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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.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

SLICE

For most of their lifetime, pebble-bed reactors (PBRs) operate at an equilibrium state in which the core is filled with fuel pebbles at various levels of burnup. A fuel pebble travels multiple times in so-called passes through the reactor before it reaches its target discharge burnup and is replaced with a fresh fuel pebble. Given the stochastic nature of the fuel pebble travel paths and consequently the individual fuel pebble histories, it is not possible with standard methods developed for traditional reactor concepts to calculate the fuel inventory in the reactor core. An iterative approach, the SCALE Leap-In method for Cores at Equilibrium (SLICE), was developed to generate region-average fuel inventory for a PBR. The SLICE code enables automatic generation of input files for the SCALE code system (https://www.ornl.gov/scale), management of the SCALE result files, and analysis of results.

Bostelmann, Friederike [Oak Ridge National Laborat↗
DOE OSTI2026

Scientific Core Library Stack (SCLS) v2026

SCLS (Scientific Core Library Stack) is an opinionated build and packaging system for scientific computing libraries developed at Lawrence Berkeley National Laboratory. It produces a coherent, reproducible stack of numerical libraries — including BLAS/LAPACK, MPI, sparse direct and iterative solvers, graph partitioners, and parallel I/O libraries (e.g., PETSc, SLEPc, HDF5, NetCDF, MUMPS, OpenBLAS) — that work together without manual repair by downstream scientific software. From a single recipe-and-flavor model, SCLS produces native RPM packages for RHEL-family Linux, DEB packages for Debian/Ubuntu, direct Unix-style prefix installs for HPC and locked-down environments, and native macOS builds. Multiple build "flavors" (e.g., GCC+OpenBLAS, GCC+MKL, Intel+MKL, debug) coexist in distinct prefixes on the same host. Compared to general-purpose meta-build frameworks, SCLS is deliberately curated rather than infinitely configurable. It enforces deterministic, audit-friendly behavior: explicit build dependencies, no silent feature autodetection, a clear open-source license policy, and rpath-based runtime linkage so installs integrate cleanly with standard package-manager workflows.

Messe, Christian [Lawrence Berkeley National Labor↗
DOE OSTI2021

Clearing a Path to Commercialization of Marine Renewable Energy Technologies Through Public–Private Collaboration

Governments are increasingly turning toward public–private partnerships to bring industry support to improving public assets or services. Here, we describe a unique public–private collaboration where a government entity has developed mechanisms to support public and private sector advancement and commercialization of monitoring technologies for marine renewable energy. These support mechanisms include access to a range of skilled personnel and test facilities that promote rapid innovation, prove reliability, and inspire creativity in technology development as innovations move from concept to practice. The ability to iteratively test hardware and software components, sensors, and systems can accelerate adoption of new methods and instrumentation designs. As a case study, we present the development of passive acoustic monitoring technologies customized for operation in energetic waves and currents. We discuss the value of testing different systems together, under the same conditions, as well as the progression through different test locations. The outcome is multiple, complementary monitoring technologies that are well suited to addressing an area of high environmental uncertainty and reducing barriers to responsible deployment of low-carbon energy conversion systems, creating solutions for the future.

16 TIDAL AND WAVE POWER↗
DOE OSTI2023

Identification of 2-Hydroxyacyl-CoA Synthases with High Acyloin Condensation Activity for Orthogonal One-Carbon Bioconversion

One-carbon (C1) compounds are emerging as cost-effective and potentially carbon-negative feedstocks for biomanufacturing, which require efficient, versatile metabolic platforms for the synthesis of value-added products. Synthetic formyl-CoA elongation (FORCE) pathways allow diverse product synthesis from C1 compounds via iterative C1 elongation, operating independently from the host metabolism with reduced engineering complexity and improved theoretical yields. However, a major bottleneck was identified as the suboptimal kinetics of the core C1–C1 condensation enzyme, 2-hydroxyacyl-CoA synthase (HACS), catalyzing the acyloin condensation reaction between formaldehyde and formyl-CoA. Furthermore, we used a combinatorial approach of bioprospecting and rational protein engineering to identify multiple HACS variants with significantly improved activities toward C1 substrates. Sequence and structure alignment of the active variants elucidated the key regions for the catalytic function, which were targeted for mutagenesis, leading to improved catalytic efficiency. In parallel, a consecutive round of bioprospecting for homologs with high similarity with active variants revealed a highly active HACS variant exhibiting up to 7-fold improvement in catalytic efficiency (k cat /K M ) and 14-fold improvement in the FORCE pathway flux in vivo compared to the previous reports. Upon further optimization of the downstream pathway, the orthogonal C1-to-product bioconversion system showed a metabolic flux of up to 700 μM glycolate OD –1 h –1 (2.1 mmol gDCW –1 h –1 ) and an industrially relevant glycolate titer, rate, and yield of 5.2 g L –1 (67.8 mM), 0.22 g L –1 h –1 , and 94% carbon yield, respectively.

2-hydroxyacyl-CoA synthase↗
DOE OSTI2026

Probing multi-dimensional composition spaces in search of strong metallic alloys

Refractory complex concentrated alloys (RCCA) offer exceptionally high-temperature strength compared to pure metals and dilute alloys, but predictive theory for RCCA design is lacking. We present large-scale molecular Dynamics (MD) simulations of crystal plasticity to explore alloy compositions for maximum mechanical strength, focusing on Fe-Ta-W and Nb-Ta-Mo-W alloy families modeled with Embedded Atom Model (EAM) and Spectral Neighbor Analysis Potentials (SNAP). To efficiently guide the search for strong alloy compositions, we employ iterative optimization using Gaussian process regression. Many simulated RCCA compositions exhibit pronounced cocktail strengthening, with strengths surpassing their strongest constituent metal, tungsten. Contrary to expectations, the highest strength is found on binary edges of the RCCA composition space. Detailed analyses of atomistic simulations reveal that, similar to pure BCC metals, plastic response in RCCA is primarily governed by screw dislocations. However, at large strains, dislocation multiplication and interactions (Taylor hardening) become the dominant mechanisms contributing to RCCA strength.

Materials science↗
DOE OSTI2021

Neutron radiation hardness of aluminum gallium nitride UV LEDs at various wavelengths

Radiation hard diagnostics are critical to the success of nuclear fusion at National Ignition Facility, Z, ITER, and prolonged space explorations. We have first demonstrated the exceptional proton radiation hardness of initial GaN devices and qualified their space flight and deployment for missions such as the Laser Interferometer Space Antenna and International Space Station. We have further conducted neutron radiation hardness experiments at Los Alamos Neutron Science Center by opening a new high fluence beam station. During 2014–2016, we irradiated multiple Aluminum Gallium Nitride (AlGaN) LEDs with a maximum fluence of 2.4 × 1013 neutrons/cm2 in 3 years and generated 54 161 current–voltage (I–V) scan traces. Our data processing program analyzes each and all I–V traces. In addition, we retrieved local temperature records to analyze and remove temperature effects in the outdoor environment. The I–V curve families of AlGaN UV LEDs with emitting wavelengths of 265, 275, and 310 nm were compared. The I–V curves of 265 nm AlGaN UV LEDs have the smallest deviations from the average value, while the I–V curves for 310 nm AlGaN LEDs showed the largest deviations from the average value. We have reached another important recommendation for the optimal use of multiple AlGaN optoelectronic devices or imaging arrays for inertially confined fusion diagnostics: Shorter wavelength devices at 265 nm exhibit more consistent radiation hardness performance than the 310 nm devices. Higher aluminum content LEDs or AlxGa1–xN devices with higher mole fraction x for generating shorter wavelengths have better radiation hardness for fusion diagnostics.

Sun, K. -X. (ORCID:0000000224659235)↗
DOE OSTI2025

A time-parallel multiple-shooting method for large-scale quantum optimal control

Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. Further, this enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Robust scalable initialization for Bayesian variational inference with multi-modal Laplace approximations

Predictive modeling typically relies on Bayesian model calibration to provide uncertainty quantification. Variational inference utilizing fully independent (“mean-field”) Gaussian distributions are often used as approximate probability density functions. This simplification is attractive since the number of variational parameters grows only linearly with the number of unknown model parameters. However, the resulting diagonal covariance structure and unimodal behavior can be too restrictive to provide useful approximations of intractable Bayesian posteriors that exhibit highly non-Gaussian behavior, including multimodality. High-fidelity surrogate posteriors for these problems can be obtained by considering the family of Gaussian mixtures. Gaussian mixtures are capable of capturing multiple modes and approximating any distribution to an arbitrary degree of accuracy, while maintaining some analytical tractability. Unfortunately, variational inference using Gaussian mixtures with full-covariance structures suffers from a quadratic growth in variational parameters with the number of model parameters. The existence of multiple local minima due to strong nonconvex trends in the loss functions often associated with variational inference present additional complications, These challenges motivate the need for robust initialization procedures to improve the performance and computational scalability of variational inference with mixture models. In this work, we propose a method for constructing an initial Gaussian mixture model approximation that can be used to warm-start the iterative solvers for variational inference. The procedure begins with a global optimization stage in model parameter space. In this step, local gradient-based optimization, globalized through multistart, is used to determine a set of local maxima, which we take to approximate the mixture component centers. Around each mode, a local Gaussian approximation is constructed via the Laplace approximation. Finally, the mixture weights are determined through constrained least squares regression. The robustness and scalability of the proposed methodology is demonstrated through application to an ensemble of synthetic tests using high-dimensional, multimodal probability density functions. Here, the practical aspects of the approach are demonstrated with inversion problems in structural dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Machine learning-driven design and self-sensing capabilities of automotive bumper lattices for adaptive impact response

We present a novel approach to design an automotive bumper energy absorber using carbon fiber reinforced polymer composites, optimized to meet conflicting performance requirements for two distinct impact scenarios. The design must satisfy both a low-speed (2.5 mph) pendulum intrusion test, simulating vehicle-to-vehicle collisions, and a high-speed (25 mph) leg flexion test, replicating pedestrian impacts. These tests demand opposing deformation characteristics: high flexibility (deformation < 85 mm) for the former and high stiffness (deformation < 22 mm) for the latter. To address these contradictory requirements, we developed a machine learning (ML) framework for inverse optimization of lattice designs and material selection. Unlike traditional iterative design processes, our ML model directly outputs optimal design parameters and material choices based on target performance inputs. The energy absorber was fabricated using advanced additive manufacturing techniques, including extrusion deposition and digital light processing. The integration of carbon fibers provides multifunctionality to the bumper structure, enabling self-sensing capabilities through changes in electrical resistivity under compression. This electrical response demonstrates high repeatability under multiple cycles at 2% compression and exhibits distinct signatures during crack formation under high deformation. This research offers adaptive performance through innovative design methodologies and smart material integration. The approach has potential applications in various fields requiring adaptive energy absorption and real-time structural health monitoring.

Chawla, Komal [ORNL] (ORCID:0000000190327565)↗
DOE OSTI2023

Technical Report on Waveform Fit Metrics for Global Models

The new WAVEFORMS Initiative in the Ground-based Nuclear Detonation Detection (GNDD) program includes an increased emphasis on the development of Earth models and methods to predict entire seismic and acoustic waveforms more accurately. In general, this increased emphasis is predicated on the need to better characterize seismic events and provide improved model-based discrimination between event types including earthquakes and explosions. More specifically, while current moment tensor inversion methods tend to work well for larger events (M>~4) using tuned 1-D Earth models, the development of state-of-the-art 3-D models and methods is required for the prediction of shorter period waves over large areas for discrimination of smaller events. There is no standard metric for model-based waveform prediction accuracy used in the waveform modeling/inversion community. However, there are several popular waveform misfit definitions; and minimizing the corresponding objective functions is the goal of waveform inversion. Some example misfit definitions employed for adjoint waveform tomography include measures of simple travel time differences (e.g. Tape et al., 2010), cross-correlation travel time differences (e.g. Luo and Schuster, 1991), multi-taper frequency dependent methods (e.g. Lei et al., 2020), time-frequency phase misfit functions (e.g. Fichtner 2010; Rodgers et al., 2022), normalized cross-correlation methods (e.g. Tao et al., 2018), and others. In some cases, these misfit definitions also involve complicated weighting schemes and summations over multiple frequency bands making it difficult to duplicate the misfit measurement with alternative models and datasets. Although each of the misfit definitions mentioned above are useful for developing waveform models, the actual misfit values are not usually meaningful outside of a given project, model, and/or dataset. Therefore, it is difficult to understand and communicate model performance for predicting waveforms and comparing to other models and/or new model iterations with a different dataset. Therefore, there is a need for a generalized method for evaluating overall model performance that is independent from the specific misfit chosen to develop the waveform models that is also intuitive and meaningful. In this report, we describe a new metric we refer to as ‘Percent of Correlated Signal’. The following sections describe and demonstrate the metric with a case study event and a more rigorous test using a random selection of globally distributed events. While the focus here is on global tomography models, the metric is meant to applicable to regional ‘wiggle-for-wiggle’ waveform models/studies as well.

58 GEOSCIENCES↗
DOE OSTI2020

Online Energy-optimal Routing for Electric Vehicles with Combinatorial Multi-arm Semi-Bandit

We have seen a rapid growth in the adoption of electric vehicle in today’s commercial mobility service market, from carrying passengers to the delivery of goods. One cardinal issue concerning the operation of EVs is the optimal routing of EV fleets with limited battery capacity. In this study, we investigate the energy-optimal online routing problem for the fleet of EVs, which focuses on identifying real-time minimum electricity consumption paths (MECP) for multiple OD pairs with limited information. We develop a multi-OD combinatorial multi-arm semi-bandit model (MCMAB) that uses the fleet of EVs as sensors in the transportation network and promotes the utilization of common information shared by different OD pairs. We further enrich the model with the path elimination policy to obtain MECP of high confidence while significantly reducing the number of learning iterations and the number of explorations needed. We demonstrate the effectiveness of the MCMAB and the efficiency of the path elimination policy with comprehensive numerical experiments in Manhattan, NYC. The results show that the proposed online routing algorithms can achieve near-optimal MECPs efficiently, and the quality of the solutions is significantly better than using the shortest travel time paths as approximate MECPs.

Chen, Xiaowei↗
DOE OSTI2024

Adaptive laboratory evolution and genetic engineering improved terephthalate utilization in Pseudomonas putida KT2440

Poly(ethylene terephthalate) (PET) is one of the most ubiquitous plastics and can be depolymerized through biological and chemo-catalytic routes to its constituent monomers, terephthalic acid (TPA) and ethylene glycol (EG). TPA and EG can be re-synthesized into PET for closed-loop recycling or microbially converted into higher-value products for open-loop recycling. Here, in this study, we expand on our previous efforts engineering and applying Pseudomonas putida KT2440 for PET conversion by employing adaptive laboratory evolution (ALE) to improve TPA catabolism. Three P. putida strains with varying degrees of metabolic engineering for EG catabolism underwent an automation-enabled ALE campaign on TPA, a TPA and EG mixture, and glucose as a control. ALE increased the growth rate on TPA and TPA-EG mixtures by 4.1- and 3.5-fold, respectively, in approximately 350 generations. Evolved isolates were collected at the midpoints and endpoints of 39 independent ALE experiments, and growth rates were increased by 0.15 and 0.20 h -1 on TPA and a TPA-EG, respectively, in the best performing isolates. Whole-genome re-sequencing identified multiple converged mutations, including loss-of-function mutations to global regulators gacS, gacA, and turA along with large duplication and intergenic deletion events that impacted the heterologously-expressed tphAB II catabolic genes. Reverse engineering of these targets confirmed causality, and a strain with all three regulators deleted and second copies of tphAB II and tpaK displayed improved TPA utilization compared to the base strain. Taken together, an iterative strain engineering process involving heterologous pathway engineering, ALE, whole genome sequencing, and genome editing identified five genetic interventions that improve P. putida growth on TPA, aimed at developing enhanced whole-cell biocatalysts for PET upcycling.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pressure head), and these equations are coupled to one another by transfer terms. On its own, Richards equation is already a nonlinear partial differential equation, and it is exceedingly difficult to solve numerically due to the extra nonlinear dependencies involving the soil water. To deal with multiple scales, our strategy is that starting from a microscopic scale, we upscale the coupled system of dual-continuum Richards equations via homogenization by the two-scale asymptotic expansion, to obtain a homogenized system, at an intermediate scale (level). Based on a hierarchical approach, the homogenization’s effective coefficients are computed through solving the arising cell problems. Furthermore, to tackle the nonlinearity, after time discretization, we use Picard iteration procedure for linearization of the homogenized Richards equations. At each Picard iteration, some degree of multiscale still remains from the intermediate level, so we utilize the generalized multiscale finite element method (GMsFEM) combining with a multi-continuum approach, to upscale the homogenized system to a macroscopic (coarse-grid) level. This scheme involves building uncoupled and coupled multiscale basis functions, which are used not only to construct coarse-grid solution approximation with high accuracy but also (with the coupled multiscale basis) to capture the interactions among continua. These prospects and convergence are demonstrated by several numerical results for the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Fast Active-Set Thresholding Method for Nonnegative Least Squares

Nonnegative Least Squares (NNLS) is a fundamental constrained optimization problem encountered in many applications such as image deblurring, signal processing, nonnegative matrix factorization, magnetic microscopy, and hyperspectral imaging. Active-set based methods are a common class of algorithms for solving NNLS which identify the optimal variable set of the NNLS solution. They do so by iteratively solving a series of unconstrained least squares problems, identifying which variables violate the nonnegativity constraints, and then swapping variables in/out of consideration until the optimal set of variables is found. Several variations improving upon this method exist in the literature. In this work, we propose an active-set swap heuristic which further improves upon existing active-set based methods for NNLS. Our optimizations are based upon adding multiple variables to the passive set within a threshold of the smallest gradient value and removing variables within a similar threshold of the closest boundary constraint. We leverage these optimizations to yield a Fast Active-Set Thresholding NNLS (FAST-NNLS) algorithm which significantly outperforms the existing state-of-the-art NNLS algorithms for a wide range of problems. Rigorous convergence guarantees are proven for the proposed method. We demonstrate the effectiveness of our proposed method on multiple synthetic datasets and two realworld text analysis applications. In doing so, we present the most comprehensive NNLS solver comparison in the literature to date.

Cobb, Benjamin [Georgia Institute of Technology]↗
DOE OSTI2023

Performance Analysis and Optimal Node-aware Communication for Enlarged Conjugate Gradient Methods

Krylov methods are a key way of solving large sparse linear systems of equations but suffer from poor strong scalability on distributed memory machines. Furthermore, this is due to high synchronization costs from large numbers of collective communication calls alongside a low computational workload. Enlarged Krylov methods address this issue by decreasing the total iterations to convergence, an artifact of splitting the initial residual and resulting in operations on block vectors. In this article, we present a performance study of an enlarged Krylov method, Enlarged Conjugate Gradients (ECG), noting the impact of block vectors on parallel performance at scale. Most notably, we observe the increased overhead of point-to-point communication as a result of denser messages in the sparse matrix-block vector multiplication kernel. Additionally, we present models to analyze expected performance of ECG, as well as motivate design decisions. Most importantly, we introduce a new point-to-point communication approach based on node-aware communication techniques that increases efficiency of the method at scale.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Ensemble Manufacturing Techniques for Steam Turbine Components Across Length Scales

Faster design to manufacturing requirements were sought for steam turbine components to meet the changing demands of today’s power grid of improved efficiency through operating temperature increases and enhanced operational flexibility from baseload to cyclic operations. Advances in multiple advanced manufacturing (AM) process enabled redesign of turbine components for extreme environments with the potential to reduce cost. AM is of particular interest to improve component functionality, higher temperature capability, and superior durability in large scale steam turbine applications. AM methods have an immense potential to open-up the design space by working directly with the 3D model to produce near-net shapes, enable fast design-manufacturing iterations, thereby significantly reducing product cost and lead-time up to 25 % from current baseline. However, these benefits cannot be fully realized due to the potential for unknown AM processing defects and their resultant effect upon component performance in service. Siemens is partnering with Oak Ridge National Laboratory (ORNL), Electric Power Research Institute (EPRI), and Connecticut Center for Advanced Technology (CCAT) to advance the knowledge of complex process-material interactions for desired microstructures and properties that are closely interlinked to component geometries across different length scales. The proposed program utilized an ensemble of multidisciplinary technologies to accelerate the development of materials, high-throughput experiments for their qualification, and design flexibility/topology optimization for repair/redesign of components to address critical failure mechanisms for improved performance and increased reliability of existing power plant components. The proposed activities, if successfully demonstrated for identified components, will enable paradigm shift in customized manufacturing and accelerated qualification/certification towards increased steam turbine component durability, increased turbine efficiency, and reduced CO 2 emissions in load-following environments compared to today’s technology. Technology maturation is built into the project as successful research will include customized process-component down-selection enabling AM methodologies to be incorporated directly into the existing supply chain. The specific activities of the proposed effort are: 1. Topology optimization of down-selected steam turbine parts that are amenable to additive and hybrid manufacturing for cost/performance improvement. 2. Process-structure-property relationships for five AM processes for steam turbine materials of interest to compare with conventional materials. 3. Perform part/assembly build process using advanced additive/hybrid machine tools followed by quality inspection of the built components for insight into qualification for production scale-up. Steam turbine rig testing of printed components under targeted, well monitored and characterized environmental conditions of for performance comparison of baseline and redesigned components.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Deep Gaussian process-based cost-aware batch Bayesian optimization for complex materials design campaigns

The accelerating pace and expanding scope of materials discovery demand optimization frameworks that efficiently navigate vast design spaces with complex response surfaces while judiciously allocating limited evaluation resources. We present a cost-aware, batch Bayesian optimization scheme powered by deep Gaussian process (DGP) surrogates and a heterotopic querying strategy. Our DGP surrogate, formed by stacking GP layers, models complex hierarchical relationships among high-dimensional compositional features and captures correlations across multiple target properties, propagating uncertainty through successive layers. We integrate evaluation cost into an upper-confidence-bound acquisition extension, which, together with heterotopic querying, proposes small batches of candidates in parallel, balancing exploration of under-characterized regions with exploitation of high-mean, low-variance predictions across correlated properties. Applied to refractory high-entropy alloys for high-temperature applications, our framework converges to optimal formulations in fewer iterations with cost-aware queries than conventional GP-based BO, highlighting the value of deep, uncertainty-aware, cost-sensitive strategies in materials campaigns.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [Zhang et al., Enabling long-range exploration in minimization of multimodal functions, UAI 2021], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by deterministic oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. Here, we also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justifying the advantage of using moderate or large smoothing radii with the method. Furthermore, if the noise level decays to zero when approaching the global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based methods in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

Tran, Hoang [Oak Ridge National Laboratory (ORNL),↗