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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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Building Operation Model (Morpheus) for Dallas Fort Worth Airport (CRADA CRD-19-16301 Final Report)

The primary objective of this project was to leverage digital twin technology to enhance the design and operation of DFW Airport terminals and their associated energy systems. To achieve this, Morpheus, a building digital twin, was developed to guide improvements in airport operations, specifically targeting reductions in peak power demand and overall energy consumption.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

Refractory-based thermal energy storage for industrial process heat: one-dimensional modeling, control, and optimization

The variable and weather-dependent output of wind and solar power plants present a substantial challenge for planning and operating electricity-systems, particularly in the absence of cost-effective and dispatchable energy storage technologies. This study investigates a high-temperature, electrically heated, refractory-based thermal energy storage (RTES) system that stores electrical energy as sensible heat in dense ceramic bricks over the 950–1800 °C range. The stored heat can be discharged as a controlled hot-gas stream for industrial heating, fuel substitution in high-temperature processes, or electricity generation. The main novelty is a comprehensive modelling, control, mapping, and optimization framework that integrates one-dimensional transient gas–solid heat transfer, fan-assisted discharge, bypass-flow regulation, reheating logic, fan-power evaluation, insulation-loss assessment, and genetic-algorithm-based design optimization. The model uses feedback from outlet temperature and delivered power to regulate discharge, while a two-stage genetic algorithm optimizes brick-channel geometry, gas-flow operation, and multilayer insulation thicknesses. Storage capacities below 50 MWh and discharge powers of 5–30 MW are analyzed to evaluate hold time, thermal delivery, fan-power penalty, heat loss, state-of-charge evolution, and indicative capital cost. Results demonstrate that optimized and well-insulated refractory-based thermal energy storage units can provide stable, efficient, and repeatable heat delivery over multiple discharge cycles. The generated performance and cost maps support modular refractory thermal energy storage as a practical option for large-scale integration of wind and solar generation and for high-temperature industrial process heat.

25 ENERGY STORAGE

Challenges and Opportunities for HVAC + Phase Change Material Thermal Energy Storage in Buildings

Phase-change material (PCM) thermal-energy storage (TES) integrated with HVAC and domestic hot water (DHW) can shift a large share of building thermal loads. By flattening and shifting loads, PCM TES reduces peak electricity use, eases stress on local and grid infrastructure, and lowers costs. It can also defer costly upgrades to service panels, distribution, and transmission. Higher energy density relative to chilled or hot water storage makes PCM TES practical for small, space limited, and retrofit projects, while packaged HVAC-integrated systems expand cost-effective load shifting to commercial buildings that previously lacked options. Despite this promise, deployment faces barriers. This paper presents challenges, opportunities, and lessons learned from lab and field integrations of PCM TES with packaged HVAC systems. Key challenges include misalignment between default heat pump controls tuned for direct-to-load operation and TES charge/discharge objectives, PCM properties that diverge from manufacturer claims and evolve with cycling, and high integration and deployment costs with off-the-shelf products. These studies underscore the need for factory built, integrated systems that arrive as prepackaged modules with proven controls, reducing design and installation effort and delivering predictable performance across projects. The paper outlines steps to enable viable and scalable PCM TES HVAC and DHW systems, including 1) validated methods that can be used to characterize PCM properties and TES system performance, 2) supervisory controls that optimize charge/discharge scheduling, and 3) factory integrated packaging that eliminates bespoke field engineering.

Dutton, Spencer

Trajectory-independent speed limits for controlled open quantum systems

Existing quantum speed limits for controlled open quantum systems depend on the specified trajectory. For example, lower bounds on quantum annealing times in the presence of dissipation depend explicitly on the chosen annealing schedule. Recently, schedule-independent speed limits have been derived for annealing in the closed quantum system setting [L. P. García-Pintos et al ., SciPost Phys. 18 , 159 (2025)]. In this work, we generalize these results to open quantum systems, deriving schedule-independent lower bounds for quantum annealing times in systems described by a Lindblad master equation. We analyze the interplay between coherent control and dissipation in single- and two-qubit examples, demonstrating that the derived lower bounds capture key scaling behavior with respect to the strength of the dissipator. Finally, we apply the bound to thermal state preparation and show that the bound matches the expected asymptotic behavior for an Ising model in the high-temperature limit.

open quantum systems & decoherence

Chiral edge state control of thermoelectric effects

Thermoelectric responses in two-dimensional electron gases subjected to magnetic fields have the potential to provide unique information about quasiparticle statistics. In this study, we show that chiral edge states play a key role in thermoelectric Hall bar measurements by completely controlling the direction of the internal thermal gradient. To this end, we perform measurements of the magnetothermoelectric responses of cadmium arsenide quantum wells. The magnetothermoelectric responses in the quantum Hall regime agree with theoretical predictions if one considers the role of chiral edge states, which flow in opposite directions on either side of the Hall bar and establish an internal temperature gradient that is perpendicular to the externally applied thermal gradient. We show that the results are self-consistent within this picture under different measurement conditions. We discuss potential applications of the findings, such as in nanoscale control of local temperature gradients and thermoelectric effects along with the characterization of other topological systems with chiral edges states.

Science & Technology - Other Topics

Nuclear Safety [Vol. 29, No. 3, July-September 1988]

Nuclear Safety is a review journal that covers significant developments in the field of nuclear safety. Its scope includes the analysis and control of hazards associated with nuclear energy, operations involving fissionable materials, and the products of nuclear fission and their effects on the environment. Primary emphasis is on safety in reactor design, construction, and operation; however, the safety aspects of the entire fuel cycle, including fuel fabrication, spent-fuel processing, nuclear waste disposal, handling of radioisotopes, and environmental effects of these operations, are also treated. Table of Contents for this issue follows. GENERAL SAFETY CONSIDERATIONS: 259 Fifteenth Water Reactor Safety Information Meeting by E. G. Silver; CONTROL AND INSTRUMENTATION: 284 Reliability Technology to Improve and/or Maintain Emergency Diesel Generator Performance by S. Karimian and J. H. Taylor, 293 A Noise Diagnostics System for Operator Advice by G. Hessel, P. Liewers, P. Schumann, W. Schmitt, and F.-P. Weiss; PLANT SAFETY FEATURES: 307 A Passive Containment System for Advanced Light-Water Reactors by O. B. Falls, Jr., and F. W. Kleimola; ENVIRONMENTAL EFFECTS: 318 Data Base Construction for a Computerized Radiological Risk Investigation System by L. M. Hively, J. E. Nyquist, J. L. Bledsoe, and A. L. Sjoreen, 326 Erratum to "Radiation Hormesis and Nuclear Safety," Vol. 29, No. 1; OPERATING EXPERIENCES: 327 Operational Safety Experience and Passive Safety Testing at the Fast Flux Text Facility by Q. L. Baird, J. L. Rathbun, D. D. Stepnewski, R. L. Stover, and A. E. Waltar, 344 Backfilling of Independent Residual Heat Removal Systems in West Germany and Switzerland by G. Eckert and Y. Salomon, 353 Reactor Shutdown Experience Compiled by J. W. Cletcher, 356 Selected Safety-Related Events Compiled by G. A. Murphy, 363 Operating U.S. Power Reactors Compiled by E. G. Silver; RECENT DEVELOPMENTS: 384 General Administrative Activities Compiled by E. G. Silver, 390 Reports, Standards, and Safety Guides by D. S. Queener, 395 Status of Power-Reactor Projects Undergoing Licensing Review Compiled by E. G. Silver, 400 Proposed Rule Changes as of Mar. 31,1988; ANNOUNCEMENTS: 283 International ENS/ANS Conference on Thermal Reactor Safety "NUCSAFE 88", 317 Northwestern University Short Course on Radiation Safety, 407 Second International Seminar on Small- and Medium-Sized Nuclear Reactors, 407 International Workshop on New Developments in Occupational Dose Control and ALARA Implementation at Nuclear Power Plants and Similar Facilities, 408 Fourth International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-4), 404 The Authors.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Overview of IMPACT Data Acquisition System and Data Reduction Process

This report documents the development of the data acquisition system (DAS) and data reduction methodologies for the Irradiated Material Property Accelerated Characterization Test (IMPACT) experiment at the Advanced Test Reactor (ATR). The IMPACT experiment is designed to enable in-pile measurement of thermal conductivity in metallic nuclear fuels, specifically U-10Zr, using an instrumented thermal conductivity probe. The DAS supports both passive temperature monitoring and active thermal interrogation of the probe through controlled AC and DC excitation. Significant modifications to laboratory-scale systems were required to accommodate the higher resistance paths associated with the in-pile application. Custom electronics and relay-controlled measurement sequencing were developed to enable the measurement and sufficient power delivery to the sensing region. A reduced-order, axisymmetric thermal model based on the thermal quadrupoles method is presented to support data interpretation. This model enables efficient evaluation of transient heat transfer behavior and facilitates solution of the inverse problem required to extract thermal properties from measured signals. Multiple boundary condition formulations are discussed to address varying experimental time scales and geometries. Additionally, machine learning techniques are introduced to support data reduction and improve confidence in inverse solutions. Convolutional neural networks are applied to identify the presence of gas gaps and other evolving geometric features that significantly impact thermal response during irradiation. These efforts contribute to the broader integration of digital twin frameworks and real-time modeling capabilities within the Advanced Fuels Campaign.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN

Testing and Validation of Wireless Communication Architecture for Heliostat Fields: SIPS Final Report

This work focuses on the development and testing of a low-cost wireless communication system for heliostat fields, enabling significant capital costs reductions for concentrating solar thermal systems. Outputs of this work include a working demonstration of a multi-node communication system, clear reporting of system performance, and technical documentation of system development and architecture for reproducibility. Through this process, an open-source repository was created for manufacturing hardware at ~$30/heliostat. The system includes software for cybersecurity, achieving sub-second communication latencies and derisking of hardware for eventual scale-up to tens of thousands of heliostats. While the system is not currently off-the-shelf ready, there is now a clearly defined pathway for scaling up and completing the commercial development process.

14 SOLAR ENERGY

Prime Time for Model-Predictive Control? Assessing the Technical and Market Readiness of Advanced Controls in Buildings

Despite three decades of extensive research and field testing that have consistently validated the benefits of Model Predictive Control (MPC) in building applications, the technology has seen limited market adoption. This paper evaluates the readiness of MPC for widespread deployment, showcases recent demonstrations and field tests across diverse building types, including residential, small commercial, large commercial, and campus settings. Our results demonstrate that MPC can optimize system operations to achieve load shifting, minimize curtailment of on-site generation, and reduce energy costs by up to 80 %, while maintaining or improving occupant comfort. We also show that MPC can effectively control large assets, such as MW-sized thermal storage systems, and respond to dynamic pricing signals. However, achieving scale remains difficult due to labor-intensive workflows, reliance on a “PhD-in-the-loop” for MPC design and maintenance, susceptibility to fragile data infrastructure, and persistent workforce education and acceptance barriers. To bridge this gap, we outline a transition from bespoke, labor intensive prototypes toward streamlined, segment-targeted deployment strategies that leverage model templates, semantic tools, and generative AI. By automating control configuration and reducing engineering effort, these recommendations provide a pathway for transforming successful research demonstrations into scalable, market ready solutions for MPC-based controls.

Pritoni, Marco

A Compact Cryogenic Environment for In Situ Neutron Diffraction Under Mechanical Loading

Understanding the deformation mechanisms of materials at cryogenic temperatures is crucial for cryogenic engineering applications. In situ neutron diffraction is a powerful technique for probing such mechanisms under cryogenic conditions. In this study, we present the development of a compact cryogenic environment (CCE) designed to facil-itate in situ neutron diffraction experiments under mechanical loading at tempera-tures as low as 77 K. The CCE features a polystyrene foam cryogenic chamber, alumi-num blocks serving as neutron-transparent cold sinks, a liquid nitrogen dosing system for cryogen delivery, a nitrogen gas flow control system for thermal management, a process controller for temperature control, and a pair of thermally isolated grip adapt-ers for mechanical testing. The CCE achieves reliable temperature control with mini-mal neutron attenuation. Utilizing this setup, we conducted three in situ neutron dif-fraction tensile tests on a 316L stainless steel at 77 , 173 , and 298 K, respectively. The results highlight the pronounced effects of cryogenic temperatures on the material's deformation mechanisms, underscoring both the significance of cryogenic deformation studies and the effectiveness of the CCE.

Yu, Dunji [ORNL] (ORCID:0000000189467851)

EXERGETIC: De-Risking Next-Generation Resilient Geothermal Hybrids via At-Scale Evaluation Using Virtual Emulation Digital Twin Environment for Efficient Operation

The DOE-GTO-funded project, award number 5.1.2.12, entitled "EXERGETIC - De-risking Next Generation Resilient Geothermal Hybrids via at-Scale Evaluation Using a Virtual Emulation Digital Twin Environment for Efficient Operation," advances the solution to these challenges by developing and validating a geothermal co-emulation environment implemented at the National Laboratory of the Rockies (NLR)'s Advanced Research on Integrated Energy Systems (ARIES) platform. This framework enables the de-risking of next-generation geothermal and geothermal hybrid systems through high-fidelity modeling, real-time digital emulation, advanced control strategies, and techno-economic assessment. The project focused on geothermal hybrid configurations that integrate geothermal power plants with concentrated solar power and underground thermal energy storage, enabling enhanced efficiency, flexibility, and grid support capabilities. The main goal of this project was the development of a geothermal digital co-emulation environment to demonstrate the technical and economic value of geothermal hybrid systems and their contribution to grid stability and flexibility. The EXERGETIC framework combined physics-based models, controls, and real assets at ARIES, including digital real-time simulators (DRTS), a 20-MW-scale controllable grid interface (CGI), and a 2-MW conventional generator. Detailed transient models were developed for the key subsystems of a hybrid geothermal plant, including parabolic trough solar collectors, reservoir thermal energy storage (RTES), and a binary Organic Rankine Cycle (ORC) power plant. The ORC model explicitly captured thermal inertia and off-design operation and integrated control strategies to dynamically respond to electric load profiles. The models were validated against published experimental and numerical studies, demonstrating strong agreement and confirming the accuracy and robustness of the modeling approach. The resulting digital twin represents geothermal-solar-storage systems at multiple scales (1 MW to 100 MW) and enables realistic emulation of grid-connected operation. The control architecture allows the geothermal resource to provide stable baseload generation, while solar and stored thermal energy supply flexible, dispatchable support during periods of high demand or variable grid conditions. A key contribution of the EXERGETIC project is the demonstration that geothermal hybrid systems can be designed to be active grid assets rather than passive baseload generators. Using the ARIES platform, the digital twin was evaluated under multiple grid scenarios, including load following, voltage support at the distribution level, and frequency response at the transmission level. Results show that hybrid geothermal systems can respond effectively to dynamic grid conditions, providing inertia-like behavior, primary frequency support, and voltage regulation through coordinated control. In addition to the performance and grid services capability analysis of geothermal and hybrid geothermal systems, the EXERGETIC project also focused on scalability and techno-economic analysis of geothermal hybrid plants. In particular, for the scalability analysis, machine-learning (ML)-based surrogate models were trained using data generated from the geothermal digital twin under different grid-connected scenarios and plant capacities. These ML models demonstrated strong interpolation and extrapolation capabilities across plant sizes, accurately reproducing both steady-state and transient responses with very low errors. Regarding the techno-economic analysis, plant performance results were integrated with cost models for hybrid geothermal systems, and the levelized cost of electricity (LCOE) was used as the main economic metric to evaluate system performance across a range of system capacities, solar shares, solar multiples, and storage durations. Results indicate that economies of scale significantly reduce geothermal LCOE as plant capacity increases, with large-scale systems (25-100 MW) achieving substantially lower costs than small plants. Hybridization with solar thermal energy and storage further improves economic performance by increasing capacity utilization and enabling flexible dispatch. In addition, thermal storage plays a critical role in reducing LCOE by maximizing geothermal, solar, and stored energy resources. In summary, the results from this project demonstrate that geothermal hybrid systems represent a promising alternative for increasing the energy conversion efficiency of geothermal technologies, contributing to the preservation of geothermal resources, and supporting the transition of geothermal plants from traditional baseload resources into flexible, resilient, and cost-competitive energy conversion technologies.

15 GEOTHERMAL ENERGY

Thermal Reservoir Networks for Modularly Expandable Thermal Microgrids

The Department of Defense (DoD) faces the substantial challenge of cost-effectively retrofitting one to two installations per month, each comprising approximately 1,000 buildings, to improve resilience, reduce energy consumption, and enhance energy supply security. Achieving these objectives requires optimal system selection and effective risk mitigation during system integration. To address this need, we introduce Platform-Based Design (PBD), a structured, hierarchical methodology adapted from other industrial sectors to the domain of energy system retrofits. We demonstrate the effectiveness of PBD through a techno-economic feasibility study comparing geothermal-coupled thermal energy networks (TENs) with conventional energy systems for heating, cooling, and powering 17 buildings at Joint Base Andrews (JBA) in Maryland. Our analysis illustrates that the PBD approach enables rigorous, data-driven, sequential decision making, resulting in a family of Pareto-optimal systems, among which the TEN emerged as the most promising solution. The selected TEN design integrates geothermal borefields, heat recovery heat pumps, photovoltaic (PV) arrays, and battery storage. Compared to the baseline system – gas heating combined with air-source chillers – the proposed TEN reduces annual imported energy by 74% and peak electricity demand by 45%, achieves a levelized cost of energy of $\$0.210$/kWh, and substantially enhances resilience. Life-cycle costs increase by approximately 6%, and initial investment costs are about 2.5 times higher than the baseline. However, if central plant infrastructure, district loops, and utility-scale PV and battery systems are privately funded and operated, the initial investment would fall below the baseline system cost. Critical to achieving these significant performance improvements were detailed nonlinear dynamic simulations coupling geothermal heat transfer, energy system operation, and realistic feedback control logic. These simulations identified essential design modifications and control strategy refinements that substantially reduced energy use, peak demand, and compressor shortcycling, thereby improving durability and reliability—issues that would have been significantly more expensive to resolve during operation. Additionally, the verification step highlighted sensitivities to key design parameters that could reduce initial investment by approximately $\$2$ million and reduce annual life-cycle costs more than $\$300,000$. We recommend adopting the PBD methodology for future feasibility studies and TEN pilot projects to gain valuable operational experience. Furthermore, we recommend that DoD invest in transferring and scaling the PBD methodology to other installations. This entails developing standardized computational frameworks and component libraries as well as training industry in conducting PBD. Such investments would enable rapid, robust, reliable, and cost-effective retrofits, supporting DoD’s ambitious energy system modernization goals.

Wetter, Michael [Lawrence Berkeley National Labora

Interaction of Soil pH and Mineralogy Controls Soil Organic Matter Persistence through Changes in the Composition and Amount of Microbial Necromass

Microbial necromass–mineral associations are key to long-term soil organic matter (SOM) persistence. However, how soil pH and mineralogy interact to regulate SOM stability remains poorly understood. Here, we used artificial soils to test how three clay minerals (bentonite, kaolinite, and goethite), adjusted to four pH levels (5–8), affect microbial activity (respiration), microbial physiology (carbon use efficiency, CUE), microbial-derived residue material (necromass), and the formation and stability of mineral-associated organic matter (MAOM). Artificial soils were inoculated with a rhizosphere-derived microbial community cultured under the same pH conditions and on two representative simulated exudate types (organic acids and carbohydrates) and incubated for 6 weeks. In two complementary experiments, we added necromass from known microbial taxa to the same minerals across pH levels to isolate the role of necromass chemistry and loading. We found that soil pH shaped MAOM chemistry by altering microbial activity and necromass composition. In interaction with mineral type, pH also controlled MAOM thermal stability. Higher necromass loading weakened mineral-organic bonding, reducing MAOM stability, consistent with zonal mineral–organic interaction models. Our results demonstrate that microbial activity, rather than carbon use efficiency, better predicts MAOM formation and that pH-dependent necromass composition and loading govern MAOM persistence. These findings advance mechanistic understanding of SOM stabilization and have implications for predicting soil carbon dynamics under shifting environmental conditions.

carbon use efficiency

Mu2e Production Target Thermal Test Project

The Mu2e experiment requires a production target that is capable of operating under extreme thermal conditions caused by an 8 GeV proton beam. This project’s objective supports the development of the Mu2e Pro- duction Target by testing the Stickman model’s thermal behavior. Angel Flores Luviano has assisted Jonathan Williams in progressing this project by contributing to the development of a Radiative Cooling Test Fixture (RCTF) that will be used to evaluate the thermal behavior of the new production target model. Engineering calculations were performed to an- alyze thermal performance and pressure drop within the cold well and wa- ter cooling circuit. These calculations also determined the optimal sizing for key components of the water system. An engineering note was made to document these calculations. CAD models of the water circuit piping, thermocouple mounting bars, and radiator chimney were developed, and prototype test rig components were fabricated using 3D printing. Future work will focus on continued RCTF development which includes control system integration, heater hardware design, and interfaces that can be scaled up to increase thermal capacity.

Flores Luviano, Angel Augusto [Unlisted, US]

Revolutionizing thermal Management in Next-Generation AI data centers: Challenges and breakthrough innovations

Data centers (DCs) serve as critical infrastructure for powering the growth and evolution of AI. Next-generation AI DCs present unique challenges in thermal management driven by unprecedented computational demands. This paper provides a comprehensive summary of key stakeholder perspectives on technology gaps, infrastructure requirements, test bed needs, emerging opportunities, and preliminary solutions related to thermal management for AI DCs. It establishes six strategic pillars of thermal management for next generation AI DC: reliability, deployability, efficiency, resilience, measurability, and valorization. The discussion spans a range of critical topics, including advanced cooling technologies, thermal strategies for emerging modular and edge DCs, system-level optimization and control frameworks, infrastructure planning and grid integration designs, benchmarking approaches, and pathways for waste heat recovery and reuse. The proposed research, development, and demonstration efforts are aimed at accelerating the deployment of AI DCs while ensuring energy efficiency, reliability, safety, and regulatory compliance.

Wang, Pengtao [ORNL] (ORCID:0000000214713429)

Coalition for Community-Supported Affordable Geothermal Energy Systems (C2SAGES)

The C2SAGES project evaluated the feasibility of a community geothermal system for the planned Windy Ridge affordable housing development in Hinesburg, Vermont. Led by GTI Energy with Vermont Gas Systems, LN Consulting, NREL, and Frontier Energy, the work assessed technical design, energy performance, costs, business models, community engagement, maintenance, workforce development, and permitting. The proposed system was designed to serve 100% of the development’s heating, cooling, and domestic hot water loads. Compared with a baseline using air-source heat pumps and natural gas water heating, the geothermal system was estimated to reduce HVAC and domestic hot water energy use by about 45% to 48%, lower operating and maintenance costs, and reduce 30-year life-cycle costs by 37% for Phase 1 and 10% for Phase 2. Technical testing and modeling indicated that the Windy Ridge site is suitable for a community-scale geothermal system. The project also developed borehole field layouts, piping concepts, pump house designs, controls, maintenance plans, and supporting engineering drawings. The business model analysis found that first cost, ownership structure, and customer affordability remain major deployment challenges. Utility-led maintenance and operation were viewed favorably, but traditional utility cost-recovery models may require subsidy or revised financing structures to be practical for affordable housing. Community engagement highlighted the need for clear public education, transparent financing, reliable long-term maintenance, trained technicians, and the potential to pair geothermal systems with weatherization. Overall, the report concludes that community geothermal is technically feasible and offers meaningful energy, emissions, and life-cycle cost benefits, but broader deployment will depend on workable financing models and workforce readiness.

15 GEOTHERMAL ENERGY

Supervisory genset control in range-extended electric vehicle

A controls system for a range-extended electric vehicle comprising an overall system control unit, an engine control module configured to control a range extender of the range-extended electric vehicle, power electronics configured to control a generator of the range-extended electric vehicle, and a supervisory control module coupled between the overall system control unit and the engine control module and the power electronics, the supervisory control module configured to receive information from the overall system control unit and provide commands to the engine control module and the power electronics.

Li, Ke

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH