods, HGQ determines the optimal bit-width for each parameter independently, making it suitable for hardware platforms supporting heterogeneous arbitrary precision arithmetic. In our experiments, HGQ shows superior performance compared to existing network compression methods, achieving orders of magnitude reduction in resource consumption and latency while maintaining the accuracy on several benchmark tasks. These improvements enable the deployment of complex models previously infeasible due to resource or latency constraints. HGQ is open-source and is used for developing next-generation trigger systems at the CERN ATLAS and CMS experiments for particle physics, enabling the use of advanced machine learning models for real-time data selection with sub-microsecond latency.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

Here we propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Structure optimization with stochastic density functional theory

Linear-scaling techniques for Kohn–Sham density functional theory are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the localization of the density matrix or accurate embedding approaches, limiting their applicability. In contrast, stochastic density functional theory (sDFT) achieves linear- and sub-linear scaling by statistically sampling the ground state density without relying on embedding or imposing localization. In return, ground state observables, such as the forces on the nuclei, fluctuate in sDFT, making optimizing the nuclear structure a highly non-trivial problem. In this work, we combine the most recent noise-reduction schemes for sDFT with stochastic optimization algorithms to perform structure optimization within sDFT. We compare the performance of the stochastic gradient descent approach and its variations (stochastic gradient descent with momentum) with stochastic optimization techniques that rely on the Hessian, such as the stochastic Broyden–Fletcher–Goldfarb–Shanno algorithm. In conclusion, we further provide a detailed assessment of the computational efficiency and its dependence on the optimization parameters of each method for determining the ground state structure of bulk silicon with varying supercell dimensions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A Bayesian Learning Approach to Wireless Outdoor Heatmap Construction using Deep Gaussian Process

We present a novel Bayesian learning approach to outdoor radio heatmap construction utilizing deep Gaussian process (GP). The proposed approach employs a two-layer hierarchy which consists of two cascaded Gaussian processes that are capable of modeling more complex input-output relations than standard single-layer Gaussian processes. Since deriving the exact model likelihood is challenging, a lower bound is optimized instead so that gradient descent-based methods can be performed to find out the optimal model parameters. Typically, inducing points are used in GPs to facilitate low-rank approximation of covariance (kernel) matrices for computation speedup. However, the inaccuracy induced by inducing points can accumulate when stacking multiple layers of GP which may hinder the performance of deep GP. Moreover, since inducing points need to be learned, having them at all layers of deep GP also incurs computational burden. To overcome the above challenges, in contrast to the canonical deep GP model, we use a modified architecture where a full standard GP resides in the first layer and inducing points are only introduced for the second layer. This modified architecture strikes a balance between model accuracy and training complexity. In the proposed model, the noise parameter of the first GP layer is also eliminated to improve the training efficiency as the noise parameter at the output of the second layer suffices to model the uncertainty in the output. The proposed approach is evaluated on real-world datasets, in the form of location-Received Signal Strength (RSS) pairs, collected from the Platform for Open Wireless Data-driven Experimental Research (POWDER) located at the campus of the University of Utah. Experiment results show that the proposed approach can achieve smaller prediction errors on various training and testing data configurations than DNN-based and GP-based methods.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗