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DOE OSTI2025

Black-box optimization of CT acquisition and reconstruction parameters: a reinforcement learning approach

Protocol optimization is critical in Computed Tomography (CT) for achieving desired diagnostic image quality while minimizing radiation dose. Due to the inter-effect of influencing CT parameters, traditional optimization methods rely on the testing of exhaustive combinations of these parameters. This poses a notable limitation due to the impracticality of exhaustive parameter testing. This study introduces a novel methodology leveraging Virtual Imaging Trials (VITs) and reinforcement learning to more efficiently optimize CT protocols. Computational phantoms with liver lesions were imaged using a validated CT simulator and reconstructed with a novel CT reconstruction Toolkit. The optimization parameter space included tube voltage, tube current, reconstruction kernel, slice thickness, and pixel size. The optimization process was done using a Proximal Policy Optimization (PPO) agent which was trained to maximize the Detectability Index (d’) of the liver lesion for each reconstructed image. Results showed that our reinforcement learning approach found the absolute maximum d’ across the test cases while requiring 79.7% fewer steps compared to an exhaustive search, demonstrating both accuracy and computational efficiency, offering a efficient and robust framework for CT protocol optimization. The flexibility of the proposed technique allows for use of varying image quality metrics as the objective metric to maximize for. Our findings highlight the advantages of combining VIT and reinforcement learning for CT protocol management.

Fenwick, David [Duke University Medical Center]↗

DOE OSTI2023

Hardware-Conscious Optimization of the Quantum Toffoli Gate

While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can mitigate the effects of imperfect hardware by optimizing quantum circuits for objectives such as critical path length. Few approaches consider quantum circuits in terms of the set of vendor-calibrated operations (i.e., native gates) available on target hardware. This manuscript expands the analytical and numerical approaches for optimizing quantum circuits at this abstraction level. We present a procedure for combining the strengths of analytical native gate-level optimization with numerical optimization. Although we focus on optimizing Toffoli gates on the IBMQ native gate set, the methods presented are generalizable to any gate and superconducting qubit architecture. Our optimized Toffoli gate implementation demonstrates an 18% reduction in infidelity compared with the canonical implementation as benchmarked on IBM Jakarta with quantum process tomography. Assuming the inclusion of multi-qubit cross-resonance (MCR) gates in the IBMQ native gate set, we produce Toffoli implementations with only six multi-qubit gates, a 25% reduction from the canonical eight multi-qubit implementations for linearly connected qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Improving Dose-Optimization Processes Used in Oncology Drug Development to Minimize Toxicity and Maximize Benefit to Patients

This review highlights strategies to integrate dose optimization into premarketing drug development and discusses the underlying statistical principles. Poor dose optimization can have negative consequences for patients, most commonly because of toxicity, including poor quality of life, reduced effectiveness because of inability of patients to stay on current therapy or receive subsequent therapy because of toxicities, and difficulty in developing combination regimens. We reviewed US Food and Drug Administration initial approvals (2019-2021) of small molecules and antibody-drug conjugates for oncologic indications to determine the proportion with a recommended dosage at the maximum tolerated dose or the maximal administered dose, to characterize the use of randomized evaluations of multiple dosages in dose selection, to describe the frequency of dose modifications at the recommended dosage, and to identify case examples that highlight key principles for premarket dose optimization during drug development. Herein, we highlight major principles for dose optimization and review examples of recent US Food and Drug Administration approvals that illustrate how investigation of dose- and exposure-response relationships and use of randomized dose trials can support dose optimization. Although there has been some progress, dose optimization through randomized dose evaluation in oncology trials is not routinely conducted. Dose optimization is essential to ensure that patients receive therapies which maximize efficacy while minimizing toxicity.

Oncology↗

DOE OSTI2024

Core Design Optimization of the Westinghouse Lead Fast Reactor

Westinghouse is pursuing an advanced Nuclear Power Plant design based on Lead Fast Reactor (LFR) technology for global commercialization. To achieve an optimal combination of key attributes, such as safety, sustainability, and economic competitiveness, Westinghouse and ANL partnered in developing and applying a formalized core design optimization strategy. An LFR analysis workflow was developed to automate a suite of reactor physics, fuels performance, safety, and economics simulations on a selected LFR concept. The workflow streamlines analysis of a wide range of LFR designs with different dimensions and fuel types to assess their viability and economic performance, significantly reducing human processing time and risks of processing errors. The LFR optimization exercise was defined, resulting in selection of the design constraints (geometric, neutronics, thermo-mechanical, safety, thermal-hydraulics, and economics) and performance metrics researched (minimization of both the fuels LCOE and the first core inventory cost). A total of 14 varied design parameters were considered, including assembly dimensions, coolant temperature, and enrichment distribution throughout the core. The LFR analysis workflow was connected to DAKOTA for sensitivity and optimization analyses. Due to the extremely large size of the potential LFR optimization solution space relative to the computing time required to characterize one LFR solution, a multi-stage optimization approach was proposed to breakdown the problem into several stages with more reasonable sizes. This optimization approach enabled finding various viable core solutions with different cost tradeoffs that were considered by Westinghouse and justify selection of a smaller core with multi-batch 2-year cycle length.

Stauff, Nicolas E.↗

DOE OSTI2019

Designing Critical Experiments Using Gaussian Process Optimization

New nuclear applications may lack similarity between the application and existing ICSBEP benchmarks. Without accurate benchmark data, predictive simulations will have high uncertainty in the estimate of a parameter of interest (such as k eff ). The design of critical experiments tuned for specific applications of interest is one solution to reducing uncertainty in the necessarily nuclear data. We propose an optimization technique to design critical experiments that match the cross-section sensitivities of an application model while minimizing the number of simulation runs in the optimization. The optimization of a critical experiment is slow because the potential design space covers many qualitative variables (types of material and geometries) and corresponding quantitative variables (e.g., material dimensions) and the evaluation of any specific design requires running an expensive code like MCNP1 and Whisper. The optimization of expensive black-box computer codes with quantitative variables has been extensively explored in the literature of design of computer experiments. We propose a modified version of standard Gaussian process (GP) optimization that optimizes over multiple discrete configurations of qualitative variables in parallel which reduces the computational cost of the entire optimization. The goal of this work is to minimize the number of MCNP evaluations while still exploring many different design configurations in parallel.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Efficient Discovery of Optimal N -Layered TMDC Hetero-Structures

ABSTRACT Vertical hetero-structures made from stacked monolayers of transition metal dichalcogenides (TMDC) are promising candidates for next-generation optoelectronic and thermoelectric devices. Identification of optimal layered materials for these applications requires the calculation of several physical properties, including electronic band structure and thermal transport coefficients. However, exhaustive screening of the material structure space using ab initio calculations is currently outside the bounds of existing computational resources. Furthermore, the functional form of how the physical properties relate to the structure is unknown, making gradient-based optimization unsuitable. Here, we present a model based on the Bayesian optimization technique to optimize layered TMDC hetero-structures, performing a minimal number of structure calculations. We use the electronic band gap and thermoelectric figure of merit as representative physical properties for optimization. The electronic band structure calculations were performed within the Materials Project framework, while thermoelectric properties were computed with BoltzTraP. With high probability, the Bayesian optimization process is able to discover the optimal hetero-structure after evaluation of only ~20% of all possible 3-layered structures. In addition, we have used a Gaussian regression model to predict not only the band gap but also the valence band maximum and conduction band minimum energies as a function of the momentum.

Bassman Oftelie, Lindsay↗

DOE OSTI2017

Testing of Strategies for the Acceleration of the Cost Optimization

The general problem addressed in the Nuclear-Renewable Hybrid Energy System (N-R HES) project is finding the optimum economical dispatch (ED) and capacity planning solutions for the hybrid energy systems. In the present test-problem configuration, the N-R HES unit is composed of three electrical power-generating components, i.e. the Balance of Plant (BOP), the Secondary Energy Source (SES), and the Energy Storage (ES). In addition, there is an Industrial Process (IP), which is devoted to hydrogen generation. At this preliminary stage, the goal is to find the power outputs of each one of the N-R HES unit components (BOP, SES, ES) and the IP hydrogen production level that maximizes the unit profit by simultaneously satisfying individual component operational constraints. The optimization problem is meant to be solved in the Risk Analysis Virtual Environment (RAVEN) framework. The dynamic response of the N-R HES unit components is simulated by using dedicated object-oriented models written in the Modelica modeling language. Though this code coupling provides for very accurate predictions, the ensuing optimization problem is characterized by a very large number of solution variables. To ease the computational burden and to improve the path to a converged solution, a method to better estimate the initial guess for the optimization problem solution was developed. The proposed approach led to the definition of a suitable Monte Carlo-based optimization algorithm (called the preconditioner), which provides an initial guess for the optimal N-R HES power dispatch and the optimal installed capacity for each one of the unit components. The preconditioner samples a set of stochastic power scenarios for each one of the N-R HES unit components, and then for each of them the corresponding value of a suitably defined cost function is evaluated. After having simulated a sufficient number of power histories, the configuration which ensures the highest profit is selected as the optimal one. The component physical dynamics are represented through suitable ramp constraints, which considerably simplify the numerical solving. In order to test the capabilities of the proposed approach, in the present report, the dispatch problem only is tackled, i.e. a reference unit configuration is assumed, and each one of the N-R HES unit components is assumed to have a fixed installed capacity. As for the next steps, the main improvement will concern the operation strategy of the ES facility. In particular, in order to describe a more realistic battery commitment strategy, the ES operation will be regulated according to the electricity price forecasts.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2018

Chance-Constrained Optimization for Critical Infrastructure Protection

Stochastic optimization deals with making highly reliable decisions under uncertainty. Chance constraints are a crucial tool of stochastic optimization to develop mathematical optimization models; they form the backbone of many important national security data science applications. These include critical infrastructure resiliency, cyber security, power system operations, and disaster relief management. However, existing algorithms to solve chance-constrained optimization models are severely limited by problem size and structure. In this investigative study, we (i) develop new algorithms to approximate chance-constrained optimization models, (ii) demonstrate the application of chance-constraints to a national security problem, and (iii) investigate related stochastic optimization problems. We believe our work will pave way for new research is stochastic optimization as well as secure national infrastructures against unforeseen attacks.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2020

Management of Risk and Uncertainty Through Optimized Co-Operation of Transmission Systems and Microgrids with Responsive Loads (Final Report)

The evolution of the power system to the reliable, efficient and sustainable system of the future will involve development of both demand- and supply-side technology and operations. Ambitious national and state-level goals around the decarbonization of electricity relies on the integration of very high levels of renewable resources, most of which are variable and intermittent. The use of demand response is an ideal approach to counterbalance the intermittency of renewable generation and brings the consumer into the spotlight. Until recently, very little research had been conducted on the co-optimization of these two systems due to computational limitations. However, advances in computational capabilities, and the judicious use of decomposition methods and innovative approximation methods for high-dimension dynamic programming made this goal a viable objective for this project, leading to a fundamental shift in the ability to integrate and fully utilize demand-side resources. To this end, the modeling framework developed introduces a novel co-optimization framework, to include the operations of both the transmission and distribution systems (or microgrids) in operational decision making. This framework was used to analyze renewable and distributed generation along with responsive demand and to compare the capability of co-optimized systems to perform with higher levels of variable renewables. Results show that the use of a bi-level optimization approach is an appropriate structure, capable of co-optimizing a transmission system with multiple distribution systems and microgrids. While increasing the number of connected systems provides increasing flexibility for renewables integration this can also the economic benefits to the low-voltage subsystems with each additional system connected. Comparison of a traditional single-level decision structure with the co-optimization approach illustrates a reduction in overall system cost under co-optimization, while specific cost allocations to transmission and distribution systems are changed.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Online Optimization of NSLS-II Dynamic Aperture and Injection Transient (Facility Improvement Project)

The Facility Improvement Project (FIP) “Methods of online optimization of NSLS-II storage ring concurrent with user operations” proposed and approved in 2018 is now complete. The first goal is the online optimization of nonlinear beam dynamics to increase the beam lifetime and injection efficiency. We have developed a model-independent optimization technique using advanced algorithms. Using this technique, we increased the NSLS-II dynamic aperture by 20% and reduced the amplitude-dependent tune shift by a factor of two. We applied sextupole optimization to the new high-chromaticity lattice, which has been developed to improve the beam stability and to increase the single-bunch beam intensity. We were able to double the injection efficiency and exceed 90%. The second goal of this project is to provide the top-off injection with minimized perturbations of the beamline user operations. To achieve the transparent injection, we optimize the matching of four storage ring injection kickers reducing the perturbation of the stored beam orbit. The first application of the online optimization resulted in a reduction of the amplitude of residual beam oscillation by a factor of six, from 1300 μm down to 200 μm. Further improvement was limited by the timing jitter of the trigger boards. Then, we replaced all trigger boards with a new design and reduced the timing jitter by a factor of five, from 5 ns down to 1 ns. This upgrade resulted in the injection transient reduction from 200 μm to 120 μm. To optimize the full set of kicker parameters, including the trigger timing, amplitude, and pulse width, we upgraded all kicker power supplies with the capability of tunable waveform width. As a result, we have reduced the injection transient to the limit of 60 μm.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

An Online Prototype Toolset for Predicting and Optimizing P&T Performance (FY23 Status Report)

A new web-based toolset is being developed to support ongoing remediation optimization efforts and implementation of an adaptive site management strategy for the 200 West Area Pump-and-Treat (P&T) system at the Hanford Site. This toolset, comprising the well performance index tool and the well optimization pre-screening tool, will offer a user-friendly interface to predict and optimize the P&T well network’s performance at a preliminary level. Efforts in fiscal year (FY) 2023 focused on three main components: updating the existing deep learning model for predicting P&T performance, designing and developing a prototype of a web-based performance index tool, and initiating the conceptual design of the well optimization pre-screening tool. The well performance index tool is based on a pre-trained deep learning model that allows users to select a target contaminant and well screen length, then visualize the predicted performance of potential new wells across the site. The well optimization pre-screening tool includes two separate modules: the pre-computed scenario viewer, which organizes and visualizes offline optimization simulation results, and the quick analysis module, which provides real-time model prediction using user-specified well locations. In FY24, the plan is to add web-based applications to SOCRATES for both the well performance prediction tool and the optimization prescreening tool, with accompanying user and theory guides. These tools are intended to enable an accessible, easily applied, and transparent approach to remedy planning and decision-making.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A Review of Quantum Computing Technologies in Power System Optimization

As modern power grids increasingly integrate variable renewable generation, distributed energy resources, and energy storage systems, classical optimization techniques are facing unprecedented challenges. This review examines the emerging application of quantum computing to overcome these challenges in power system optimization, including optimal power flow (OPF), unit commitment (UC), economic dispatch (ED), and intelligent switching and topology optimization (IS-TO). Recent research has introduced various quantum methodologies—such as gate-based, annealing-based, variational algorithms, and quantum-inspired algorithms—to address the combinatorial complexity inherent in grid reconfiguration and energy management. The review summaries the quantum algorithms, quantum devices and the power system test cases, highlighting hybrid quantum–classical strategies that leverage the complementary strengths of both paradigms. Some quantum advantages have been observed, including theoretical speedup, accurate simulation results, scalable qubit usage, efficient QUBO mapping. In particular, the review emphasizes the importance of integrating quantum optimization techniques with classical control frameworks, these hybrid approaches demonstrate the potential to improve real-time grid management and operational reliability. A significant portion of the analysis is devoted to the practical limitations of current quantum devices. Present-day quantum hardware, operating in the noisy intermediate-scale quantum (NISQ) era, remains highly sensitive to noise and limited in qubit connectivity, which constrains the scale and accuracy of implemented algorithms. The review delves into specific challenges such as the need for qubit-efficient encoding techniques and error mitigation strategies that are critical for handling real-world grid optimization problems. In addition, the work draws attention to the performance discrepancies between theoretical quantum speedups and experimental validations, underscoring the importance of rigorous benchmark studies using representative power grid test cases. In summary, this review highlights both the promise and limitations of quantum computing for power system optimization. It provides a comprehensive overview of the state-of-the-art technologies, categorizes recent advancements in algorithm design, and discusses practical considerations for implementation, and serves as an informative resource on current research. Future research directions include developing robust hybrid frameworks, advancing qubit-efficient formulations, and scaling up experimental demonstrations to confirm the theoretical advantages of quantum methods in large-scale power system operations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Sensor System and Observer Algorithm Co-Design For Modern Internal Combustion Engine Air Management Based on H2 Optimization

This paper outlines a novel sensor selection and observer design algorithm for linear time-invariant systems with both process and measurement noise based on H 2 optimization to optimize the tradeoff between the observer error and the number of required sensors. The optimization problem is relaxed to a sequence of convex optimization problems that minimize the cost function consisting of the H 2 norm of the observer error and the weighted l 1 norm of the observer gain. An LMI formulation allows for efficient solution via semi-definite programing. The approach is applied here, for the first time, to a turbo-charged spark-ignited engine using exhaust gas circulation to determine the optimal sensor sets for real-time intake manifold burnt gas mass fraction estimation. Simulation with the candidate estimator embedded in a high fidelity engine GT-Power model demonstrates that the optimal sensor sets selected using this algorithm have the best H 2 estimation performance. Sensor redundancy is also analyzed based on the algorithm results. This algorithm is applicable for any type of modern internal combustion engines to reduce system design time and experimental efforts typically required for selecting optimal sensor sets.

Zhang, Xu↗

DOE OSTI2019

Route-Optimized Energy Management of Connected and Automated Multi-Mode Plug-In Hybrid Electric Vehicle Using Dynamic Programming

This paper presents a methodology to optimize the blending of charge-depleting (CD) and charge-sustaining (CS) modes in a multi-mode plug-in hybrid electric vehicle (PHEV) that reduces overall energy consumption when the selected route cannot be completely driven in all-electric mode. The PHEV used in this investigation is the second-generation Chevrolet Volt and as many as four instrumented vehicles were utilized simultaneously on road to acquire validation data. The optimization method used is dynamic programming (DP) paired with a reduced-order powertrain model to enable onboard embedded controller compatibility and computational efficiency in optimally blending CD, CS modes over the entire drive route. The objective of the optimizer is to enable future Connected and Automated Vehicles (CAVs) to best utilize onboard energy for minimum overall energy consumption based on speed and elevation profile information from Intelligent Transportation Systems (ITS), Internet of Things (IoT), High-definition Mapping, and onboard sensing technologies. Emphasis is placed on runtime minimization to quickly react and plan an optimal mode scheme in highly dynamic road conditions with minimal computational resources. On-road performance of the optimizer paired with automated CD and CS mode selection is evaluated on a fleet of four instrumented Chevrolet Volts in a variety of driving scenarios. Here, the results indicate variable energy savings depending on the drive route and initial battery SOC with potential ranging between 2 to 12% and less than 7 seconds initial optimization for a 24-mile drive cycle.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2024

Performance Analysis of an Optimization Algorithm for Metamaterial Design on the Integrated High-Performance Computing and Quantum Systems

Optimizing metamaterials with complex geometries is a big challenge. Although an active learning algorithm, combining machine learning (ML), quantum computing, and optical simulation, has emerged as an efficient optimization tool, it still faces difficulties in optimizing complex structures that have potentially high performance. In this work, we comprehensively analyze the performance of an optimization algorithm for metamaterial design on the integrated HPC and quantum systems. We demonstrate significant time advantages through message-passing interface (MPI) parallelization on the high-performance computing (HPC) system showing approximately 54% faster ML tasks and 67 times faster optical simulation against serial workloads. Furthermore, we analyze the performance of a quantum algorithm designed for optimization, which runs with various quantum simulators on a local computer or HPC-quantum system. Results showcase ~24 times speedup when executing the optimization algorithm on the HPC-quantum hybrid system. This study paves a way to optimize complex metamaterials using the integrated HPC-quantum system.

Kim, Seongmin↗

DOE OSTI2018

Optimization study of B4C filter thickness for shifting to fast spectrum at experimental position in NRAD core

The Japan Atomic Energy Agency (JAEA) has investigated an accelerator-driven system (ADS) to transmute minor actinides (MAs) partitioned from the high level waste. In the nuclear transmutation system such as the ADS, the nuclear data validation of MA is required to reduce the uncertainty caused by the nuclear data of MA. In order to validate the nuclear data, many independent experimental data need to be mutually compared. The Idaho National Laboratory (INL) considers the measurement of fission rate ratio and sample worth with a wide spectral indices by inserting several types of thermal neutron shielding filters in the experimental position in Neutron RADiography (NRAD) which is the thermal neutron reactor. The JAEA has a plan to perform integral experiments with fission chambers in the NRAD because of the expansion of the experimental data contributing to nuclear data validation of MA. In this study, the optimization of the NRAD core configuration, the B4C filter thickness, and the experimental position design was conducted to acquire the high-accuracy and the beneficial experimental data by using MCNP 6.1 and ENDF/B-VII.1. First, by locating the experimental position as close to the center of the core as possible and concentrating the fuel around that position, the neutron flux of the optimized model could be constructed 2.5 times as much as that of the previous model. Second, the optimized B4C filter thickness was determined to be 3mm based on the comprehensive evaluation from the viewpoints of the shielding ability of low energy neutrons, the level of the total neutron flux, and the influence of fabrication accuracy of the B4C filter. Third, we constructed the experimental position model that could further reduce the influence of the low energy neutrons by adopting the aluminum dry box and the bottom filter. Moreover, the neutron energy spectrum of the tentative optimized model constructed by following the above results was compared with that of the fast neutron reactors such as the ADS and the Fast Critical Assembly (FCA). As a result, the tentative optimized model would be able to be obtained the beneficial experimental data for the verification of FCA-IX series data and the validation of MA nuclear data for accuracy improvement of ADS design. Furthermore, the adoption of the tentative optimized model would be acquired the experimental data such as fission reaction rate and sample worth with the wider spectral indices than the previous one because the tentative optimized model would be able to increase the ratio of the fast neutrons by almost completely eliminating the effect of the thermal neutrons.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Experimental Validation of Approximate Dynamic Programming Based Optimization and Convergence on Microgrid Applications

Stochastic optimization can better address uncertainties in power system problems. However, when state space and action space become large, many existing approaches become computationally expensive and even infeasible. Approximate dynamic programming (ADP) attracts researchers’ attention as a powerful tool for solving power system optimization problems with reduced computational cost. In this paper, in light of the existing literature, we investigate how the ADP approach with post-decision value function approximation converges to the nearly optimal solution with improved computational speed and experimentally validate the performance of the approach for a microgrid energy optimization problem. The approximation error versus the number of iteration is studied for convergence analysis of the post-decision ADP. A flowchart is provided to illustrate the proposed ADP algorithm for a microgrid energy optimization problem. The performance of ADP and dynamic programming (DP) is compared in terms of optimization error and computational time. It has found that the post-decision ADP approach can achieve competitive optimality with improved computational speed compared to the traditional DP.

Das, Avijit↗

DOE OSTI2020

Do optimization methods in deep learning applications matter?

With advances in deep learning, exponential data growth and increasing model complexity, developing efficient optimization methods are attracting much research attention. Several implementations favor the use of Conjugate Gradient (CG) and Stochastic Gradient Descent (SGD) as being practical and elegant solutions to achieve quick convergence, however, these optimization processes also present many limitations in learning across deep learning applications. Recent research is exploring higher-order optimization functions as better approaches, but these present very complex computational challenges for practical use. Comparing first and higher-order optimization functions, in this paper, our experiments reveal that Levemberg-Marquardt (LM) significantly supersedes optimal convergence but suffers from very large processing time increasing the training complexity of both, classification and reinforcement learning problems. Our experiments compare off-the-shelf optimization functions(CG, SGD, LM and L-BFGS) in standard CIFAR, MNIST, CartPole and FlappyBird experiments.The paper presents arguments on which optimization functions to use and further, which functions would benefit from parallelization efforts to improve pretraining time and learning rate convergence.

Ozyildirim, Buse Melis↗