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DOE OSTI2026

Machine learning-enhanced MPC for demand flexibility in small commercial buildings: An experimental study

Small- and medium-sized commercial buildings (SMCBs) represent the majority of U.S. commercial building stock and a significant share of peak electricity demand, yet they often lack centralized building automation systems, representing a significant untapped resource for urban energy management. This infrastructure gap makes advanced control implementation challenging, limiting the potential for widespread demand flexibility. Model Predictive Control (MPC) has shown strong potential for load shifting, peak demand reduction, and cost savings, but its effectiveness is hindered by unmeasured disturbances such as internal heat gains. This paper presents a Hybrid MPC framework that integrates a physics-based gray-box building thermal model, identified using a lumped disturbance (LD) approach, with a machine learning (ML) model for forecasting unmeasured disturbances. The hybrid approach is designed for buildings with multiple individually controlled heat pump and thermostat pairs, common in SMCBs, and aims to optimize coordinated scheduling of multiple heat pumps under dynamic electricity pricing while respecting comfort constraints. The methodology is validated through both simulations of case study buildings and experimental studies at a highly-instrumented test facility. Simulation results show that the Hybrid MPC achieves substantial load shifting and peak demand reduction, approaching the performance of an ideal MPC with perfect disturbance knowledge, and outperforming a conventional MPC without disturbance forecasting. In experiments, the Hybrid MPC reduced daily HVAC energy costs by 8.7%, peak-price time load (load shifting) by 41.7%, and peak demand by 29.2% compared to baseline control, demonstrating comparable benefits to the 11.6% cost savings, 42.9% load shifting, and 23.2% peak reduction of the ideal MPC. These results demonstrate that the proposed hybrid modeling approach can significantly improve MPC performance in real-world SMCB applications without requiring additional disturbance measurements.

Demand Flexibility↗

DOE OSTI2023

The first field application of a low-cost MPC for grid-interactive K-12 schools: Lessons-learned and savings assessment

K-12 schools are the largest energy consumers in the public sector, with their HVAC energy consumption representing the largest portion of their total energy use. While transitioning these schools to grid-interactive HVAC system operation through advanced controls offers significant financial and environmental benefits, and model predictive control (MPC) has been identified as a promising solution to achieve that, very few MPCs are affordable and have been deployed in K-12 schools. This situation raises concerns about the unclear real-world benefits of MPC technology among facility managers and industries. To address this gap, this paper presents a low-cost MPC solution that requires minimal control infrastructure costs and a unique field demonstration at a K-12 school, conducted for both cooling and heating seasons. This work adopted a previously developed MPC and extended it for use in the school application. The MPC aims to coordinate multiple packaged units to eliminate unnecessary peaks and shift cooling or heating loads in response to grid signals based on load conditions, while maintaining thermostat temperatures within school-defined bounds. Throughout the field tests, the MPC achieved a 24% reduction in peak demand during the cooling season and shifted cooling or heating loads by up to 16% in response to the school's utility tariff, considering load conditions, while also allowing end-users to override thermostat setpoints. Further, the paper also discusses the limitations of this study and future research directions for better performance of the MPC at K-12 schools.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

MPC solution for optimal load shifting for buildings with ON/OFF staged packaged units: Experimental demonstration, and lessons learned

Small and medium-sized commercial buildings (SMCB) are significant demand response resources, and it is important to develop grid-responsive control algorithms that exploit those resources and create financial benefits for building owners and HVAC service providers. Furthermore, unlike large-sized commercial buildings, there is an opportunity to have universally applicable control solutions for many SMCBs since those buildings have a consistent HVAC system configuration: SMCBs are commonly served by multiple-staged air conditioning units controlled by their own thermostats. Despite the demand response potential and scalability, however, very few control solutions are available for SMCBs. Typical model predictive control (MPC) and heuristic control approaches for cooling load shifting that lower thermostat setpoints before an electric price jump are suitable mainly for large-sized commercial buildings where a continuous capacity modulation is possible, e.g., via dampers in variable air volume terminal units. However, those approaches can cause undesired, high peaks for SMCBs due to the nature of ON/OFF unit staging and narrow thermostat deadbands. This could discourage the use of advanced grid-responsive controls for SMCBs due to the concern of high demand charges, and has to be resolved. This paper presents a MPC solution that overcomes this challenge. It has a hierarchical MPC structure where an upper level MPC is responsible for electrical load shifting in response to an electric price signal while a lower level MPC is responsible for coordinating compressor stages to eliminate unnecessary peaks and follows the setpoints determined by the upper level MPC. In this work, two one-month, comprehensive laboratory tests have been carried out to demonstrate load shifting and cost savings for the algorithm. Interesting trade-offs between energy efficiency and load flexibility were observed and are discussed, and lessons learned for applying MPCs for SMCBs are also presented.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2026

Comparative Analysis of Model Predictive Control and MPC-Informed Rule-Based Control for Thermal Storage Operation in Ultra-Low Temperature 4th Generation District Heating Networks

The integration of thermal storage and heat pumps in district heating networks (DHNs) can significantly enhance operational flexibility and energy efficiency; however, the practical deployment of advanced control strategies is often hindered by forecasting requirements and computational complexity. This study presents a comparative analysis of thermal storage control strategies in an ultra-low-temperature fourth-generation DHN, focusing on the development of a simplified rule-based control (RBC) explicitly informed by Model Predictive Control (MPC) behavior. The proposed methodology systematically analyzes the charging and discharging decisions of an MPC-controlled system under ideal forecasting conditions and extracts recurrent control patterns as a function of key system variables, including outdoor temperature, thermal demand, and electricity price. These patterns are translated into a set of structured time- and condition-based rules, resulting in an MPC-informed RBC that embeds predictive insights while preserving implementation simplicity and operational transparency. The approach is validated on a realistic mixed-use urban district in Denver, Colorado, USA, equipped with a centralized air-source heat pump, distributed water-to-water heat pumps, and a central thermal storage unit. Results show that the tuned RBC attains approximately 96% of ideal MPC economic performance (-27% of costs), preserves values of technical and environmental indicators (reduction only of 2-3%), and substantially reduces complexity. Sensitivity analyses further demonstrate the robustness of the RBC under varying operational conditions (i.e., ambient temperature, electricity price). Overall, the study demonstrates that MPC-informed rule-based control represents an effective trade-off between control performance and real-world applicability, enabling the integration of additional system components while maintaining simplicity, robustness, and ease of implementation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2026

Dwarf Galaxy Number Counts within 25 Mpc: Predictions from Local Group Analogs in TNG50

The modern generation of wide-field galaxy surveys, such as LSST, Euclid, and Roman, will enable studies of dwarf galaxies (10 6 ≤ M * /M ⊙ ≤ 10 9 ) beyond the Local Group (LG) in unprecedented detail. Improved theoretical understanding of this population is necessary to guide these observations, since predictions in this regime are generally limited to specific environments like the LG. We present predictions for the population of dwarf galaxies from the TNG50 run of the IllustrisTNG suite of cosmological hydrodynamical simulations, focusing on the environments within 1 < D/Mpc < 25 of LG analogs at z = 0. In the simulated sample, there are ∼1000 and ∼12,000 dwarf galaxies within 10 and 25 Mpc, respectively. We compare our results with the 50 Mpc Galaxy Catalog and estimate that current observations are highly incomplete at low masses: for 10 6 ≤ M * /M ⊙ ≤ 10 7 (−13 ≲ M r ≲ −10), we find completeness fractions of ∼23% within 10 Mpc and ∼4% within 25 Mpc. The simulated galaxies below the completeness limits of the observations exist in a range of environments, with notable populations of field dwarfs at all distances and satellites around centrals with masses 10 8 ≲ M * /M ⊙ ≲ 10 11 within 10–25 Mpc. We find that there are ∼8 times more quiescent dwarf galaxies in the TNG50 sample than are currently cataloged. Our results suggest that upcoming observations should uncover a substantial population of dwarf galaxies, and that ≳15% of these will be red, currently quenched galaxies in the field.

Shread, Evangela E. [California Institute of Techn↗

DOE OSTI2025

Multistage economic MPC for systems with a cyclic steady state: A gas network case study

Multistage model predictive control (MPC) provides a robust control strategy for dynamic systems with uncertainties and a setpoint tracking objective. Moreover, extending MPC to minimize an economic cost instead of tracking a pre-calculated optimal setpoint improves controller performance. This paper presents a novel multistage economic nonlinear model predictive control (E-NMPC) framework for dynamic systems operating under uncertainty, with specific application to natural gas transmission networks. A key innovation lies in the integration of cyclic steady-state (CSS) constraints within the multistage MPC formulation, enabling the controller to manage periodic operating conditions commonly observed in energy systems. A Lyapunov-based descent condition is enforced to ensure robust stability of the controller. The multistage economic MPC framework is validated on two gas pipeline case studies, where it successfully minimizes net energy consumption, respects operational constraints under uncertain demand profiles, and guides the network to optimal cyclic operation. The Lyapunov function remains bounded in both case studies, validating the robust stability of multistage E-NMPC.

03 NATURAL GAS↗

DOE OSTI2022

HI-STORM Overpack and MPC-32 Thermal-Hydraulic Model with MOOSE Framework

Nuclear power is a significant source of electricity in the United States, but the average age of nuclear power plants is around 40 years old. The safe management of the spent nuclear fuel (SNF) is a key aspect of the back-end of the nuclear fuel cycle. Spent fuel dry storage systems are becoming a popular and effective solution in this area, given the absence of a final disposal system. The spent fuel cask system (dry cask method) provides a feasible solution to maintain spent fuel for 60 years before final disposal. Dry cask storage has many characteristics that make it attractive. It fulfills the safety requirements of the Nuclear Regulatory Commission (NRC) while providing modularity and flexibility to contractors. The HI-STORM overpack and MPC-32 canister are the main parts of the HI-STORM 100 dry cask storage system. These components remove heat from the system using natural circulation, requiring no human intervention. This is the characteristic that provides passive heat removal and low maintenance features in dry cask storage systems. To develop a thermal model for a dry cask storage system, the physics behind the system should be defined clearly. There are two natural circulation loops in the system; circulation of helium cools down the nuclear assemblies in the MPC, while circulation of air cools down the walls of the MPC. This work aims to develop a thermal model of the MPC-32 canister and HI-STORM overpack using the Multiphysics Object-Oriented Simulation Environment (MOOSE). MOOSE is an open-source framework developed by Idaho National Laboratory (INL) for multiscale, multiphysics simulations. In this study, we will investigate and demonstrate the thermal-hydraulics modeling capabilities of the MOOSE framework, including natural circulation, heat transfer, and porous flow.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Development of a MOOSE thermal model of the MPC-32 canister and HI-STORM overpack

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

A Hybrid Reinforcement Learning-MPC Approach for Distribution System Critical Load Restoration: Preprint

This paper proposes a hybrid control approach for distribution system critical load restoration, combining deep reinforcement learning (RL) and model predictive control (MPC) aiming at maximizing total restored load following an extreme event. RL determines a policy for quantifying operating reserve requirements, thereby hedging against uncertainty, while MPC models grid operations incorporating RL policy actions, i.e., the reserve requirement, renewable (wind and solar) power predictions, and load demand forecasts. We formulate the reserve requirement determination problem as a sequential decision making problem based on the Markov Decision Process (MDP) and design an RL learning environment based on the OpenAI Gym framework and MPC. The RL agent reward and MPC objective function aim to maximize and monotonically increase total restored load and minimize load shedding and renewable power curtailment. The RL algorithm is trained off-line using historical forecast of renewable generation and load demand. The method is tested using a modified IEEE 13-bus distribution test feeder containing wind turbine, photovoltaic, microturbine and battery. Case studies demonstrated that the proposed method outperforms other operating reserve determination methods.

distribution system↗

DOE OSTI2022

A Hybrid Reinforcement Learning-MPC Approach for Distribution System Critical Load Restoration

This paper proposes a hybrid control approach for distribution system critical load restoration, combining deep reinforcement learning (RL) and model predictive control (MPC) aiming at maximizing total restored load following an extreme event. RL determines a policy for quantifying operating reserve requirements, thereby hedging against uncertainty, while MPC models grid operations incorporating RL policy actions (i.e., reserve requirements), renewable (wind and solar) power predictions, and load demand forecasts. We formulate the reserve requirement determination problem as a sequential decision-making problem based on the Markov Decision Process (MDP) and design an RL learning environment based on the OpenAI Gym framework and MPC simulation. The RL agent reward and MPC objective function aim to maximize and monotonically increase total restored load and minimize load shedding and renewable power curtailment. The RL algorithm is trained offline using a historical forecast of renewable generation and load demand. The method is tested using a modified IEEE 13-bus distribution test feeder containing wind turbine, photovoltaic, microturbine, and battery. Case studies demonstrated that the proposed method outperforms other policies with static operating reserves.

distribution system↗

DOE OSTI2024

Practical challenges of model predictive control (MPC) for grid interactive small and medium commercial buildings

To the urgent call for mitigating climate change, substantial initiatives have been undertaken to deploy grid-interactive heating, ventilation, and air-conditioning (HVAC) controls, such as model predictive control (MPC) for buildings. These efforts typically aim to curtail peak energy demand, shift load and enhance overall energy efficiency. With the recent development of low-cost MPC technologies that don’t require extensive instrumentation or manual modeling, small and medium commercial buildings (SMCBs), which rarely utilize advanced HVAC control systems, have become candidates for grid-interactive efficient buildings (GEBs). However, despite the potential benefits and maturity of the technology itself, several practical challenges remain in real-world implementation. In this paper, we share the practical challenges that we have encountered in implementing and testing three types of MPC solutions (ON/OFF unit, dualfuel, and VRF systems) on multiple SMCB sites. We describe the MPC deployment process and discuss the lessons learned. The site selection, eligibility, and retrofit availability (e.g., utility price structure, thermostat communications, etc.) are the main discussion points at the beginning of the project. Also, the modeling automation and the best practices for interacting with endusers and handling erroneous situations are presented for successful operations.

woo Ham, Sang↗

DOE OSTI2022

Site demonstration and performance evaluation of MPC for a large chiller plant with TES for renewable energy integration and grid decarbonization

Thermal energy storage (TES) for a cooling plant is a crucial resource for load flexibility. Traditionally, simple, heuristic control approaches, such as the storage priority control which charges TES during the nighttime and discharges during the daytime, have been widely used in practice, and shown reasonable performance in the past benefiting both the grid and the end-users such as buildings and district energy systems. However, the increasing penetration of renewables changes the situation, exposing the grid to a growing duck curve, which encourages the consumption of more energy in the daytime, and volatile renewable generation which requires dynamic planning. The growing pressure of diminishing greenhouse gas emissions also increases the complexity of cooling TES plant operations as different control strategies may apply to optimize operations for energy cost or carbon emissions. This paper presents a model predictive control (MPC), site demonstration and evaluation results of optimal operation of a chiller plant, TES and behind-meter photovoltaics for a campus-level district cooling system. The MPC was formulated as a mixed-integer linear program for better numerical and control properties. Compared with baseline rule-based controls, the MPC results show reductions of the excess PV power by around 25%, of the greenhouse gas emission by 10%, and of peak electricity demand by 10%.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

The discovery of a radio galaxy of at least 5 Mpc

Context. Giant radio galaxies (GRGs, or colloquially ‘giants’) are the Universe’s largest structures generated by individual galaxies. They comprise synchrotron-radiating active galactic nucleus ejecta and attain cosmological (megaparsec-scale) lengths. However, the main mechanisms that drive their exceptional growth remain poorly understood. Aims. To deduce the main mechanisms that drive a phenomenon, it is usually instructive to study extreme examples. If there exist host galaxy characteristics that are an important cause for GRG growth, then the hosts of the largest GRGs are likely to possess them. Similarly, if there exist particular large-scale environments that are highly conducive to GRG growth, then the largest GRGs are likely to reside in them. For these reasons, we aim to perform a case study of the largest GRG available. Methods. We reprocessed the LOFAR Two-Metre Sky Survey DR2 by subtracting compact sources and performing multi-scale CLEAN de-convolutions at 60" and 90" resolution. The resulting images constitute the most sensitive survey yet for radio galaxy lobes, whose diffuse nature and steep synchrotron spectra have allowed them to evade previous detection attempts at higher resolution and shorter wavelengths. We visually searched these images for GRGs. Results. We have discovered Alcyoneus, a low-excitation radio galaxy with a projected proper length l p = 4.99 ± 0.04 Mpc. Both its jets and lobes are detected at very high significance, and the SDSS-based identification of the host, at spectroscopic redshift z spec = 0.24674 ± 6 × 10 -5 , is unambiguous. The total luminosity density at ν = 144 MHz is L ν = 8 ± 1 × 10 25 W Hz -1 , which is below average, though near median (percentile 45 ± 3%) for GRGs. The host is an elliptical galaxy with a stellar mass M* = 2.4 ± 0.4 × 10 11 M ⊙ and a super-massive black hole mass M• = 4 ± 2 × 10 8 M ⊙ , both of which tend towards the lower end of their respective GRG distributions (percentiles 25 ± 9% and 23 ± 11%). The host resides in a filament of the Cosmic Web. Through a new Bayesian model for radio galaxy lobes in three dimensions, we estimate the pressures in the megaparsec-cubed-scale northern and southern lobes to be P min,1 = 4.8 ± 0.3 × 10 -16 Pa and P min,2 = 4.9 ± 0.6 × 10 -16 Pa, respectively. The corresponding magnetic field strengths are B min,1 = 46 ± 1 pT and B min,2 = 46 ± 3 pT. Conclusions. We have discovered what is in projection the largest known structure made by a single galaxy – a GRG with a projected proper length l p = 4.99 ± 0.04 Mpc. The true proper length is at least l min = 5.04 ± 0.05 Mpc. Beyond geometry, Alcyoneus and its host are suspiciously ordinary: the total low-frequency luminosity density, stellar mass, and super-massive black hole mass are all lower than, though similar to, those of the medial GRG. Thus, very massive galaxies or central black holes are not necessary to grow large giants, and, if the observed state is representative of the source over its lifetime, neither is high radio power. A low-density environment remains a possible explanation. The source resides in a filament of the Cosmic Web, with which it might have significant thermodynamic interaction. The pressures in the lobes are the lowest hitherto found, and Alcyoneus therefore represents the most promising radio galaxy yet to probe the warm–hot inter-galactic medium.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2004

An 80 Mpc Filament of Galaxies at Redshift z=2.38

We present the detection of 34 Lyman-alpha emission-line galaxy candidates in a 80 x 80 x 60 co-moving Mpc region surrounding the known z=2.38 galaxy cluster J2143-4423. We have confirmed 15 of these candidates in followup spectroscopy with 2dF at the AAT. The peak space density is a factor of 4 greater than that found by field samples at similar redshifts. The distribution of these galaxy candidates contains several 5-10 Mpc scale voids. We compare our observations with mock catalogs derived from the VIRGO consortium Lambda-CDM N-body simulations. Fewer than 1\% of the mock catalogues contains voids as large as we observe. Our observations thus tentatively suggest that the galaxy distribution at redshift 2.38 contains larger voids than predicted by current models. The distribution of galaxies suggests a filament or cross-section of a great wall at least 80 x 10 Mpc in transverse extent. Three of the candidate galaxies and one previously discovered galaxy have the large luminosities and extended morphologies of "Lyman-alpha blobs". X-ray properties and physical characteristics of those blobs will be discussed in an accompanying poster by Williger et al.

Woodgate, B.↗

DOE OSTI2026

Field testing and validation of a low-cost MPC for demand flexibility for grid-interactive K-12 schools

K-12 school buildings account for the highest energy consumption within the public sector. Implementing advanced HVAC controls in grid-interactive K-12 schools could bring substantial economic advantages and grid flexibility. Our previous study demonstrated that a low-cost model predictive control (MPC) solution, which coordinates multiple packaged units, can enable demand flexibility without major hardware upgrades. However, a significant gap remains between academic pilots and market-ready scalable solutions. This paper extends the previous single-site pilot to a multi-site demonstration involving three school campuses (95 total units) through a commercial technology transfer process. Addressing the challenge of verifying performance with sparse field data, we present a new statistical approach using Bayesian methods to estimate the MPC’s effect on peak demand. Unlike traditional methods, this approach robustly quantifies uncertainty in non-normal, limited datasets. The results confirm the solution’s replicability, achieving a 21.6–38.9% reduction in HVAC peak demand (10.8–22.1% at the site-level) with > 98% probability across diverse locations. Finally, we document critical barriers to scaling software-as-a-service (SaaS) solutions–such as API instability and diverse legacy systems–and offer practical strategies to accelerate the commercial adoption of grid-interactive efficient buildings.

Ham, Sang Woo↗

DOE OSTI2025

LLM-Based Adaptive Distribution Voltage Regulation Under Frequent Topology Changes: An In-Context MPC Framework

This paper proposes a large language model (LLM) based adaptive inverter control for distribution voltage regulation under frequent topology changes. We leverage the ability of the LLM to perform in-context learning and create a topology-adaptive surrogate model for power flow calculation. The surrogate model is then integrated with a long short-term memory-based load forecaster and a model predictive control (MPC) scheme to achieve the optimal inverter control that adapts to frequent topology changes. Unlike many existing works that assume fixed-topology grids or require the knowledge of all possible topologies when training a model, the proposed in-context MPC method tackles the distribution voltage control problem under various topologies and adapts to unknown topologies with limited data requirement for fine-tuning. The effectiveness of our method is demonstrated on a modified IEEE 123-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

HP-FLEX MPC v0.1.0

HP-FLEX MPC is control software developed by Lawrence Berkeley National Laboratory with support from the California Energy Commission (CEC) through EPIC-19-301. HP-FLEX aims to provide load flexibility for heat pumps (HPs) in response to dynamic grid signals (including Time-of-Use, Dynamic Pricing, and Critical Peak Pricing) while maintaining thermostat temperatures within user-specified bounds. The software includes a system-identification module, which models the dynamics of the building envelope with thermostat data, and a control module based on a model predictive controller (MPC) to make optimal decisions. HP-FLEX receives forecasts of outdoor air temperature, solar irradiation, and internal gain (if available), as well as trajectories of energy price, temperature lower and upper bounds over a prediction horizon. It then optimizes heating and cooling capacities to minimize energy cost and peak power (with a user-defined weight on peak power) over the prediction horizon, while maintaining room air temperature within the temperature constraints, and outputs the optimal thermostat setpoints.

Kim, Donghun↗

DOE OSTI2023

H 0 = 69.8 ± 1.3 km s - 1 Mpc - 1 , Ω m 0 = 0.288 ± 0.017 , and other constraints from lower-redshift, non-CMB, expansion-rate data

Here, we use updated Type Ia Pantheon+ supernova, baryon acoustic oscillation, and Hubble parameter (now also accounting for correlations) data, as well as new reverberation-measured C $\tiny{IV}$ quasar data, and quasar angular size, H $\tiny{II}$ starburst galaxy, reverberation-measured Mg $\tiny{II}$ quasar, and Amati correlated gamma-ray burst data to constrain cosmological parameters. We show that these data sets result in mutually consistent constraints and jointly use them to constrain cosmological parameters in six different spatially-flat and non-flat cosmological models. Our analysis provides summary model independent determinations of two key cosmological parameters: the Hubble constant, H 0 = 69.8 ± 1.3 km s -1 Mpc -1 , and the current non-relativistic matter density parameter, Ω m0 = 0.288 ± 0.017. Our summary error bars are 2.4 and 2.3 times those obtained using the flat ΛCDM model and Planck TT,TE,EE + lowE + lensing cosmic microwave background (CMB) anisotropy data. Our H 0 value is very consistent with that from the local expansion rate based on the Tip of the Red Giant Branch and Type Ia supernova (SN Ia) data, is 2σ lower than that from the local expansion rate based on Cepheid and SN Ia data, and is 2σ higher than that in the flat ΛCDM model based on Planck TT,TE,EE + lowE + lensing CMB data. Our data compilation shows at most mild evidence for non-flat spatial hypersurfaces, but more significant evidence for dark energy dynamics, 2σ or larger in the spatially-flat dynamical dark energy models we study.

79 ASTRONOMY AND ASTROPHYSICS↗