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DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗

DOE OSTI2023

Adaptive Load Shedding as Part of Primary Frequency Response To Support Networked Microgrid Operations

Global changes in the deployment of distributed energy resources, control and communications technologies, business models, and regulatory policy are increasing the operational options for future distribution systems. One such option is the coordinated operation of distributed resources to form microgrids and networks of microgrids to support traditional bulk power systems during normal operations and critical end-use loads during outages. While individual standalone microgrids have been extensively studied and deployed, the coordinated operation of networked microgrids is operationally more challenging due to the dynamic boundaries and changing mix of generation resources. Here, this paper presents a method of using a distributed control architecture to support primary frequency response in networked microgrids operations. The support of primary frequency response is accomplished using the Open Field Message Bus reference architecture and Grid Friendly Appliance controllers.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

Incentivizing and Supporting Early-Stage Solar Innovation in the United States

In 2018, the U.S. Department of Energy's Solar Energy Technologies Office and the National Renewable Energy Laboratory set out to develop a repeatable, predictable prize model (the American-Made Challenges) and an entrepreneurial innovation network (the American-Made Network) to support participants along their innovation journeys. This began with the launch of the Solar Prize. Five years and six rounds later, the Solar Prize is the longest-standing competition of the American-Made Challenges. It has awarded $\$20.1$ million in cash prizes and $\$5.5$ million in technical support vouchers to 140 teams across all aspects of the solar industry. By sharing the outputs of the prize, we hope that our lessons learned will help continue to build the clean tech entrepreneurship support ecosystem.

14 SOLAR ENERGY↗

DOE OSTI2023

Regulating Gas Transport in Molecularly Engineered Polymer Membranes (Final Technical Report)

Energy-efficient separation processes are essential for a wide range of applications ranging from clean fuels (e.g., hydrogen purification) and petroleum refining (e.g., natural gas processing) to water purification and carbon capture. Membrane-mediated separations have shown tremendous promise in providing high productivity and high separation efficiency at significantly lower energy consumption, e.g., up to 90% less energy cost than traditional thermally driven processes such as distillation. Polymeric membranes–the dominant separation membrane materials–have yet to reach their full potential due to their limitations in long-term durability (e.g., productivity loss over the period of their lifetime due to physical aging) or insufficient stability under harsh conditions (e.g., high temperature, chemically complex feeds). This research seeks to establish a new paradigm in polymer membrane material design by harnessing crosslinked model networks with well-defined yet finely tailorable microstructure to facilitate fast and selective gas transport and simultaneously enhance membrane stability. Unlike traditional randomly crosslinked polymers, which suffer from structural inconsistencies and consequently suboptimal gas separation performance, crosslinked model network membranes prepared via a precisely controlled end-linking process enables the creation of previously unattainable microstructure tunability, which, in turn, results in versatile crosslinked membranes with high separation performance that meet the needs of various challenging gas separations. Using model network framework as a fundamental tool by applying this concept in diverse polymer categories, this work has led to the development of various innovative crosslinked membrane structures such as unimodal, bimodal and clustered model networks. These advanced crosslinked polymer membranes not only demonstrate exceptional gas separation performance that significantly outperform existing randomly crosslinked membranes, but also possess excellent long-term durability and robust stability under complex operating conditions. From a fundamental perspective, results from this research provide critical mechanistic insights into gas separation in crosslinked polymer membranes, addressing key knowledge gaps and opening new avenues for membrane design to meet various separation needs. The new membrane materials produced from this research enable the use of polymeric membranes for high temperature gas separations, offering substantial energy and cost savings by eliminating the need for repeated cooling-heating cycles in industrial processes.

02 PETROLEUM↗

DOE OSTI2023

Computationally Robust Line Outage Detection and Identification in Three-Phase Networks

Detection and identification of individual phase outages remains a challenging problem due to insufficient metering in three-phase unbalanced power networks. This problem was tackled for the transmission systems in our previous work as documented in [1]. In this paper, this work is extended to detect phase outages in three-phase unbalanced systems using only the sparse estimation method. In addition, further improvements are introduced to increase the estimation accuracy for the virtual power injections at the terminal buses of disconnected lines, once the disconnected line is identified by sparse estimation methods. Simulation results are provided to experimentally validate the increased accuracy in detecting phase outages while decreasing the computational time by using the proposed approach.

Sparse Estimation, Line Outage, Phase Outage, LASS↗

DOE OSTI2023

Expandable Li Percolation Network: The Effects of Site Distortion in Cation-Disordered Rock-Salt Cathode Material

Cation-disordered rock-salt (DRX) materials receive intensive attention as a new class of cathode candidates for high-capacity lithium-ion batteries (LIBs). Unlike traditional layered cathode materials, DRX materials have a three-dimensional (3D) percolation network for Li + transportation. The disordered structure poses a grand challenge to a thorough understanding of the percolation network due to its multiscale complexity. In this work, we introduce the large supercell modeling for DRX material Li 1.16 Ti 0.37 Ni 0.37 Nb 0.10 O 2 (LTNNO) via the reverse Monte Carlo (RMC) method combined with neutron total scattering. Here, through a quantitative statistical analysis of the material’s local atomic environment, we experimentally verified the existence of short-range ordering (SRO) and uncovered an element-dependent behavior of transition metal (TM) site distortion. A displacement from the original octahedral site for Ti 4+ cations is pervasive throughout the DRX lattice. Density functional theory (DFT) calculations revealed that site distortions quantified by the centroid offsets could alter the migration barrier for Li + diffusion through the tetrahedral channels, which can expand the previously proposed theoretical percolating network of Li. The estimated accessible Li content is highly consistent with the observed charging capacity. The newly developed characterization method here uncovers the expandable nature of the Li percolation network in DRX materials, which may provide valuable guidelines for the design of superior DRX materials.

25 ENERGY STORAGE↗

DOE OSTI2025

A Parallel Alternative for Energy-Efficient Neural Network Training and Inferencing

Energy efficiency of training and inferencing with large neural network models is a critical challenge facing the future of sustainable large-scale machine learning workloads. This paper introduces an alternative strategy, called phantom parallelism, to minimize the net energy consumption of traditional tensor (model) parallelism, the most energy-inefficient component of large neural network training. The approach is presented in the context of feed-forward network architectures as a preliminary, but comprehensive, proof-of-principle study of the proposed methodology. We derive new forward and backward propagation operators for phantom parallelism, implement them as custom autograd operations within an end-to-end phantom parallel training pipeline and compare its parallel performance and energy-efficiency against those of conventional tensor parallel training pipelines. Formal analyses that predict lower bandwidth and FLOP counts are presented with supporting empirical results on up to 256 GPUs that corroborate these gains. Experiments are shown to deliver ∼50% reduction in the energy consumed to train FFNs using the proposed phantom parallel approach when compared with conventional tensor parallel methods. Additionally, the proposed approach is shown to train smaller phantom models to the same model loss on smaller GPU counts as larger tensor parallel models on larger GPU counts offering the possibility for even greater energy savings.

Seal, Sudip [ORNL] (ORCID:0000000332330656)↗

DOE OSTI2026

Multidimensional Distributional Neural Network Output Demonstrated in Super‐Resolution of Surface Wind Speed

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic uncertainty, few offer closed-form, multidimensional distributions that preserve spatial correlation while remaining computationally tractable. In this work, we present a framework for training neural networks with a multidimensional Gaussian loss, generating a closed-form predictive distribution over outputs informed by non-identically distributed training data. Our approach captures aleatoric uncertainty by iteratively estimating the means and covariance matrices, and is demonstrated on a super-resolution example out-of-training-sample. We leverage a Fourier representation of the covariance matrix to stabilize network training and preserve spatial correlation. We introduce a novel regularization strategy—referred to as information sharing—that interpolates between image-specific and global covariance estimates, enabling convergence of the super-resolution downscaling network trained on image-specific distributional loss functions. This framework allows for efficient sampling, explicit correlation modeling, and extensions to more complex distribution families all without disrupting prediction performance. We demonstrate the method on a surface wind speed downscaling task and discuss its broader applicability to uncertainty-aware prediction in scientific models.

17 WIND ENERGY↗

DOE OSTI2025

Deep Reinforcement Learning for Distribution System Operations: A Tutorial and Survey

Here, the rapid evolution of modern electric power distribution systems into complex networks of interconnected active devices, distributed generation (DG), and storage poses increasing difficulties for system operators. The large-scale integration of distributed energy resources (DERs) and the rapid exchange of measurement data via communication networks present major opportunities for advancing grid operations but also introduce greater uncertainty, higher data dimensionality, more complex network and device models, and challenging control and optimization problems. Deep reinforcement learning (DRL) algorithms are promising in addressing these challenges. However, they have not been effectively adapted for power systems applications, requiring extensive customization for implementation and evaluation. This has resulted in reproducibility challenges and a steep learning curve for researchers new to applying DRL algorithms to the power systems domain. To bridge these gaps, this tutorial aims to serve as a valuable resource for researchers interested in exploring learning-based algorithms to operate active power distribution networks. Specifically, this work presents a generalized process for translating sequential decision-making problems in power distribution systems into Markov decision process (MDP) formulations, illustrated through concrete grid service examples. Additionally, we introduce a simple environment design strategy to develop and evaluate example DRL algorithms for distribution system applications, complete with an included code repository to guide users through environment construction.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Distributionally Robust Decentralized Volt-Var Control With Network Reconfiguration

Here, this paper presents a decentralized volt-var optimization (VVO) and network reconfiguration strategy to address the challenges arising from the growing integration of distributed energy resources, particularly photovoltaic (PV) generation units, in active distribution networks. To reconcile control measures with different time resolutions and empower local control centers to handle intermittency locally, the proposed approach leverages a two-stage distributionally robust optimization; decisions on slow-responding control measures and set points that link neighboring subnetworks are made in advance while considering all plausible distributions of uncertain PV outputs. We present a decomposition algorithm with an acceleration scheme for solving the proposed model. Numerical experiments on the IEEE 123 bus distribution system are given to demonstrate its outstanding out-of-sample performance and computational efficiency, which suggests that the proposed method can effectively localize uncertainty via risk-informed proactive timely decisions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Position Papers for the ASCR Workshop on Basic Research Needs in Quantum Computing and Networking

We invite community input in the form of two-page position papers that identify and discuss key challenges and opportunities in quantum computing and networking. In addition to providing an avenue for identifying workshop participants, these position papers will be used to shape the workshop agenda, identify panelists, and contribute to the workshop report. Position papers should not describe the authors’ current or planned research, contain material that should not be disclosed to the public, nor should they recommend specific solutions or discuss narrowly focused research topics. Rather, they should aim to improve the community’s shared understanding of the problem space, identify challenging research directions, and help to stimulate discussion.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

xGFabric: Coupling Sensor Networks and HPC Facilities with Private 5G Wireless Networks for Real-Time Digital Agriculture

Advanced scientific applications require coupling distributed sensor networks with centralized high-performance computing facilities. Citrus Under Protective Screening (CUPS) exemplifies this need in digital agriculture, where citrus research facilities are instrumented with numerous sensors monitoring environmental conditions and detecting protective screening damage. CUPS demands access to computational fluid dynamics codes for modeling environmental conditions and guiding real-time interventions like water application or robotic repairs. These computing domains have contrasting properties: sensor networks provide low-performance, limited-capacity, unreliable data access, while high-performance facilities offer enormous computing power through high-latency batch processing. Private 5G networks present novel capabilities addressing this challenge by providing low latency, high throughput, and reliability necessary for near-real-time coupling of edge sensor networks with HPC simulations. This work presents xGFabric, an end-to-end system coupling sensor networks with HPC facilities through Private 5G networks. The prototype connects remote sensors via 5G network slicing to HPC systems, enabling real-time digital agriculture simulation.

Digital Agriculture↗

DOE OSTI2024

Layer-by-Layer Organic Solar Cells Enabled by 1,3,4-Selenadiazole-Containing Crystalline Small Molecule with Double-Fibril Network Morphology

A double-fibril network of the photoactive layer morphology is recognized as an ideal structure facilitating exciton diffusion and charge carrier transport for high-performance organic solar cells (OSCs). However, in the layer-by-layer processed OSCs (LbL-OSCs), polymer donors and small molecule acceptors (SMAs) are separately deposited, and it is challenging to realize a fibril network of pure SMAs with the absence of tight interchain entanglement as polymers. Here, in this work, crystalline small molecule donors (SMDs), named TDZ-3TR and SeDZ-3TR, were designed and introduced into the L8-BO acceptor solution, forcing the phase separation and molecular fibrilization. SeDZ-3TR showed higher crystallinity and lower miscibility with L8-BO acceptor than TDZ-3TR, enabling more driving force to favor the phase separation and better molecular fibrilization of L8-BO. On the other hand, two donor polymers of PM6 and D18 with different fibril widths and lengths were put together to optimize the fibril network of the donor layer. The simultaneously optimization of the acceptor and donor layers resulted in a more ideal double-fibril network of the photoactive layer and an impressive power conversion efficiency (PCE) of 19.38 % in LbL-OSCs.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Editorial: Edge computation and digital distribution networks

The development of digital technologies is penetrating all areas of energy revolution. Based on the in-depth integration of advanced digital technologies, distribution networks are gradually transforming into digital distribution networks (DDNs) with tremendous changes from the structure to the operation mode. DDNs is the digitalized appearance of the physical distribution network, in which ubiquitous connections and massive data are the basic characteristics (Huo et al., 2022). It is an important task to utilize the massive data and propose novel operation modes to construct more efficient and intelligent distribution networks (Jian et al., 2022). Among the advanced digital technologies in DDNs, edge computing has received wide attention (Zhao et al., 2022). It has superior performance in local sensing and intelligent computation, which can effectively relieve huge communication pressure. However, the limited computing resources and the complex computing tasks at the edge side significantly challenge the collaboration of distribution network regulation and advanced digital technologies (Hu et al., 2022). It is necessary to find out proper methods to utilize advanced digital technology to construct DDNs. This Research Topic is organized to introduce the recent progress in the construction, operation and advanced computational methods for DDNs. Finally, seven papers have been accepted, which can be sorted into the following three categories: 1) Evolution and technical features of DDNs, 2) Intelligent operation control of DDNs, 3) Advanced simulation for large-scale DDNs. The three sections below respectively introduce the major research and contributions of the papers covered in each category.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Recent advances in ink-based additive manufacturing for porous structures

The use of porous structures is an ancient wisdom, people found its importance ever since we began to understand nature. The evolution of porous structure gives rise to multi-scale (combined nano-, micro-, and macro-) porous networks. Traditional manufacturing technologies have challenges in creating shape-complex and conformable porous structures for real-world applications. Additive manufacturing (AM) with the capability of assembling various materials with complex and customized architectures is rapidly developing. With the advancement of material development, the integration of AM and porous structure offers unparalleled and emerging opportunities for concept-to-design-to-fabrication of multi-scale porous networks, enabling the multi-functionalities of the 3D printed specimen and broadening its applications. In this work, we provide a comprehensive review of the state-of-the-art ink-based AM techniques for 3D printing porous structures. The ink design principle, ink composition, and printability are thoroughly discussed. The methodologies of various AM technologies for porous structures are analyzed. Readers can find a clear experimental guidance toward 3D printing multi-scale porous structures. The synergistic and collective merits of additive manufacturing and porous structure are highlighted and systematically discussed in this review. The challenges and promises of this field for future research are also outlined.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Convex Relaxations of Maximal Load Delivery for Multi-Contingency Analysis of Joint Electric Power and Natural Gas Transmission Networks

Recent increases in gas-fired power generation have engendered increased interdependencies between natural gas and power transmission systems. These interdependencies have amplified existing vulnerabilities in gas and power grids, where disruptions can require the curtailment of load in one or both systems. Although typically operated independently, coordination of these systems during severe disruptions can allow for targeted delivery to lifeline services, including gas delivery for residential heating and power delivery for critical facilities. To address the challenge of estimating maximum joint network capacities under such disruptions, we consider the task of determining feasible steady-state operating points for severely damaged systems while ensuring the maximal delivery of gas and power loads simultaneously, represented mathematically as the nonconvex joint Maximal Load Delivery (MLD) problem. To increase its tractability, we present a mixed-integer convex relaxation of the MLD problem. Then, to demonstrate the relaxation’s effectiveness in determining bounds on network capacities, exact and relaxed MLD formulations are compared across various multi-contingency scenarios on nine joint networks ranging in size from 25 to 1191 nodes. The relaxation-based methodology is observed to accurately and efficiently estimate the impacts of severe joint network disruptions, often converging to the relaxed MLD problem’s globally optimal solution within ten seconds.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2023

The State of the Art in Visualizing Dynamic Multivariate Networks

Abstract Most real‐world networks are both dynamic and multivariate in nature, meaning that the network is associated with various attributes and both the network structure and attributes evolve over time. Visualizing dynamic multivariate networks is of great significance to the visualization community because of their wide applications across multiple domains. However, it remains challenging because the techniques should focus on representing the network structure, attributes and their evolution concurrently. Many real‐world network analysis tasks require the concurrent usage of the three aspects of the dynamic multivariate networks. In this paper, we analyze current techniques and present a taxonomy to classify the existing visualization techniques based on three aspects: temporal encoding, topology encoding, and attribute encoding. Finally, we survey application areas and evaluation methods; and discuss challenges for future research.

Kale, Bharat↗

DOE OSTI2024

An Evaluation of the Effect of Network Cost Optimization for Leadership Class Supercomputers

Dragonfly-based networks are an extensively deployed network topology in large-scale high-performance computing due to their cost-effectiveness and efficiency. The US will soon have three Exascale supercomputers for leadership class workloads deployed using dragonfly networks. Compared to indirect networks of similar scale, the dragonfly network has considerably reduced cable lengths, cable counts, and switch counts, resulting in significant network cost savings for a given system size, however, these cost reductions result in reduced global minimal paths and more challenging routing. Additionally, large scale dragonfly networks often require a taper at the global link level, resulting in less bisection bandwidth than is achievable in other traditional non-blocking topologies of equivalent scale. While dragonfly networks have been extensively studied, they have yet to be fully evaluated in an extreme scale (i.e., exascale) system that targets capability workloads. In this paper, we present the results of the first large scale evaluation of a dragonfly network on an exascale system (Frontier) and compare its behavior to a similar scale fat-tree network on a previous generation TOP500 system (Summit). This evaluation aims to determine the effect of network cost optimizations by measuring a tapered topology’s impact on capability workloads. Our evaluation is based on a collection of synthetic microbenchmarks, mini-apps, and full scale applications. It compares the scaling efficiencies of each benchmark between the dragonfly-based Frontier and the fat-tree-based Summit systems. Our results show that a dragonfly network is $\sim \mathbf{3 0 \%}$ more cost efficient than a fat-tree topology, which amortizes to $\sim 3 \%$ of an exascale system cost. Furthermore, while tapered dragonfly networks impose significant tradeoffs, the impacts are not as broad as initially thought and are mostly seen in applications with global communication patterns, particularly all-to-all (e.g., FFT-based algorithms), but also local communication patterns (e.g., nearest-neighbor algorithms) that are sensitive to network performance variability.

Khan, Awais↗