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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 OSTI2017

Understanding the Hierarchy of Dense Subgraphs in Stationary and Temporally Varying Setting

Graphs are widely used to model relationships in a wide variety of domains such as sociology, bioinformatics, infrastructure, the WWW, to name a few. One of the key observations is that while real-world graphs are often globally sparse, they are locally dense. In other words, the average degree is often quite small (say at most 10 in a million vertex graph), but vertex neighborhoods are often dense. Finding dense subgraphs is a critical aspect of graph mining It has been used for finding communities and spam link farms in web graphs, graph visualization, real-time story identification, DNA motif detection in biological networks, finding correlated genes, epilepsy prediction, finding price value motifs in financial data, graph compression, distance query indexing, and increasing the throughput of social networking site servers. However, most standard formulations of this problem (like clique, quasi-clique, k-densest subgraph) are NP-hard. Furthermore, current dense subgraph finding algorithms usually optimize some objective, and only find a few such subgraphs without providing any structural relations, whereas the goal is rarely to find the "true optimum," but to identify many (if not all) dense substructures, understand their distribution in the graph, and ideally determine relationships among them. In this project, we first aim to devise algorithms and provide 3 implementations with nice visualizations to find the hierarchy between dense subgraphs, and then understand the structure of the hierarchy to gain more insight on the hidden patterns in real-world networks. Another important aspects in graph analysis is the temporal nature of networks. Networks evolve over time and in many applications data arrives at a high velocity, and thus it is important to design algorithms that can process data efficiently. We report three main results towards identifying dense structures in large evolving graphs. First, we will show how the hierarchical connectedness structure can be maintained efficiently, where connectedness is defined by increasing levels of connectivity strength. Next, we present dense structure can be identified in bipartite graphs without building projection graphs. And finally, we present a new method for peeling algorithms This new approach avoids sequential nature of peeling algorithms and is amenable to parallelization, which is crucial for processing high velocity data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Optimization of biogenic methane production from coal

Given continuously increasing global energy needs, diversified efforts have been made to find and exploit new natural gas resources. These include coalbed methane (CBM), which represents an important global, unconventional source of natural gas. Efforts have been underway for some time to more effectively generate methane in-situ in coal plays by introduction of nutrients and/or microbial consortia. However, much is still to be learned about the limitations and environmental conditions that support microbial growth and are conducive to biogenic methane production from coal. Here we evaluated environmental conditions that led to increased methane production from subbituminous coal by introducing a foreign methanogenic consortium that included Methanobacterium sp. Furthermore, we used a central composite design (CCD) to explore a broad range of operational conditions, examine the effects of the important environmental factors, such as temperature, pH and salt concentration, and query a feasible region of operation to maximize methane production from coal. An anticipated detrimental effect of NaCl concentration on methane production was observed for the consortium assessed. The range of feasible operational conditions comprised initial pH values between 4.2 and 6.8, temperatures between 23 °C and 37 °C, and NaCl concentrations between 3.7 mg/cm 3 and 9.0 mg/cm 3 . Coal biogasification was optimal for this consortium at an initial pH value of 5.5, at 30 °C, and at a NaCl concentration 3.7 mg/cm 3 (i.e., 145,165 ppm, which is 25.6 sft 3 /ton).

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2020

Shape Optimization for Control and Isolation of Structural Vibrations in Aerospace and Defense Applications

Among the main challenges in shape optimization is the coupling of Finite Element Method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multi-physics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. There are two mathematically equivalent approaches to computing the shape derivative: the volume method, and the boundary method. Each has a major drawback: the boundary method is less accurate, while the volume method is more invasive to the FEM code. Prior implementations of shape derivatives at Sandia have been based on the volume method. We introduce the strip method, which computes shape derivatives on a strip adjacent to the boundary. The strip method makes code coupling simple. Like the boundary method, it queries the state and adjoint solutions at quadrature nodes, but requires no knowledge of the FEM code implementations. At the same time, it exhibits the higher accuracy of the volume method. The development of the strip method also offers us the opportunity to share some lessons learned about implementing the volume method and boundary method, to show shape optimization results on problems of interest, and to begin addressing the other main challenges at hand: constraints on optimized shapes, and their interplay with optimization algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Materials Databases Infrastructure Constructed by First Principles Calculations: A Review

The First Principles calculations, especially the calculation based on High-Throughput Density Functional Theory, have been widely accepted as the major tools in atom scale materials design. The emerging super computers, along with the powerful First Principles calculations, have accumulated hundreds of thousands of crystal and compound records. The exponential growing of computational materials information urges the development of the materials databases, which not only provide unlimited storage for the daily increasing data, but still keep the efficiency in data storage, management, query, presentation and manipulation. This review covers the most cutting edge materials databases in materials design, and their hot applications such as in fuel cells. By comparing the advantages and drawbacks of these high-throughput First Principles materials databases, the optimized computational framework can be identified to fit the needs of fuel cell applications. The further development of high-throughput DFT materials database, which in essence accelerates the materials innovation, is discussed in the summary as well.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Training quantum neural networks using the quantum information bottleneck method

Abstract We provide in this paper a concrete method for training a quantum neural network to maximize the relevant information about a property that is transmitted through the network. This is significant because it gives an operationally well founded quantity to optimize when training autoencoders for problems where the inputs and outputs are fully quantum. We provide a rigorous algorithm for computing the value of the quantum information bottleneck quantity within error ε that requires O ( log 2 ⁡ ( 1 / ϵ ) + 1 / δ 2 ) queries to a purification of the input density operator if its spectrum is supported on { 0 } ⋃ [ δ , 1 − δ ] for δ > 0 and the kernels of the relevant density matrices are disjoint. We further provide algorithms for estimating the derivatives of the QIB function, showing that quantum neural networks can be trained efficiently using the QIB quantity given that the number of gradient steps required is polynomial.

Çatlı, Ahmet Burak (ORCID:0000000152294141)↗
DOE OSTI2024

Efficient Unitary Designs from Random Sums and Permutations

A unitary k-design is an ensemble of unitaries that matches the first k moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques. Our first construction is based on exponentiating sums of random i.i.d. Hermitian matrices and uses O(k2n2)-many gates. In the spirit of central limit theorems, we show that this random sum approximates the Gaussian Unitary Ensemble (GUE). We then show that the product of just two exponentiated GUE matrices is already approximately Haar random. Our second construction is based on products of exponentiated sums of random permutations and uses Õ(k poly (n)) many gates. The k dependence is optimal (up to polylogarithmic factors) and is inherited from the efficiency of existing k-wise independent permutations. Furthermore, replacing random permutations with quantum-secure pseudorandom permutations (PRPs), we also obtain a pseudorandom unitary (PRU) ensemble that is secure under nonadaptive queries. A central feature of both proofs is a new connection between the polynomial method in quantum query complexity and the large-dimension (N) expansion in random matrix theory. In particular, the first construction uses the polynomial method to control high moments of certain random matrix ensembles without requiring delicate Weingarten calculations. In doing so, we define and solve a moment problem on the unit circle, asking whether a finite number of equally weighted points can reproduce a given set of moments. In our second construction, the key step is to exhibit an orthonormal basis for irreducible representations of the partition algebra that has a low-degree large-N expansion. This allows us to show that the distinguishing probability is a low-degree rational polynomial of the dimension N.

algebra↗
DOE OSTI2021

Optimizing FPGA-based Accelerator Design for Large-Scale Molecular Similarity Search (Special Session Paper)

Molecular similarity search has been widely used in drug discovery to rapidly identify structurally similar compounds from large molecular databases. With the increasing size of chemical libraries, there is growing interest in the efficient ac- celeration of large-scale similarity search. Existing works mainly focus on CPU and GPU to accelerate the computation of Tatimoto coefficient in measuring the pairwise similarity between different molecular fingerprints. In this paper, we propose and optimize an FPGA-based accelerator design on exhaustive and approximate search algorithms. On exhaustive search using BitBound & fold- ing, we analyze the similarity cutoff and folding level relationship with search speedup and accuracy, and propose a scalable on- the-fly query engine on FPGAs to reduce the resource utilization and pipeline interval. We achieve a 450 million compounds-per- second processing throughput for a single query engine. On approximate search using hierarchical navigable small world (HNSW), a popular algorithm with high recall and query speed, we propose an FPGA-based graph traversal engine to utilize high throughput register array based priority queue and fine- grained distance calculation engine to increase the processing capability. Experimental results show that the proposed FPGA- based HNSW implementation achieves a 35× speedup than existing works on CPU. To the best of our knowledge, our FPGA- based implementation is the first attempt to accelerate molecular similarity search on FPGA and has the highest performance among existing approaches.

Peng, Hongwu↗
DOE OSTI2019

Diventi

Diventi provides a write optimized index of network logs such as netflow or zeek. The program will ingest various network traffic logs (zeek connection logs or NetflowV5, v9 or IPFix logs) and index each IP address and time of its activity. This database can then be queried for timely tracking of network activity. It currently uses the ft-index library from Percona but is adaptable to any key-value store that supports the Berkeley DB api.SAND2019-15037 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Kroeger, Thomas↗
DOE OSTI2025

Investigating Kinetic Mechanisms of Soot Formation in Plasma Pyrolysis of Methane via Active Learning (Final Technical Report)

Plasma pyrolysis of methane is an effective route for zero-carbon hydrogen production. Yet, soot generated from pyrolysis of hydrocarbons is detrimental to the climate and human health. There is ample experimental and theoretical evidence that suggests polycyclic aromatic hydrocarbons (PAHs) are the molecular precursors to soot particles. The reaction pathways of PAH formation are intricately dependent on a multitude of process parameters, whose kinetic mechanisms are not well-understood in plasma pyrolysis. This project aims to leverage advances in the kinetic modeling of soot formation in combustion, as well as in surrogate modeling and active learning, to systematically investigate the effects of process parameter on the kinetics of PAH formation in plasma pyrolysis of methane. To this end, we propose to use the PAH formation kinetics model developed by the PPPL/PU group based on the well-established ABF and HACA mechanisms, coupled with low-temperature plasma models. We will develop an active learning (AL) framework based on Bayesian optimization to systematically and data-efficiently explore the complex and multivariable parameter space of plasma pyrolysis in order to quantify the effects of plasma and feed parameters on the ABF and HACA kinetic pathways. AL is the branch of machine learning concerned with systematically querying samples from a system (experimental or computational) to train a data-driven model that maps design parameters to a performance criterion. We will use the data generated via AL to perform global sensitivity analysis, combined with uncertainty quantification, to elucidate the impact of different reaction pathways on minimizing formation of soot precursors. This study will result in an improved understanding of kinetics of PAH formation in plasma pyrolysis and can pave the way for more advanced mechanistic studies (e.g., soot nucleation mechanisms). Additionally, the findings will be useful for establishing practical strategies for increasing the pyrolysis efficiency and producing high-grade carbon for synthesis of nanomaterials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Scalability Testing Approach for Internet of Things for Manufacturing SQL and NoSQL Database Latency and Throughput

The proliferation of low-cost sensors and industrial data solutions has continued to push the frontier of manufacturing technology. Machine learning and other advanced statistical techniques stand to provide tremendous advantages in production capabilities, optimization, monitoring, and efficiency. The tremendous volume of data gathered continues to grow, and the methods for storing the data are critical underpinnings for advancing manufacturing technology. This work aims to investigate the ramifications and design tradeoffs within a decoupled architecture of two prominent database management systems (DBMS): sql and NoSQL. A representative comparison is carried out with Amazon Web Services (AWS) DynamoDB and AWS Aurora MySQL. The technologies and accompanying design constraints are investigated, and a side-by-side comparison is carried out through high-fidelity industrial data simulated load tests using metrics from a major US manufacturer. The results support the use of simulated client load testing for comparing the latency of database management systems as a system scales up from the prototype stage into production. As a result of complex query support, MySQL is favored for higher-order insights, while NoSQL can reduce system latency for known access patterns at the expense of integrated query flexibility. Here, by reviewing this work, a manufacturer can observe that the use of high-fidelity load testing can reveal tradeoffs in IoTfM write/ingestion performance in terms of latency that are not observable through prototype-scale testing of commercially available cloud DB solutions.

AWS↗
DOE OSTI2022

Data-driven wind turbine wake modeling via probabilistic machine learning

Wind farm design primarily depends on the variability of the wind turbine wake flows to the atmospheric wind conditions and the interaction between wakes. Physics-based models that capture the wake flow field with high-fidelity are computationally very expensive to perform layout optimization of wind farms, and, thus, data-driven reduced-order models can represent an efficient alternative for simulating wind farms. In this work, we use real-world light detection and ranging (LiDAR) measurements of wind-turbine wakes to construct predictive surrogate models using machine learning. Specifically, we first demonstrate the use of deep autoencoders to find a low-dimensional latent space that gives a computationally tractable approximation of the wake LiDAR measurements. Then, we learn the mapping between the parameter space and the (latent space) wake flow fields using a deep neural network. Additionally, we also demonstrate the use of a probabilistic machine learning technique, namely, Gaussian process modeling, to learn the parameter-space-latent-space mapping in addition to the epistemic and aleatoric uncertainty in the data. Finally, to cope with training large datasets, we demonstrate the use of variational Gaussian process models that provide a tractable alternative to the conventional Gaussian process models for large datasets. Furthermore, we introduce the use of active learning to adaptively build and improve a conventional Gaussian process model predictive capability. Overall, we find that our approach provides accurate approximations of the wind-turbine wake flow field that can be queried at an orders-of-magnitude cheaper cost than those generated with high-fidelity physics-based simulations.

Deep neural networks↗
DOE OSTI2023

Data-Centric AI and the Open Energy Data Initiative (OEDI)

This presentation emphasizes the critical importance of data-centric AI. The limitations of model-centric AI when dealing with poor or insufficient data are highlighted, and it is illustrated how training models on inaccurate or noisy data leads to suboptimal results. This talk advocates for a hybrid approach that combines a focus on data quality and model parameters to achieve optimal results. The Open Energy Data Initiative (OEDI) is introduced as a valuable resource for obtaining high-quality energy-related datasets, hosting nearly 2,000 publicly accessible datasets, including 99 solar-related datasets, totaling over 2.7 petabytes of data. OEDI's data lakes enable users to query and work with data without extensive transfers. In conclusion, the significance of data-centric AI and adherence to data curation best practices is emphasized, positioning OEDI as a prime source of high-quality data for AI and machine learning in the renewable energy sector.

AI↗
DOE OSTI2016

WarpIV: In situ visualization and analysis of ion accelerator simulations

The generation of short pulses of ion beams through the interaction of an intense laser with a plasma sheath offers the possibility of compact and cheaper ion sources for many applications--from fast ignition and radiography of dense targets to hadron therapy and injection into conventional accelerators. To enable the efficient analysis of large-scale, high-fidelity particle accelerator simulations using the Warp simulation suite, the authors introduce the Warp In situ Visualization Toolkit (WarpIV). WarpIV integrates state-of-the-art in situ visualization and analysis using VisIt with Warp, supports management and control of complex in situ visualization and analysis workflows, and implements integrated analytics to facilitate query- and feature-based data analytics and efficient large-scale data analysis. WarpIV enables for the first time distributed parallel, in situ visualization of the full simulation data using high-performance compute resources as the data is being generated by Warp. The authors describe the application of WarpIV to study and compare large 2D and 3D ion accelerator simulations, demonstrating significant differences in the acceleration process in 2D and 3D simulations. WarpIV is available to the public via https://bitbucket.org/berkeleylab/warpiv. The Warp In situ Visualization Toolkit (WarpIV) supports large-scale, parallel, in situ visualization and analysis and facilitates query- and feature-based analytics, enabling for the first time high-performance analysis of large-scale, high-fidelity particle accelerator simulations while the data is being generated by the Warp simulation suite. Furthermore, this supplemental material https://extras.computer.org/extra/mcg2016030022s1.pdf provides more details regarding the memory profiling and optimization and the Yee grid recentering optimization results discussed in the main article.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

HBMax: Optimizing Memory Efficiency for Parallel Influence Maximization on Multicore Architectures

The goal of influence maximization is to select k most-influential vertices or seeds in a network, where influence is defined by a given diffusion process. The problem has a number of important applications such as viral marketing, information spread, and epidemic control. Although computing optimal seed set is NP-Hard, due to the submodular nature of the problem efficient approximation algorithms exist. However, even state-of-the-art parallel implementations are limited by a sampling step that incurs large memory footprints. This in turn limits the problem size reach and approximation quality. In this work, we study the memory footprint of the sampling process collecting reverse reachability information in the IMM algorithm over large real-world social networks. We present an adaptive and memory-efficient optimization approach for a state-of-the-art multi-threaded parallel influence maximization algorithm. Our approach,HuffMax, uses a portion of the reverse reachable (RR) sets collected by the algorithm to learn the characteristics of the graph. Then, it compresses the intermediate reverse reachability information with Huffman coding, and queries directly on the compressed data to preserve the memory savings obtained through compression. We also propose an efficient sampling strategy based on the distribution of RR sets, which can further reduce the computation time for typical social networks with long-tail distributions. Considering a NUMA architecture, we scale up our solution on 128-core CPUs and reduce the memory footprint by up to 45.7% with negligible time overhead (or even faster) and without perceivable loss of accuracy.

Chen, Xinyu↗
DOE OSTI2015

Final technical report for: Insertional Mutagenesis of Brachypodium distachyon DE-AI02-07ER64452

Several bioenergy grasses are poised to become a major source of energy in the United States. Despite their increasing importance, we know little about the basic biology underlying the traits that control the utility of grasses as energy crops. Better knowledge of grass biology (e.g. identification of the genes that control cell wall composition, plant architecture, cell size, cell division, reproduction, nutrient uptake, carbon flux, etc.) could be used to design rational strategies for crop improvement and shorten the time required to domesticate these species. The use of an appropriate model system is an efficient way to gain this knowledge. Brachypodium distachyon is a small annual grass with all the attributes needed to be a modern model organism including simple growth requirements, fast generation time, small stature, small genome size and self-fertility. These attributes led to the recommendation in the DOE’s “Breaking the Biological Barriers to Cellulosic Ethanol: A Joint Research Agenda” report to propose developing and using B. distachyon as a model for energy crops to accelerate their domestication. Strategic investments (e.g. genome sequencing) in B. distachyon by the DOE are now bearing fruit and B. distachyon is being used as a model grass by hundreds of laboratories worldwide. Sequence indexed insertional mutants are an extremely powerful tool for both forward and reverse genetics. They allow researchers to order mutants in any gene tagged in the collection by simply emailing a request. The goal of this project was to create a collection of sequence indexed insertional mutants (T-DNA lines) for the model grass Brachypodium distachyon in order to facilitate research by the scientific community. During the course of this grant we created a collection of 23,649 B. distachyon T-DNA lines and identified 26,112 unique insertion sites. The collection can be queried through the project website (http://jgi.doe.gov/our-science/science-programs/plant-genomics/brachypodium/brachypodium-t-dna-collection/) and through the Phytozome genome browser (http://phytozome.jgi.doe.gov/pz/portal.html). The collection has been heavily utilized by the research community and, as of October 23, 2015, 223 orders for 12,069 seeds packets have been filled. In addition to creating this resource, we also optimized methods for transformation and sequencing DNA flanking insertion sites.

09 BIOMASS FUELS↗
DOE OSTI2023

EI_MS_ML

The unambiguous identification of compounds from their electron ionization mass (EI-MS) spectra remains a significant unsolved problem in the field of metabolomics and analytical chemistry as a whole. Typically EI-MS spectra are compared using various mathematical operations that convert the spectral similarity or differences into a distance-like metric that roughly approximates the similarity of any two spectra. A commonly used metric for this is the cosine similarity metric which has values close to one for very similar spectra and a value of zero for very dissimilar spectra; however, no metric is perfect. Due to the prevalence of structurally-similar compounds such as isomers and the prevalence of certain fragmentation patterns across structurally-dissimilar compounds, the unambiguous assignment of EI-MS spectra compounds remains difficult. Frequently, querying an observed EI-MS spectrum against a large database such as the NIST17 library yields multiple possible assignments requiring the end user to distinguish between multiple high scoring hits, or multiple low scoring hits while keeping in mind that the correct hit may not be in the database at all. Although techniques such as orthogonal information from techniques such as chromatography can greatly aid in unambiguous assignment, this also requires more complicated experimental designs and access to more complicated analytical instrumentation. Substructures can be trivially detected and represented as strings using a previously published technique called node coloring from a known chemical structure. However, for experimentally-derived EI-MS spectra this information must be derived from the spectra itself (i.e., because we do not know what compound it represents). To achieve this, the software uses techniques from the field of machine learning and a large training dataset of EI-MS spectra corresponding to known structures annotated with substructure strings, to build models that can predict the presence of a given chemical substructure from an EI-MS spectrum directly.If these predictions are of high-quality (i.e., are unlikely to be false positives), the presence of one or more predicted substructures can be used to constrain the number of possible hits for a query spectrum. Mathematically, this restriction could be expressed in many forms, but the most straight-forward implementation is to weight the cosine similarity of a query spectrum and a plausible database match with a Tanimoto-like coefficient based on the ratio of the number of substructures predicted to the number of substructures present in the potential database hit. Determining which combination of models best reduces assignment ambiguity will be achieved using a combination of manual curation and optimization techniques such as genetic algorithms. This software will perform all the steps necessary to construct said models from a training dataset and evaluate them using a holdout dataset. Various statistical analyses can be performed to determine if this approach does decrease assignment ambiguity. For example, if this approach works, on average, the rank-order of the correct assignment for the holdout set of EI-MS spectra should decrease and the weighted cosine similarities for most of the possible matches in the database should be better than the unweighted cosine similarities. Furthermore, this same pipeline can be used on real experimental data to generate less ambiguous assignments.

Mitchell, Joshua↗
DOE OSTI2020

Extending the Publish/Subscribe Abstraction for High-Performance I/O and Data Management at Extreme Scale

The Adaptable I/O System (ADIOS) represents the culmination of substantial investment in Scientific Data Management, and it has demonstrated success for several important extreme-scale science cases. However, looking towards the exascale and beyond, we see the development of yet more stringent data management requirements that require new abstractions. Therefore, there is an opportunity to attempt to connect the traditional realms of HPC I/O optimization with the Database / Data Management community. As such, in this paper we offer some specific examples from our ongoing work in managing data structures, services, and performance at the extreme scale for scientific computing. Using the publish/subscribe model afforded by ADIOS, we demonstrate a set of services that connect data format, metadata, queries, data reduction, and high-performance delivery. The resulting publish/subscribe framework facilitates connection to on-line workflow systems to enable the dynamic capabilities that will be required for exascale science.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2022

Distributionally Robust Decision Making Leveraging Conditional Distributions

Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making with some auxiliary information, and DRO in the context of conditional distributions is not straightforward. We propose a conditional kernel distributionally robust optimization (CKDRO) method that enables robust decision making under conditional distributions through kernel DRO and the conditional mean operator in the reproducing kernel Hilbert space (RKHS). In particular, we consider problems where there is a correlation between the unknown variable y and an auxiliary observable variable x. Given past data of the two variables and a queried auxiliary variable, CKDRO represents the conditional distribution P(y|x) as the conditional mean operator in the RKHS space and quantifies the ambiguity set in the RKHS as well, which depends on the size of the dataset as well as the query point. To justify the use of RKHS, we demonstrate that the ambiguity set defined in RKHS can be viewed as a ball under a metric that is similar to the Wasserstein metric. The DRO is then dualized and solved via a finite dimensional convex program. The proposed CKDRO approach is applied to a generation scheduling problem and shows that the result of CKDRO is superior to common benchmarks in terms of quality and robustness.

Chen, Yuxiao↗