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DOE OSTI2021

Quantum dynamics of a nucleon in the Fermi accelerator

Highlights: • In nuclear physics, the Fermi accelerator is a coherent open quantum system. • There is not a true equilibrium for a nucleon‘s mean-energy in the Fermi accelerator. • Occupation of higher energy eigen-states remains even after the mean-energy plateaus. • This work paves the way for work on quantum tunnelling in the Fermi accelerator. The quantum dynamics of a particle in a one-dimensional box with an oscillating wall (the Fermi accelerator) is investigated. The model is applied to the motion of a single nucleon in the mean-field potential of a heavy atomic nucleus whose surface vibrates. By directly solving the time-dependent Schrödinger equation, both the state of the particle and its mean-energy are studied. The effects of the frequency of the wall oscillation on the nucleon’s energy are addressed. Its energy oscillates in phase with the moving wall for all frequencies, showing no chaotic behaviour. There is a large initial peak of the nucleon’s energy as the particle adjusts to the sudden change in the size of the box and a varying relaxation time as it plateaus towards lower energy and a partial equilibrium. Small oscillations in energy continue, since there cannot be a true equilibrium while the wall is moving. The quantum coherence between the different parts of the nucleon’s wave-function in real space is very much preserved. This research lays the foundation for future investigations into quantum tunnelling in the Fermi accelerator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Low-energy effective quantum field theoretic description of excitations about soliton configurations

Solitons are the classical field configurations connecting two trivial vacua. These are also the solutions of classical field equations of motion with particle-like properties. Moreover, they are localized in space, having finite energy, and are stable against decay into radiation. The coherent state description of kink-solitons is discussed in the present article. Further, the relation between topological solitons and occupation numbers corresponding to low momentum excitations are also discussed coherently. The description of the low energy excitations about solitons in quantum field theory is the main theme of this article. Further, a few physical observables, namely some low order correlation functions, are computed up to certain integral forms. Furthermore, we have shown that it is possible to detect the presence of soliton-like classical configurations in many-particle systems from the nature of the one-point function and non-conservation of momentum feature of one-point, two-point and three-point functions in this low-energy effective field theory of these excitations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Optimal electric-distribution-grid planning considering the demand-side flexibility of thermal building systems for a test case in Singapore

The planning of district-scale electric grids, i.e., distribution grids, has traditionally relied on finding the most cost-effective design such that they are able to supply the peak loads in a district. With the advent of electric demand side flexibility (DSF), there is the opportunity to reshape peak loads such that the investment cost of the electric grid decreases in exchange for a minor increase in the operation cost. This paper formulates an optimal planning approach for the electric grid at the district scale, which incorporates the DSF from thermal building systems, e.g., heating ventilation and air-conditioning (HVAC) systems. The problem is formulated as a mixed-integer linear program (MILP) and aims at minimizing the investment cost for the grid along with the operation cost of the flexible loads. This is subjected to the fixed electricity demand and thermal comfort constraints of building occupants. To this end, linear models for the thermal comfort in the buildings and the power flow in electric grid are considered. The approach is tested on a district planning test case based in Singapore, where the results show up to 30.9 % reductions in investment cost and up to 3.7 % reduction in total annualized cost. Urban planning authorities, developers and utility companies can all benefit from the presented approach to make optimized investment decisions. For building operators, the results point to the need of adopting their control systems for DSF.

Troitzsch, Sebastian↗

DOE OSTI2020

Data-driven evaluation of HVAC operation and savings in commercial buildings

Commercial buildings consumed 36% of electricity, or 1.35 trillion kWh, in the United States in 2017, and almost 30% of this energy was wasted. Much of this loss can be attributed to inefficient heating ventilation and air conditioning (HVAC) systems. By improving the operational conditions of HVAC, significant savings can be achieved. However, most buildings and building equipment do not use costly sub-meters to monitor and address performance issues, and on-site auditing can be expensive and insufficient. Alternatively in this study, we propose a data-driven method to identify savings opportunities using only whole building meter data and without setting foot in the building. For this purpose, we introduced two algorithms that virtually quantify the value of a thermostat setpoint setback and HVAC rescheduling. Additionally, we developed novel methods for detecting occupancy patterns and quantifying the baseload of the HVAC operation. Using a clustering algorithm, we identified those buildings for which HVAC savings was significant and further categorized the buildings based on their potential for savings. A population study of over 432 commercial buildings demonstrated a median percentage energy savings of 1.6% from a baseload reduction and 2.1% from HVAC rescheduling. Additionally, results indicate that retail buildings have the highest potential for savings among the building types studied.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2020

Intelligent multi-zone residential HVAC control strategy based on deep reinforcement learning

Residential heating, ventilation, and air conditioning (HVAC) has been considered as an important demand response resource. However, the optimization of residential HVAC control is no trivial task due to the complexity of the thermal dynamic models of buildings and uncertainty associated with both occupant-driven heat loads and weather forecasts. In this paper, we apply a novel model-free deep reinforcement learning (RL) method, known as the deep deterministic policy gradient (DDPG), to generate an optimal control strategy for a multi-zone residential HVAC system with the goal of minimizing energy consumption cost while maintaining the users’ comfort. Here, the applied deep RL-based method learns through continuous interaction with a simulated building environment and without referring to any prior model knowledge. Simulation results show that compared with the state-of-art deep Q network (DQN), the DDPG-based HVAC control strategy can reduce the energy consumption cost by 15% and reduce the comfort violation by 79%; and when compared with a rule-based HVAC control strategy, the comfort violation can be reduced by 98%. In addition, experiments with different building models and retail price models demonstrate that the well-trained DDPG-based HVAC control strategy has high generalization and adaptability to unseen environments, which indicates its practicability for real-world implementation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

OCHRE: The Object-oriented, Controllable, High-resolution Residential Energy Model for Dynamic Integration Studies

Electrification and the growth of distributed energy resources (DERs), including flexible loads, are changing the energy landscape of electric distribution systems and creating new challenges and opportunities for electric utilities. Changes in demand profiles require improvements in distribution system load models, which have not historically accounted for device controllability or impacts on customer comfort. Although building modeling research has focused on these features, there is a need to incorporate them into distribution load models that include DERs and can be used to study grid-interactive buildings. In this paper, we present the Object-oriented, Controllable, High-resolution Residential Energy (OCHRE) model. OCHRE is a controllable thermal-electric residential energy model that captures building thermal dynamics, integrates grid-dependent electrical behavior, contains models for common DERs and end-use loads, and simulates at a time resolution down to 1 minute. It includes models for space heaters, air conditioners, water heaters, electric vehicles, photovoltaics, and batteries that are externally controllable and integrated in a co-simulation framework. Using a proposed zero energy ready community in Colorado, we co-simulate a distribution grid and 498 all-electric homes with a diverse set of efficiency levels and equipment properties. We show that controllable devices can reduce peak demand within a neighborhood by up to 73% during a critical peak period without sacrificing occupant comfort. We also demonstrate the importance of modeling load diversity at a high time resolution when quantifying power and voltage fluctuations across a distribution system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Model predictive control for integrated control of air-conditioning and mechanical ventilation, lighting and shading systems

Modern buildings are increasingly automated and often equipped with multiple building services (e.g., air-conditioning and mechanical ventilation (ACMV), dynamic shading, dimmable lighting). These systems are conventionally controlled individually without considering their interactions, affecting the building’s overall energy inefficiency and occupant comfort. A model predictive control (MPC) system that features a multi-objective MPC scheme to enable coordinated control of multiple building services for overall optimized energy efficiency, indoor thermal and visual comfort, as well as a hybrid model for predicting indoor visual comfort and lighting power is proposed. The MPC system was implemented in a test facility having two identical, side-by-side experimental cells to facilitate comparison with a building management system (BMS) employing conventional reactive feedback control. The MPC system coordinated the control of the ACMV, dynamic façade and automated dimmable lighting systems in one cell while the BMS controlled the building services in the other cell in a conventional manner. The MPC side achieved 15.1–20.7% electricity consumption reduction, as compared to the BMS side. Simultaneously, the MPC system improved indoor thermal comfort by maintaining the room within the comfortable range (-0.5 < predicted mean vote < 0.5) for 98.3% of the time, up from 91.8% of the time on the BMS side. Visual comfort, measured by indoor daylight glare probability (DGP) and horizontal illuminance level at work plane height, was maintained for the entire test period on the MPC side, improving from having visual comfort for 94.5% and 85.7% of the time, respectively, on the BMS side.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Home energy management under realistic and uncertain conditions: A comparison of heuristic, deterministic, and stochastic control methods

We report home energy management systems (HEMS) have been shown to reduce energy bills and to provide grid services including peak demand reduction and demand flexibility. However, uncertainty in residential energy systems is a significant issue and can reduce the benefits of a HEMS to the homeowner or grid operator. Sources of uncertainty include weather forecasts, predictions of energy-related occupant activities (e.g., hot water draws), and parameter estimation for the building envelope and energy-consuming equipment. This paper tackles the problem of uncertainty by developing a framework that simulates HEMS in uncertain conditions and evaluates the performance of multiple control strategies. A linear, reduced-order residential building model for model predictive control applications is derived and compared to a full-order model. Stochastic model predictive control is shown to perform better than deterministic and heuristic methods when considering realistic forecasts with uncertainty. The framework can evaluate the performance of HEMS in real-world applications, which can help de-risk HEMS deployment.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Using discrete Bayesian networks for diagnosing and isolating cross-level faults in HVAC systems

Fault detection and diagnosis (FDD) technologies are critical to ensure satisfactory building performance, such as reducing energy wastes and negative impacts on occupant comfort and productivity. Existing FDD technologies mainly focus on component-level FDD solutions, which could lead to mis-diagnosis of cross-level faults in heating, ventilating, and air-conditioning (HVAC) systems. Cross-level faults are those faults that occur in one component or subsystem, but cause operational abnormalities in other components or subsystems, and result in a building level performance degradation. How to effectively diagnose the root cause of a cross-level fault is the focus of this study. Here, this paper presents a novel discrete Bayesian Network (DisBN)-based method for diagnosing cross-level faults in an HVAC system commonly used in commercial buildings. A two-level DisBN structure model is developed in this study. The parameters used in the DisBN model are obtained either from expert knowledge or through machine-learning strategies from normal system operation data. Meanwhile, the probability parameters are discretized to incorporate the uncertainties associated with typical expert knowledge. Thus, the developed DisBN method addresses the challenges many other BN based FDD methods face, i.e., the lack of fault data for BN parameter training. The developed DisBN represents causal relationships between a fault and its cross-level system impacts (i.e., fault symptoms or fault indicators) by considering how fault impacts propagate across different levels in an HVAC system. A weather and schedule information-based Pattern Matching (WPM) method is employed to automatically create WPM baseline data sets for each incoming real time snapshot data from the building systems. Consequently, BN inference and real-time diagnostics are achieved by comparing incoming snapshot data and the WPM baseline data set. The proposed method is evaluated using experimental fault data collected in a campus building. Fault diagnosis results demonstrate that the WPM-DisBN method is effective at locating the root causes of cross-level faults in an HVAC system.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2023

Online transfer learning strategy for enhancing the scalability and deployment of deep reinforcement learning control in smart buildings

In recent years, advanced control strategies based on Deep Reinforcement Learning (DRL) proved to be effective in optimizing the management of integrated energy systems in buildings, reducing energy costs and improving indoor comfort conditions when compared to traditional reactive controllers. However, the scalability and implementation of DRL controllers are still limited since they require a considerable amount of time before converging to a near-optimal solution. This issue is currently addressed in literature through the offline pre-training of the DRL agent. However this solution results in two main critical issues: (1) the need to develop a building surrogate model to perform the training task, and (2) the need to perform a fine-tuning process over several training episodes to obtain a near-optimal control policy. In this context, this paper introduces an Online Transfer Learning (OTL) strategy that exploits two knowledge-sharing techniques, weight-initialization and imitation learning, to transfer a DRL control policy from a source office building to various target buildings in a simulation environment coupling EnergyPlus and Python. A DRL controller based on discrete Soft Actor–Critic (SAC) is trained on the source building to manage the operation of a cooling system consisting of a chiller and a thermal storage. Several target buildings are defined to benchmark the performance of the OTL strategy with that of a Rule-Based Controller (RBC) and two DRL-based control strategies, deployed in offline and online fashion. The strategy adopted for OTL emulates the real world implementation with a simulation process by implementing the transferred DRL agent for a single episode in the target buildings. Target buildings have the same geometrical features and are served by the same energy system as the source building, but differ in terms of weather conditions, electricity price schedules, occupancy patterns, and building envelope efficiency levels. The results show that the OTL strategy can reduce the cumulated sum of temperature violations on average by 50% and 80% respectively when compared to RBC and online DRL while enhancing the energy system operation with electricity cost savings ranging between 20% and 40%. Furthermore, the OTL agent performs slightly worse than the offline DRL controller but it does not require any modeling effort and can be implemented directly on target buildings emulating a real-world implementation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Household energy resilience in extreme weather events: An investigation of energy service importance, HVAC usage behaviors, and willingness to pay

Household energy resilience, particularly maintaining essential energy services within an acceptable and affordable level, is critical during extreme weather events (e.g., winter storms, heat waves) with power shortages or outages. However, the research on the importance and acceptable compromise levels of energy services, HVAC usage behavior changes, and willingness to pay (WTP) for energy services during disasters is limited. Therefore, this study investigates the importance and compromise of household energy services, HVAC usage behaviors, and WTP, as three key dimensions of household energy resilience, in both normal days and disaster scenarios through surveys (n=485). First, 12 common residential end-uses are grouped into high, mid, and low-priority services using hierarchical clustering, in which high-priority services (perceived as important and un-compromisable) include food cooking and storage (refrigerator and freezer) and thermal comfort (space heating and cooling), mid-priority services involve water heating and lighting, while low-priority services are mostly related to entertainment and housework (e.g., TV, laundry). Also, HVAC use patterns demonstrate that occupants become more energy conservative during disasters, e.g., reducing durations of running HVAC and adjusting temperature setpoints to save energy. In terms of energy cost, approximately 60% of respondents are willing to pay more to maintain energy services during disasters, although only 13% are prepared to pay over double the normal energy prices. The regression models further reveal that household energy resilience varies across different sociodemographic groups (e.g., age, income, family size) and is impacted by disaster experience and beliefs in clean energy and climate. In conclusion, these research findings provide important perspectives to understand household energy resilience and inform measures for disaster adaptation of households in extreme weather events.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

Operator learning for energy-efficient building ventilation control with computational fluid dynamics simulation of a real-world classroom

Energy-efficient ventilation control plays an important role in reducing building energy consumption while ensuring occupant health and comfort. While Computational Fluid Dynamics (CFD) simulations provide detailed and physically accurate representations of indoor airflow, their high computational cost limits their use in real-time building control. In this work, we present a neural operator learning framework that combines the physical accuracy of CFD with the computational efficiency of machine learning to enable building ventilation control with the high-fidelity fluid dynamics models. Our method jointly optimizes the airflow supply rates and vent angles to reduce energy use and adhere to air quality constraints. We train an ensemble of neural operator transformer models to learn the mapping from building control actions to airflow fields using high-resolution CFD data. This learned neural operator is then embedded in an optimization-based control framework for building ventilation control. Experimental results show that our approach achieves significant energy savings compared to maximum airflow rate control, rule-based control, as well as data-driven control methods using spatially averaged CO 2 prediction and deep learning–based reduced-order models, while consistently maintaining safe indoor air quality. These results highlight the practicality and scalability of our method in maintaining energy efficiency and indoor air quality in real-world buildings.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2026

A transfer learning approach to energy-efficient control of small and medium-sized commercial buildings

Model-free reinforcement learning (RL) provides a data-driven and adaptive approach to optimize building energy use while satisfying occupant comfort. This powerful tool does not need any prior knowledge about the environment and system it is optimizing and can adapt its policy based on the changes in captures. Like any other data-driven tool, it faces high training costs due to the extensive agent-environment interactions required to capture long-term building dynamics and user comfort. Transfer learning, particularly policy distillation, offers a promising way to accelerate training by leveraging pretrained RL agents in different building and system types. Here, this study investigates online student distillation, in which the student model updates its neural network weights using outputs from teacher models. The work introduces a student distillation strategy designed for efficient knowledge transfer, along with a teacher selection method that ensures high-quality guidance. The approach is validated using a highly calibrated whole building energy model for a small/medium commercial building test facility. Results show substantial reductions in training time and data requirements while surpassing the performance of ASHRAE Guideline 36, an advanced rule-based control strategy. The distilled RL model required 45% less data and achieved 20% higher cumulative rewards than a state-of-the-art RL model, with faster convergence and lower energy consumption. These outcomes demonstrate that effective transfer learning enables a scalable and data-efficient energy management solution for commercial buildings.

ASHRAE guideline 36↗

DOE OSTI2026

Consumer safety-oriented scheduling of rotating power outages during heat waves

Extreme heat events have widespread effects on power systems, reducing available generation capacity, limiting transmission capabilities, and causing unusual demand patterns on the consumer side. As these combined effects expose bulk transmission systems to potential large-scale blackouts, utilities may be required to schedule and apply rotating outages, by temporarily and alternately disconnecting distribution substations to reduce overload. However, utilities lack mechanisms to inform these events, exacerbating the negative effects of heat waves on affected communities. This paper introduces a novel framework for scheduling rotating outages during heat waves while considering impacts on consumers’ safety. Instead of random sequential load shedding, we propose a methodology to rotate power outages considering a metric that quantifies the indoor overheating risk of groups of consumers during a power outage. The overheating risk is derived from a detailed building simulation using CityBES, where the buildings are modeled based on available data—use type, year built, floor area, number of stories, location—while presence of air conditioning and occupancy are calibrated from smart meter data. Based on the metric, an algorithm to schedule the rotating outages is applied to prioritize feeders for disconnection at each hour according to their overheating risk to meet a utility load reduction target. Applied to two substations and seven feeders in the Portland General Electric territory, the results show that this approach effectively leads to the lowest overheating risk during the resulting outage schedules, with an average 10.1% lower overheating compared to uninformed schedules.

Building thermal simulation↗

DOE OSTI2021

Parametric and sensitivity analysis of a PCM-integrated wall for optimal thermal load modulation in lightweight buildings

Load modulation in buildings is becoming increasingly important due to growing disparity in energy demand during peak and off-peak hours. Integrating phase change material (PCM) in building envelopes and using a controlled precooling strategy can provide substantial thermal load modulation; however, it may greatly increase the total energy use. Previous studies have employed PCM in building envelopes primarily for energy savings and, to some extent, peak load shedding and shifting. However, the load modulation capacity of a PCM-integrated envelope has not been well explored in the literature. In this study, we perform an extensive parametric and sensitivity analysis on PCM-integrated lightweight building walls and examine the combinatory effects of various PCM parameters on thermal load modulation and wall-related heat gains in buildings. Using numerical simulations, we investigate eight PCM parameters: PCM location in the wall, transition temperature, thickness, latent heat, transition range, density, specific heat, and thermal conductivity. Here, we evaluate their impact and relative importance to achieve maximum load modulation in buildings without compromising occupants’ thermal comfort or total energy use. The results show that the optimized PCM proposed in this study can completely invert the transient heat gain profile of the wall, providing up to 70% reduction of wall-related heat gain during peak hours without a major increase in the cumulative heat gain.

42 ENGINEERING↗

DOE OSTI2024

Implementation and validation of optimal start control strategy for air conditioners and heat pumps

Commercial buildings are responsible for approximately 20 % of the total energy consumption and greenhouse gas emissions in the United States. Over 85 % of these buildings lack building automation systems, and many are small (<50,000 square feet), underserved, and use rooftop units (RTUs) for heating, ventilation, and air-conditioning needs. Because these buildings lack proper energy management systems, several operational deficiencies lead to excess energy consumption. Studies have shown that managing the RTUs’ heating and cooling set points, schedules, setbacks, and optimal start can result in a 20 % to 25 % reduction in electricity consumption in small commercial buildings. These buildings typically use fixed schedules to start the RTUs 60 to 120 min before occupancy begins, which results in excess energy consumption. This paper presents research that demonstrates and evaluates the performance of four optimal start methods, which utilize data-based modeling as a key element in facilitating adaptive control in response to time-varying inputs while requiring minimal sensor inputs. The evaluation found energy savings in two commercial buildings equipped with RTUs by periodically alternating four different optimal start models during the cooling and heating season. The resulting energy savings are positive for all models and range from 2 to 5 kWh/day/unit. The units on the east side of the building showed higher savings, while interior units showed greater variability in savings due to the differences in capacities and room sizes. Savings were considerably greater during the heating season compared to the cooling season. The performance of all four models on Mondays was poor; models suggested a shorter optimal start time, which resulted in relatively larger errors. Finally, the future work will look at using a different model for the days after weekends and holidays.

42 ENGINEERING↗

DOE OSTI2023

A critical review of cyber-physical security for building automation systems

Modern Building Automation Systems (BASs), as the brain that enable the smartness of a smart building, often require increased connectivity both among system components as well as with outside entities, such as the cloud, to enable low-cost remote management, optimized automation via outsourced cloud analytics, and increased building-grid integrations. As smart buildings move towards open communication technologies, providing access to BASs through the building's intranet, or even remotely through the Internet, has become a common practice. However, increased connectivity and accessibility come with increased cyber security threats. BASs were historically developed as closed environments with limited cyber-security considerations. As a result, BASs in many buildings are vulnerable to cyber-attacks that may cause adverse consequences, such as occupant discomfort, excessive energy usage, and unexpected equipment downtime. Therefore, there is a strong need to advance the state-of-the-art in cyber-physical security for BASs and provide practical solutions for attack mitigation in buildings. However, an inclusive and systematic review of BAS vulnerabilities, potential cyber-attacks with impact assessment, detection & defense approaches, and cyber resilient control strategies is currently lacking in the literature. This review paper fills the gap by providing a comprehensive up-to-date review of cyber-physical security for BASs at three levels in commercial buildings: management level, automation level, and field level. The general BASs vulnerabilities and protocol-specific vulnerabilities for the four dominant BAS protocols (i.e., BACnet, KNX, LonWorks, and Modbus) are reviewed, followed by a discussion on four attack targets and seven potential attack scenarios. Furthermore, the impact of cyber-attacks on BASs is summarized as signal corruption, signal delaying, and signal blocking. The typical cyber-attack detection and defense approaches are identified at the three levels. Cyber resilient control strategies for BASs under attack are categorized into passive and active resilient control schemes. Open challenges and future opportunities are finally discussed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Constraining Galaxy-Halo connection using machine learning

We investigate the potential of machine learning (ML) methods to model small-scale galaxy clustering for constraining Halo Occupation Distribution (HOD) parameters. Our analysis reveals that while many ML algorithms report good statistical fits, they often yield likelihood contours that are significantly biased in both mean values and variances relative to the true model parameters. This highlights the importance of careful data processing and algorithm selection in ML applications for galaxy clustering, as even seemingly robust methods can lead to biased results if not applied correctly. ML tools offer a promising approach to exploring the HOD parameter space with significantly reduced computational costs compared to traditional brute-force methods if their robustness is established. Using our ANN-based pipeline, we successfully recreate some standard results from recent literature. Properly restricting the HOD parameter space, transforming the training data, and carefully selecting ML algorithms are essential for achieving unbiased and robust predictions. Among the methods tested, artificial neural networks (ANNs) outperform random forests (RF) and ridge regression in predicting clustering statistics, when the HOD prior space is appropriately restricted. We demonstrate these findings using the projected two-point correlation function (w p (r p )), angular multipoles of the correlation function (ξ ℓ (r)), and the void probability function (VPF) of Luminous Red Galaxies from Dark Energy Spectroscopic Instrument mocks. Our results show that while combining w p (r p ) and VPF improves parameter constraints, adding the multipoles ξ 0 , ξ 2 , and ξ 4 to w p (r p ) does not significantly improve the constraints.

cosmology↗