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DOE OSTI2020

Adapting In Situ Accelerators for Sparsity With Granular Matrix Reordering

Neural network (NN) inference is an essential part of modern systems and is found at the heart of numerous applications ranging from image recognition to natural language processing. In situ NN accelerators can efficiently perform NN inference using resistive crossbars, which makes them a promising solution to the data movement challenges faced by conventional architectures. Although such accelerators demonstrate significant potential for dense NNs, they often do not benefit from sparse NNs, which contain relatively few non-zero weights. Processing sparse NNs on in situ accelerators results in wasted energy to charge the entire crossbar where most elements are zeros. To address this limitation, this paper proposes Granular Matrix Reordering (GMR): a preprocessing technique that enables an energy-efficient computation of sparse NNs on in situ accelerators. GMR reorders the rows and columns of sparse weight matrices to maximize the crossbars' utilization and minimize the total number of crossbars needed to be charged. The reordering process does not rely on sparsity patterns and incurs no accuracy loss. Finally, GMR achieves an average of 28% and up to 34% reduction in energy consumption over seven pruned NNs across four different pruning methods and network architectures.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Case Study: NREL Campus Chilled Water Storage Potential: Benchmark Datasets Development and Applications, Task 4 - Use Case Demonstration

The Benchmark Datasets Development and Applications project is a three-year collaboration between the National Renewable Energy Laboratory (NREL), Oak Ridge National Laboratory, Pacific Northwest National Laboratory, and Lawrence Berkeley National Laboratory. The project seeks to collect and curate high-resolution, well-calibrated time series of building operational and indoor/outdoor environmental data, which are crucial to understanding and optimizing building energy efficiency performance and demand flexibility capabilities as well as benchmarking energy algorithms. Project outcomes include approximately twelve high-fidelity building datasets, enhanced data representation tools, and four case studies to illustrate example applications. The goal of these case studies is to define and execute analyses that demonstrate how one or more datasets collected through this project can address a data gap or challenge historically faced by building stakeholders. This technical paper summarizes the findings of one of these case studies, in which we studied the operational efficiencies of the central cooling system at NREL. We looked at three years of data from the three chillers in the Field Test Laboratory Building (FTLB), from 2019 to 2021, to compare equipment operation and demand throughout the time period. Our analysis indicates that all three chillers are operating at or below the optimal loading conditions for most of the operation time, and thus there was no efficiency drop due to loading of the chillers at full capacity. Our recommendation is that no chiller capacity increase is needed; instead, the central plant could benefit from adopting advanced control logics for optimal sequencing of chillers during part load operations. Analysis of adding chilled water thermal storage to the central plant indicated 34% savings in demand cost and 24.5% savings in total cost (energy consumption and demand charge cost). The payback period is estimated to be 11-22 years with an assumed TES cost of $\$$100-$200 per ton. This case study shows how a selected dataset is used to solve a practical building problem - learning the operational status of its components, analyzing the effectiveness of a proposed new technique, and aiding decision-making for the building operations and maintenance team.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2023

The Generalized Green’s function Cluster Expansion: A Python package for simulating polarons

We present an efficient implementation of the Generalized Green’s function Cluster Expansion (GGCE), which is a new method for computing the ground-state properties and dynamics of polarons (single electrons coupled to lattice vibrations) in model electron-phonon systems. The GGCE works at arbitrary temperature and is well suited for a variety of electron-phonon couplings, including, but not limited to, site and bond Holstein and Peierls (Su-SchriefferHeeger) couplings, and couplings to multiple phonon modes with different energy scales and coupling strengths. Quick calculations can be performed efficiently on a laptop using solvers from NumPy and SciPy, or in parallel at scale using the PETSc sparse linear solver engine.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Generic Discretization Library

The GenDiL library is a collection of C++ software abstractions designed to discretize and solve partial differential equations (PDEs) for high-performance computing (HPC) applications. Its primary focus is on modern C++ generic programming, which helps ensure portability across various hardware architectures. The central idea behind the library is to provide building blocks for numerical algorithms-such as discretization methods and iteration patterns-so that domain experts can focus on the math, rather than the low-level details of hardware or implementation. By defining abstractions for data types, iteration over computational grids, and scheduling of operations, the library isolates the high-level PDE algorithms from the platform-specific optimizations needed to achieve efficient performance.

Dudouit, Yohann [Lawrence Livermore National Labor↗

DOE OSTI2024

Field Study of 120-volt Heat Pump Water Heaters in the Big Easy

To meet long-term goals for reducing carbon emissions and lessen the impacts of climate change, the U.S. plans to decarbonize its building stock, which includes the replacement of fossil fuel-burning end uses with energy efficient electric alternatives. As part of this strategy, the replacement of fossil fuel water heaters with heat pump water heaters (HPWH) has the potential to avoid substantial carbon emissions. An estimated 10-15 million single-family homes with fossil fuel water heaters do not have the electrical panel capacity to install a 240-volt, 30-amp HPWH. For these homes, a technology recently introduced to the market, the 120-volt plug-in HPWH, can provide energy efficient electrification of water heating without an expensive panel and wiring retrofit. This paper presents the results of an ongoing 120-volt HPWH field study conducted in 17 homes in New Orleans, LA. Key installation scenarios are profiled for retrofitting from gas-fired water heaters to 120-volt HPWHs, accounting for space, air volume, air temperature, condensate drainage, and electrical. Each HPWH had its surrounding air temperature, relative humidity, inlet and outlet water temperature, flow, and energy consumption monitored. Using these data, hot water delivery and energy efficiency performance were analyzed based on home characteristics. Hot water run outs were investigated to understand how hot water usage, inlet water temperature, and surrounding air temperature impact the HPWH’s ability to meet load. From these results, best practices for 120-volt HPWH siting, sizing, and installation were developed. In addition, results are explored further to add insight for electrification policies and product development.

heat pump water heater, 120-volt, Residential buil↗

DOE OSTI2025

Explainable AI for Multivariate Time Series Pattern Exploration: Latent Space Visual Analytics With Temporal Fusion Transformer and Variational Autoencoders in Power Grid Event Diagnosis

Detecting and analyzing complex patterns in multivariate time-series data is crucial for decision-making in urban and environmental system operations. However, challenges arise from the high dimensionality, intricate complexity, and interconnected nature of complex patterns, which hinder the understanding of their underlying physical processes. Existing AI methods often face limitations in interpretability, computational efficiency, and scalability, reducing their applicability in real-world scenarios. This paper proposes a novel visual analytics framework that integrates two generative AI models, Temporal Fusion Transformer (TFT) and Variational Autoencoders (VAEs), to reduce complex patterns into lower-dimensional latent spaces and visualize them in 2D using dimensionality reduction techniques such as PCA, t-SNE, and UMAP with DBSCAN. These visualizations, presented through coordinated and interactive views and tailored glyphs, enable intuitive exploration of complex multivariate temporal patterns, identifying patterns’ similarities and uncover their potential correlations for a better interpretability of the AI outputs. The framework is demonstrated through a case study on power grid signal data, where it identifies multi-label grid event signatures, including faults and anomalies with diverse root causes. Additionally, novel metrics and visualizations are introduced to validate the models and assess the performance, efficiency, and consistency of latent maps generated by VAE, which have been utilized in prior studies for latent space cartography and used as a benchmark in this study, and the emerging TFT architecture under various configurations. These analyses provide actionable insights for model parameter tuning and reliability improvements. Comparative results highlight that TFT achieves shorter run times and superior scalability to diverse time-series data shapes compared to VAE. This work advances fault diagnosis in multivariate time series, fostering explainable AI to support critical system operations.

Explainable AI↗

DOE OSTI2025

Improving Trustworthiness of Data-Driven Power Grid Contingency Analysis With Bayesian Residual Graph Neural Networks

The evolving energy landscape requires novel tools to efficiently perform contingency analysis and reliability assessment of power grids, potentially in real-time. The high computational cost of traditional power flow solvers limits their applicability in practice. Machine learning (ML) surrogates such as deep neural networks (NNs) accelerate power flow solvers computations, enabling high-order contingency analysis and real-time decision-making by learning highly nonlinear functions and integrating grid topology via graph architectures. However, (graph) NNs lack predictive power away from training data and do not provide predictive confidence estimates. Here, we present a Bayesian residual graph NN that integrates knowledge from low-fidelity data via residual training and embeds granular quantification of uncertainties, improving trustworthiness critical for high-consequence decision-making. Applying Bayesian concepts to NNs is challenging due to the high-dimensionality of both the parameter space, complicating derivation of a meaningful prior, and the output space in large grid systems, requiring enhanced techniques to assess the predicted high-dimensional uncertainties. Our contributions include: (1) Deriving a prior for fully connected and graph NNs that leverages low-fidelity data to guide mean predictions and appropriately control prior predictive uncertainty. (2) Integrating this prior within an ensembling with anchoring scheme for efficient approximate posterior inference. (3) Deriving enhanced metrics to assess accuracy of both the mean and uncertainty predictions in high dimensions, appropriately accounting for correlations propagated through graph layers. The resulting Bayesian residual graph NN is tested on a contingency analysis task for 14-bus and 118-bus grids.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Position Papers for the ASCR Workshop on Reimagining Codesign

On behalf of the Advanced Scientific Computing Research (ASCR) program in the US Department of Energy (DOE) Office of Science, we are organizing a Workshop on Reimagining Codesign (ReCoDe). Codesign is the process of jointly designing interoperating components of a computing system—in particular: applications, algorithms, system software, programming models, and the hardware on which they run. The goal is to maximize the overall performance, efficiency, and other desirable qualities of the system as a whole. Codesign is a standard methodology in the embedded-systems community, where space, power, and cost constraints are commonly pitted against execution speed for a tightly constrained feature set. Over the last decade, the DOE has invested in codesign efforts to foster the development of exascale computing systems for broad classes of scientific and engineering applications. The ReCoDe workshop hopes to explore how scientific applications of interest to the DOE can be accelerated through close interactions with hardware designers and software-stack developers, in which all components adapt to each other’s requirements and constraints. We want to answer the question of what are the key tools and methodologies for accomplishing codesign in today’s computing landscape, and what will be the highest impact targets for meeting DOE’s emerging mission requirements. This workshop aims to bring together DOE, industry, and academia to identify opportunities to build on past codesign successes and identify new areas that are either emerging or that may need reimagining for the future. We want to continue to find opportunities that can be pursued as a joint effort and continue to break down the traditional customer/vendor dichotomy with true partnerships. From this work, DOE will benefit from increased application performance relative to what stock hardware or existing general-purpose roadmaps can provide, and vendors will benefit from expanding their hardware’s capabilities to address needs they might have not otherwise anticipated and thereby create more widespread interest in their products. The workshop will be structured around a set of breakout sessions, with every attendee expected to participate actively in the discussions. Afterward, workshop attendees—from DOE, industry, and academia—will produce a report for ASCR that summarizes the findings made during the workshop.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

I.1 Heavy-Duty Diesel Combustion (Sandia National Laboratories)

Regulatory drivers and market demands for lower pollutant emissions, lower carbon dioxide emissions, and lower fuel consumption motivate the development of cleaner and more fuel-efficient engine operating strategies. Most current production heavy-duty diesel engines use a combination of both in-cylinder and exhaust emissions-control strategies to achieve these goals. The emissions and efficiency performance of in-cylinder strategies depend strongly on flow and mixing processes that can be influenced by using multiple fuel injections. Past work performed under this project showed that adding a second injection can reduce soot to levels below what would have been produced by an unchanged first injection, thereby increasing load while decreasing soot and potentially reducing brake specific fuel consumption. Information characterizing the important in-cylinder processes with multiple injections has been gleaned from ensemble-averaged planar laser-induced incandescence (PLII) imaging visualizing the soot cloud and planar induced fluorescence (PLIF) of OH characterizing the soot oxidation regions. PLII showed a consistent disruption of the first injection soot cloud by the second injection. In conjunction with OH-PLIF, differences in soot oxidation patterns for multiple injections compared to single injections were observed. This understanding was further enhanced in FY20, when high-speed imaging resolving the above-mentioned effects in a single cycle were combined with direct numerical simulations investigating the multiple-injection ignition process on the microscopic level of turbulence and chemistry interaction. In FY21, these findings in conjunction with findings from other researchers published in the scientific literature were composed into a preliminary multiple-injection conceptual model of fuel-mixing, injection and ignition processes. Remaining key research questions were also highlighted. In addition, wall heat flux was investigated experimentally and with numerical simulations to understand the potential of multiple injections to reduce the engine heat losses and further enhance the efficiency.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2024

The Maintainable Fusion Pilot Plant

The US fusion community has coalesced around the goal of building an FPP as described by the National Academies of Science, Engineering, and Medicine (NASEM). In addition to demonstrating the viability of the technologies necessary to operate such a plant, including demonstration of net energy and electricity production, NASEM found that a “fusion pilot plant will need to demonstrate the ability to efficiently perform remote maintenance and replacement in support of the design of a power plant, taking into account details of the consequences of the fusion environment, such as material activation and tritium retention in components.” Current designs of fusion demonstration reactors do usually foresee a regular exchange of their first wall modules, including the tritium breeding blankets. In the European Power Plant Conceptual Studies, it is assumed that a fusion reactor will need to change its divertor every 2 years and its first wall blanket module every 5 to 6 years to reach acceptable availability. Underlying this capability are remote-handling technologies to keep the outage for the exchange of these components short. There are many uncertainties in the remote-handling schemes, and most schemes are at a preconceptual level at best. In addition, the exchange of these components would either produce an enormous rad-waste stream or would require an enormous refurbishment activity with huge cost-prohibitive hot-cells. Past Fusion Nuclear Science Facility (FNSF) preconceptual studies have led to hot cell dimensions of an unbelievable size, likely costing tens of billions of dollars. Already at The Way (previously International Thermonuclear Experimental Reactor, ITER), hot-cells have become cost-prohibitive, demanding redesigns of the ITER first wall to reduce the toxic rad-waste/inventory. In this in-situ PFC repair project, a concept for a long-life, maintainable first wall module concept is developed and tested. This first wall concept relies on innovative remote handling to repair the first wall modules in-situ, avoiding costly refurbishments outside of the tokamak vessel. This approach was highlighted in the Fusion Energy Sciences Advisory Committee (FESAC) report on Transformative Enabling Capabilities for Efficient Advance Toward Fusion Energy. In general, the damage of the first wall armor is due to particle and radiation exposures. Load conditions vary from one fusion reactor design to another. In tokamaks, first wall Plasma Facing Components (PFCs) are exposed to far-Scrape-Off-Layer plasma fluxes, electromagnetic radiation, energetic CX neutrals, and potentially runaway electron beams. Protecting the first wall to the worst-case load conditions would require the design of a very thick first wall armor. Transient heat and particle fluxes due to disruptions or edge localized modes can lead to excessive heat loads resulting potentially in melting PFCs down to the cooling channel. Catastrophic events like these need to be avoided by appropriate disruption mitigation systems. However, failure of these systems will still put a first wall at an unacceptable risk. Hence, a first wall design needs to accommodate the occasional transient heat loads by introducing sacrificial limiters, which will absorb these transients.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Tunable Stochasticity in an Artificial Spin Network

Metamaterials present the possibility of artificially generating advanced functionalities through engineering of their internal structure. Artificial spin networks, in which a large number of nanoscale magnetic elements are coupled together, are promising metamaterial candidates that enable the control of collective magnetic behavior through tuning of the local interaction between elements. In this work, the motion of magnetic domain-walls in an artificial spin network leads to a tunable stochastic response of the metamaterial, which can be tailored through an external magnetic field and local lattice modifications. This type of tunable stochastic network produces a controllable random response exploiting intrinsic stochasticity within magnetic domain-wall motion at the nanoscale. An iconic demonstration used to illustrate the control of randomness is the Galton board. In this system, multiple balls fall into an array of pegs to generate a bell-shaped curve that can be modified via the array spacing or the tilt of the board. A nanoscale recreation of this experiment using an artificial spin network is employed to demonstrate tunable stochasticity. Furthermore, this type of tunable stochastic network opens new paths toward post-Von Neumann computing architectures such as Bayesian sensing or random neural networks, in which stochasticity is harnessed to efficiently perform complex computational tasks.

Artificial spin network↗

DOE OSTI2025

Operando Neutron Imaging of Lithium Flux and Gradient Cathode Design for Enhanced Kinetics in High‐Loading All‐Solid‐State Li─S Batteries

All-solid-state Li–sulfur batteries (ASSLSBs) are considered promising candidates for next-generation energy storage owing to their inherent safety, high energy density, and abundant sulfur resources. However, slow redox kinetics greatly limit sulfur utilization during solid-solid sulfur reactions, leading to significant challenges to achieve efficient performance in high-mass-loading ASSLSBs. Here, operando neutron image is employed to directly visualize, for the first time, that sluggish Li + transport kinetics and the uneven distribution of Li + during cathodic reactions are critical factors limiting sulfur conversion. To address this issue, gradient cathode architectures comprising three and five layers are designed, in which catholyte concentrations are strategically varied to optimize Li-ion flux and enhance ionic conductivity of the whole composite cathode electrode. Operando neutron imaging distinctly visualizes and confirms that three-layer gradient approach significantly enhances Li-ion mobility, resulting in more uniform redox reactions and greatly improved sulfur utilization compared to traditional non-gradient structures. Consequently, the three-layer gradient cathode achieves superior rate performance and reduced electrode polarization at high sulfur mass loadings of 4.5 and 6.0 mg cm −2 . Furthermore, the applicability and scalability of this design are demonstrated in a five-layer gradient cathode architecture, achieving an impressive discharge specific capacity increase from 656 mAh g −1 (three-layer gradient) to 1232 mAh g −1 at 1/20 C for ultra-high sulfur loading of 7.5 mg cm −2 . In conclusion, this innovative gradient cathode design offers substantial advancements in understanding and overcoming Li-ion transport limitations, paving the way toward practical, high-energy-density ASSLSBs.

25 ENERGY STORAGE↗

DOE OSTI2021

Cell-Type-Specific Proteomics Analysis of a Small Number of Plant Cells by Integrating Laser Capture Microdissection with a Nanodroplet Sample Processing Platform

Plant organs and tissues contain multiple cell types, which are well organized in 3-dimensional structure to efficiently perform physiological functions such as homeostasis, response to environmental perturbation, pathogen infection. It is critically important to perform molecular measurements at the cell-type-specific level to discover mechanisms and unique features of cell populations that govern differentiation and respond to external perturbations. Although mass spectrometry-based proteomics has been demonstrated as an enabling discovery tool to study plant physiology, conventional approaches require millions of cells to generate robust biological conclusions. Such requirements mask the cell-to-cell heterogeneities and limit the comprehensive profiling of plant proteins at spatially resolved and cell-type-specific resolutions. This protocol describes a recently-developed proteomics workflow for studying a small number of plant cells by integrating laser capture microdissection, microfluidic nanodroplet-based sample preparation, with ultrasensitive liquid chromatography-mass spectrometry. Using poplar as a model tree species, we provide detailed protocols, including plant tissue harvest, tissue preparation, cryosectioning, laser microdissection, protein digestion, mass spectrometry measurement, and data analysis. We show the workflow enables the precise identification and quantification of thousands of proteins from hundreds of isolated plant root and leaf cells.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Detecting multi‐scale riverine topographic variability and its influence on Chinook salmon habitat selection

Abstract Quantifying geomorphic conditions that impact riverine ecosystems is critical in river management due to degraded riverine habitat, changing flow and thermal conditions, and increasing anthropogenic pressure. Geomorphic complexity at different scales directly impacts habitat heterogeneity and affects aquatic biodiversity resilience. Here we showed that the combination of continuous spatial survey at high resolution, topobathymetric light detection and ranging (LiDAR), and continuous wavelet analysis can help identify and characterize that complexity. We used a continuous wavelet analysis on 1‐m resolution topobathymetry in three rivers in the Salmon River Basin, Idaho (USA), to identify different scales of topographic variability and the potential effects of this variability on salmonid redd site selection. On each river, wavelet scales characterized the topographic variability by portraying repeating patterns in the longitudinal profile. We found three major representative spatial wavelet scales of topographic variability in each river: a small wavelet scale associated with local morphology such as pools and riffles, a mid‐wavelet scale that identified larger channel unit features, and a large wavelet scale related to valley‐scale controls. The small wavelet scale was used to identify pools and riffles along the entire lengths of each river as well as areas with differing riffle‐pool development. Areas along the rivers with high local topographic variability (high wavelet power) at all wavelet scales contained the largest features (i.e., deepest or longest pools) in the systems. By comparing the wavelet power for each wavelet scale to Chinook salmon redd locations, we found that higher small‐scale wavelet power, which is related to pool‐riffle topography, is important for redd site selection. The continuous wavelet methodology objectively identified scales of topographic variability present in these rivers, performed efficient channel‐unit identification, and provided geomorphic assessment without laborious field surveys.

Duffin, Jenna↗

DOE OSTI2025

Polymers in direct air capture: a mini review

The urgent need to mitigate climate change has intensified interest in direct air capture (DAC) technology, which targets extracting carbon dioxide (CO2) directly from the atmosphere. Among the various sorbents used in DAC, polymers have emerged as a promising solution, either as active sorbents or as structural supports for active DAC materials, due to their customizable properties, scalability and low cost. This mini-review investigates the latest trends in polymer-based materials for DAC and identifies critical research gaps, such as the need for thorough lifecycle assessments and in-depth studies on the degradation of polymeric materials. It also outlines future directions, emphasizing the importance of developing cost-effective, scalable and durable polymers that can perform efficiently across diverse climatic conditions, including the unique challenges presented by cold weather regions abundant in renewable energy. This mini-review aims to inform ongoing efforts in the design and utilization of polymeric sorbents, providing insights that could guide the development of economically viable and environmentally sustainable DAC technologies.

climate change↗

DOE OSTI2022

The Importance of Nonequilibrium to Equilibrium Transition Pathways for the Efficiency and Stability of Organic Solar Cells

Controlled morphology of solution-processed thin films have realized impressive achievements for non-fullerene acceptor (NFA)–based organic solar cells (OSCs). Given the large set of donor–acceptor pairs, employing various processing conditions to realize optimal morphology for high efficiency and stable OSCs is a strenuous task. Therefore, comprehensive correlations between processing conditions and morphology evolution pathways have to be developed for efficient performance and stability of devices. Within the framework of the blend system, crystallization transitions of NFA molecules are tracked utilizing the first heating scan of differential scanning calorimeter (DSC) measurement correlating with respective morphology evolution of blend films. Real-time dynamics measurements and morphology characterizations are combined to provide optimal morphology transition pathways as NFA molecules are shown to be released from the mixed phase to form balanced ordered packing with variant processing conditions. Polymer:NFA films are fabricated using blade coating incorporating solvent additive or thermal annealing as processing conditions as a correlation is formulated between performance and stability of solar cells with morphology transition pathways. In conclusion, this work demonstrates the significance of processing condition-controlled transition pathways for the realization of optimal morphology leading to superior OSC devices.

14 SOLAR ENERGY↗

DOE OSTI2024

IRIS Reimagined: Advancements in Intelligent Runtime System for Task-Based Programming

Task-based programming models are gaining traction in scientific computing. IRIS is a portable runtime system that exploits multiple heterogeneous programming systems and can discover available resources and manage multiple diverse programming systems (e.g., CUDA, Hexagon, HIP, Level Zero, OpenCL, and OpenMP) simultaneously. It accounts for the constraints of task dependencies and provides customizable scheduling policies to map those tasks to heterogeneous devices. In this paper, we present new capabilities added to IRIS to improve its portability for heterogeneous programming, build-friendliness, and performance efficiency. The new additions include vendor-specific kernel support, a runtime system with a foreign function interface to eliminate writing wrapper or boilerplate code for heterogeneous kernels, an easy-to-use and configurable CMake-based build environment, automatic and efficient data transfers and orchestration, and the Hunter and DAGGER toolchains to evaluate IRIS’s task scheduling algorithms.

Miniskar, Narasinga Rao↗

DOE OSTI2021

Coaction and double-copy properties of configuration-space integrals at genus zero

We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory. For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction. We present methods to efficiently perform and organize the expansions of configuration-space integrals in the inverse string tension α' or the dimensional-regularization parameter ϵ of Feynman integrals. Generating-function techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures. We present a compact recursion for a generalized KLT kernel and discuss its origin from intersection numbers of Stasheff polytopes and its implications for correlation functions of two-dimensional conformal field theories. We find a non-trivial example of correlation functions in (p, 2) minimal models, which can be normalized to become uniformly transcendental in the p → ∞ limit.

Conformal Field Theory↗