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NASA NTRSDate not supplied

Validation of Accurate Cryogenic Fluid Vapor-Liquid Boundary Conditions Via Molecular Simulations

Vapor-liquid interfaces drive many important phenomena in cryogenic fluid management, including heat transfer, evaporation, and capillary flow. Design of cryogenic fluid systems, such as propellant storage, requires accurate predictions of fluid behavior, including evaporation rates. Many models have been proposed for heat and mass transfer at vapor liquid interfaces, but the accuracy of these models in the context of cryogenic fluids has not been performed. We use molecular dynamics simulations, which allow for nanometer scale resolution of fluid phenomena, to evaluate the accuracy of a variety of vapor-liquid boundary conditions at evaporating and condensing interfaces. We find that an anisotropic temperature distribution is a critical ingredient for accurate prediction of intensive evaporation and condensation.

Daniel Vigil↗

NASA NTRS1995

Reliability Analysis of Single Crystal NiAl Turbine Blades

As part of a co-operative agreement with General Electric Aircraft Engines (GEAE), NASA LeRC is modifying and validating the Ceramic Analysis and Reliability Evaluation of Structures algorithm for use in design of components made of high strength NiAl based intermetallic materials. NiAl single crystal alloys are being actively investigated by GEAE as a replacement for Ni-based single crystal superalloys for use in high pressure turbine blades and vanes. The driving force for this research lies in the numerous property advantages offered by NiAl alloys over their superalloy counterparts. These include a reduction of density by as much as a third without significantly sacrificing strength, higher melting point, greater thermal conductivity, better oxidation resistance, and a better response to thermal barrier coatings. The current drawback to high strength NiAl single crystals is their limited ductility. Consequently, significant efforts including the work agreement with GEAE are underway to develop testing and design methodologies for these materials. The approach to validation and component analysis involves the following steps: determination of the statistical nature and source of fracture in a high strength, NiAl single crystal turbine blade material; measurement of the failure strength envelope of the material; coding of statistically based reliability models; verification of the code and model; and modeling of turbine blades and vanes for rig testing.

Joseph Palko↗

NASA NTRSDate not supplied

NASA Space Launch System Artemis I & II Post Flight Ascent Aerothermal Environments Overview

Since 2011 the Aerosciences Branch/EV33 at NASA Marshall Space Flight Center has been involved with the development of ascent external aerothermal environments for the NASA Space Launch System (SLS) Block 1 launch vehicle for the purposes of supporting thermal analysis and the design of thermal protection systems. The SLS Block 1 Artemis I and II launch vehicles successfully launched from Pad39B at NASA Kennedy Space Center on November 16th, 2022 and April 1st, 2026, respectively. Over 70 aerothermal islands, consisting of over 265 operational instruments captured aerodynamic heating and plume induced environments throughout the launch vehicles. Gauges consisted of calorimeters, radiometers, gas temperature probes, pressure transducers, bi-directional pressure probes and thermocouples. Prior to launch, aerothermal design environment models were generated to predict ascent aerodynamic heating and plume induced environments over a design space that covered a range of vehicle trajectories that varied atmospheric, vehicle performance, and off-nominal, engine-out conditions. Post flight reconstruction models were developed for each flight island using the Day-of-Launch (DOL) Best Equivalent Trajectory (BET) that provided freestream conditions and propulsion system boundary conditions. This paper discusses a summary of the ascent aerothermal environments observed during the flights and the respective modelling approaches and the performance of them through comparisons of flight data and predictions.

aerothermodynamics↗

DOE OSTI2026

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↗

NASA NTRS2026

Petermann Glacier on the Brink: Progress, Challenges and Insights

Petermann Glacier, the largest marine-terminating glacier in northern Greenland based on catchment area and ice discharge, plays a key role in regulating ice discharge from the Greenland Ice Sheet into the Arctic Ocean. With an upstream catchment connected to the ice sheet interior via a deep subglacial canyon, its future stability has major implications for sea level rise. In this review, we synthesize recent advances in understanding Petermann’s dynamics across three critical interfaces: the ice–ocean, ice–atmosphere, and ice–bed boundaries. At the surface, observations show that reanalysis products underestimate air temperatures and melt, while regional climate models diverge significantly in their estimates of surface mass balance, underscoring the need for improved in situ data and models. At the ocean boundary, enhanced basal melting driven by both subglacial runoff and Atlantic water intrusions is identified as the dominant driver of recent mass loss of Petermann Glacier, with continued warming posing a serious threat to the stability of the floating tongue. At the bed, new geophysical synthesis reveals complex geology, likely spatial variability in geothermal heat flux, and the influence of the megacanyon on seasonal hydrology and velocity fluctuations. Petermann’s mass balance has been negative in recent decades without corresponding flow acceleration. However, the glacier has undergone significant calving events, and the current rifting that began in September 2025 highlights its vulnerability. This upcoming calving event underscores the timeliness of this review, as it will put Petermann Glacier’s terminus at its most retreated position since records began in 1923. The anticipated retreat of the ice tongue also reduces buttressing and brings the terminus closer to the grounding zone, and modeling studies suggest that calving within 12 km of the grounding zone could potentially trigger dynamic retreat, accelerating ice discharge, and a doubling of flow speeds. We conclude that improved observations, sustained monitoring of oceanographic and atmospheric properties, and high-resolution modeling are critical to constraining projections of Petermann Glacier’s future and its role in the stability of the Greenland Ice Sheet.

Dominik Fahrner↗

DOE OSTI2026

The impact of aerosol mixing state on immersion freezing: insights from classical nucleation theory and particle-resolved simulations

Immersion freezing, initiated by ice-nucleating particles (INPs) in supercooled aqueous droplets, plays an important role in the formation of ice crystals within clouds. The efficiency of immersion freezing depends strongly on INP composition and, crucially, on the mixing state – how chemical species are distributed across the particle population. Here, we quantify the impact of aerosol mixing state on immersion freezing using a combined theoretical and particle-resolved modeling approach. We derive analytical expressions for the frozen fraction of internally and externally mixed INP populations based on classical nucleation theory, showing that the frozen fraction is sensitive to whether ice-active species are present in all particles or only in a subset of the population. We introduce a multi-species immersion freezing scheme into the particle-resolved model PartMC, using the water activity-based immersion freezing model (ABIFM) to compute freezing probabilities for mixed-composition particles. To improve computational efficiency, we implement a Binned Tau-Leaping algorithm and demonstrate an order-of-magnitude speedup with minimal accuracy loss. Simulations reproduce the analytical trends in limiting cases and extend the analysis to more general aerosol populations, where mixing state continues to exert a substantial control on frozen fraction. Sensitivity analyses across particle size, species type, and cooling condition reveal that the mixing state effect is most pronounced when small amounts of highly efficient INPs are mixed with less efficient materials. These findings underscore the need to represent aerosol mixing state explicitly in models of heterogeneous ice nucleation to reduce uncertainty in cloud-phase partitioning.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1985

Nickel-cadmium Battery Cell Reversal from Resistive Network Effects

During the individual cell short-down procedures often used for storing or reconditioning nickel-cadmium (Ni-Cd) batteries, it is possible for significant reversal of the lowest capacity cells to occur. The reversal is caused by the finite resistance of the common current-carrying leads in the resistive network that is generally used during short-down. A model is developed to evaluate the extent of such a reversal in any specific battery, and the model is verified by means of data from the short-down of a f-cell, 3.5-Ah battery. Computer simulations of short-down on a variety of battery configurations indicate the desirability of controlling capacity imbalances arising from cell configuration and battery management, limiting variability in the short-down resistors, minimizing lead resistances, and optimizing lead configurations.

Zimmerman, A. H.↗

NASA NTRSDate not supplied

A GPU-based Approach for Turbomachinery Application

Accurate modeling of coolant airflows, which form protective films over turbine blades, is essential for designing fuel-efficient and environmentally sustainable gas turbine engines. Excessive coolant reduces thermal efficiency, while insufficient coolant leads to blade overheating and causes damage. Therefore, precise prediction of flow field interactions with cooling air is critical for optimizing turbine performance. This study numerically investigates the cooling effectiveness of purge and film cooling flows within a high-pressure turbine (HPT) rotor using Large Eddy Simulation (LES). The study utilizes NASA Glenn Research Center’s Glenn-HT solver. The simulation models ethe conditions of the Penn State University START rotating rig. A high-fidelity structured mesh comprising up to 800 million cells is employed to resolve high-Reynolds number flow (Re ≈ 350,000) and to capture intricate secondary flow structures, including tip leakage and purge-induced vortices. Film cooling effectiveness computations are highly sensitive to boundary conditions at the cooling holes and to grid resolution. Even with well-resolved grids and included plena, strong mixing challenges traditional eddy viscosity models. To address this, a simplified configuration is simulated: a truncated row of shaped holes on the suction side near the leading edge and a row on the pressure side, both fed from internal plena while the purge slot and tip clearance are also modeled. Two isothermal LES cases are conducted at two distinct wall temperatures, which yield the adiabatic wall temperature and the heat transfer coefficient. The definition and means of computation of the effectiveness is discussed in this paper. The simulations reveal detailed three-dimensional unsteady flow features, including coherent vortical structures and secondary flows originating from the purge cavity. Film cooling effectiveness and Nusselt number distributions are presented for both the blade surface and tip, highlighting regions of elevated heat transfer and complex thermal behavior. These findings underscore the importance of high-resolution LES and realistic boundary conditions in capturing the dynamics of purge and film cooling, offering valuable insights for improving turbine blade design and thermal management strategies.

Gas Turbine↗

DOE OSTI2026

Dark Energy Survey year 6 results: Magnification modeling and its impact on galaxy clustering and galaxy-galaxy lensing cosmology

Gravitational lensing magnification alters the observed spatial distribution of galaxies and must be accounted for to prevent biases in cosmological probes of the large-scale structure. We investigate its effects on the Dark Energy Survey Year 6 galaxy clustering and galaxy-galaxy lensing analyses using the fiducial lens (position tracer) sample M ag L im++. Magnification bias is parameterized by a coefficient that describes the response of the number of selected objects per unlensed area element to a change in the lensing convergence. We quantify this coefficient using the BALROG synthetic source injection catalog to account for the complexity of the selection function, and compare these results with simplified estimates. The resulting values of the magnification coefficients for each redshift bin are [3.16 ± 0.08, 2.76 ± 0.21, 4.09 ± 0.15, 4.42 ± 0.16, 4.90 ± 0.29, 4.83 ± 0.25]. Relative to Year 3, this analysis provides more precise and accurate magnification bias estimates through a larger BALROG area and reweighting to better match the data properties. Here, the cosmological results are robust when tested against various magnification parameter prior choices and also when adding cross-clustering between lens redshift bins. Neglecting magnification, however, introduces significant systematic shifts: relative to the fiducial analysis with Gaussian priors centered on the BALROG -derived estimates, we observe shifts of 1.37σ in S 8 and -0.84σ in Ω m (with cosmic shear included: -0.61σ in S 8 and -0.71σ in Ω m ), in agreement with findings from simulated data, demonstrating that magnification must be modeled to avoid biases. Freeing the magnification bias in lens bin 2 leads to unphysical negative values, further justifying its exclusion from the fiducial Year 6 analysis.

Cosmological parameters↗

DOE OSTI2024

Collective excitations and low-energy ionization signatures of relativistic particles in silicon detectors

Abstract Solid-state detectors with a low energy threshold have several applications, including searches of non-relativistic halo dark-matter particles with sub-GeV masses. When searching for relativistic, beyond-the-Standard-Model particles with enhanced cross sections for small energy transfers, a small detector with a low energy threshold may have better sensitivity than a larger detector with a higher energy threshold. In this paper, we calculate the low-energy ionization spectrum from high-velocity particles scattering in a dielectric material. We consider the full material response including the excitation of bulk plasmons. We generalize the energy-loss function to relativistic kinematics, and benchmark existing tools used for halo dark-matter scattering against electron energy-loss spectroscopy data. Compared to calculations commonly used in the literature, such as the Photo-Absorption-Ionization model or the free-electron model, including collective effects shifts the recoil ionization spectrum towards higher energies, typically peaking around 4–6 electron-hole pairs. We apply our results to the three benchmark examples: millicharged particles produced in a beam, neutrinos with a magnetic dipole moment produced in a reactor, and upscattered dark-matter particles. Our results show that the proper inclusion of collective effects typically enhances a detector’s sensitivity to these particles, since detector backgrounds, such as dark counts, peak at lower energies.

Physics↗

NASA NTRS1977

Heat Flow and Thermal History of the Moon

An analysis was made of current heat flow data and thermal models of lunar evolution which satisfy the diverse information that has accumulated on internal processes.

Ye A Lyubimova↗

NASA NTRSDate not supplied

LES-Based Analysis of Film Cooling in a High-Pressure Turbine Rotor Including Effects of Purge and Tip Flow

Secondary Flows↗

NASA NTRS2026

LAI Assimilation Schedules to Constrain Uncertain Cultivars and Soils in CERES-Maize

In anticipation of large-domain crop model applications where precise local configuration and calibration is not possible, we describe benefits and potential drawbacks of employing a crop pest module to achieve leaf area index (LAI) assimilation into a high performing CERES-Maize crop model configuration at a field experiment site in Perry, Iowa. Simulation experiments explore the use of MODIS satellite-derived LAI to constrain and adjust LAI to counter imprecise cultivar and soil configurations often occurring in the absence of high-quality local information. Simulations using single-day, window, and continuous LAI replacement across 5 cultivars and 2 soil calibration approaches for nine corn rotation years from 2004 to 2020 led to different yield outcomes and reverberations throughout the field environment. Evaluating variance and mean bias, results indicate minimal interventions in early vegetative and grain-filling stages were more beneficial than use of continuous LAI adjustments, as they minimized disruptions to the internal resource balances governing plant stresses and grain production. LAI adjustment was particularly helpful in constraining growth related to uncertain thermal unit requirements and leaf tip appearance rates (P1 and PHINT cultivar parameters, respectively). Findings underscore the need to assimilate additional state variables to ensure internal biophysical coherence. This approach shows promise for applications spanning wider domains with prediction time pressure where detailed configuration, more complex assimilation methods, or recalibration of crop model parameters may not be practical.

Phenology↗

NASA NTRS2026

A Summary of Test and Analysis Results from a Second Lift+Cruise Full-Scale Drop Test

The realization of advanced air mobility markets is enabling new forms of transportation to take shape in the United States and around the world. Though currently in development, as these markets mature, new types of vertical take-off and landing (VTOL) vehicles have been undergoing development for use. There are many factors which must be addressed prior to these types of vehicles becoming viable alternative forms of transportation in these markets. These factors include incorporation into the existing airspaces, the logistics of operating in urban environments, along with numerous factors associated with safety and reliability. To address some of the safety aspects associated with the development of these new types of vehicles, NASA has been conducting research into the performance of an example electric VTOL (eVTOL) aircraft as a part of the Revolutionary Vertical Lift Technology (RVLT) project. Over the course of this research, many aspects including the development of energy absorbing components, the evaluation of seating systems, the development of advanced finite element material model systems and the acquisition of full-scale vehicle impact data were investigated. The report will discuss aspects related to the acquisition of full-scale vehicle data which occurred in the form of a full-scale impact test conducted in the Summer of 2025. This test was on a NASA designed Lift+Cruise composite cabin test article and represented a partial capstone in the entirety of previous eVTOL research conducted for the project. In this test, a variety of experiments were included in order to investigate the effect of a full-scale environment on the experiment results. In parallel, the development of a computational impact model to simulate the full-scale test will be discussed in this report. A model of the Lift+Cruise test article was developed utilizing data collected from previous sub- and full-scale test data and then simulated in the current test environment. The model development, its use in pre-test predictions, and its use in post-test correlation will all be presented. This report will present the test data acquired from the Lift+Cruise test and document several of the results obtained. One intended result is to determine the effect of a complex full-scale crash impact on the identification of occupant injury risk within seat and vehicle designs. A second intended result is to determine whether high-fidelity models can be used with some confidence in the prediction of test events and can allow for additional test cases to be simulated without the need of having to conduct additional tests. The overall goal of the test is to provide the community with data that can be used for design, development or certification efforts, along with providing data on what an example eVTOL crash incident could entail.

energy storage systems↗

DOE OSTI2024

Phonon screening and dissociation of excitons at finite temperatures from first principles

The properties of excitons, or correlated electron–hole pairs, are of paramount importance to optoelectronic applications of materials. A central component of exciton physics is the electron–hole interaction, which is commonly treated as screened solely by electrons within a material. However, nuclear motion can screen this Coulomb interaction as well, with several recent studies developing model approaches for approximating the phonon screening of excitonic properties. While these model approaches tend to improve agreement with experiment, they rely on several approximations that restrict their applicability to a wide range of materials, and thus far they have neglected the effect of finite temperatures. Here, we develop a fully first-principles, parameter-free approach to compute the temperature-dependent effects of phonon screening within the ab initio GW -Bethe–Salpeter equation framework. We recover previously proposed models of phonon screening as well-defined limits of our general framework, and discuss their validity by comparing them against our first-principles results. We develop an efficient computational workflow and apply it to a diverse set of semiconductors, specifically AlN, CdS, GaN, MgO, and SrTiO 3 . We demonstrate under different physical scenarios how excitons may be screened by multiple polar optical or acoustic phonons, how their binding energies can exhibit strong temperature dependence, and the ultrafast timescales on which they dissociate into free electron–hole pairs.

Science & Technology - Other Topics↗

DOE OSTI2024

A novel digital lifecycle for Material‐Process‐Microstructure‐Performance relationships of thermoplastic olefins foams manufactured via supercritical fluid assisted foam injection molding

Abstract This research significantly enhances the applicability of thermoplastic olefins (TPOs) in the automotive industry using supercritical N 2 as a physical foaming agent, effectively addressing the limitations of traditional chemical agents. It merges experimental results with simulations to establish detailed material‐process‐microstructure‐performance (MP2) relationships, targeting 5–20% weight reductions. This innovative approach labeled digital lifecycle (DLC) helps accurately predict tensile, flexural, and impact properties based on the foam microstructure, along with experimentally demonstrating improved paintability. The study combines process simulations with finite element models to develop a comprehensive digital model for accurately predicting mechanical properties. Our findings demonstrate a strong correlation between simulated and experimental data, with about a 5% error across various weight reduction targets, marking significant improvements over existing analytical models. This research highlights the efficacy of physical foaming agents in TPO enhancement and emphasizes the importance of integrating experimental and simulation methods to capture the underlying foaming mechanism to establish material‐process‐microstructure‐performance (MP2) relationships. Highlights Establishes a material‐process‐microstructure‐performance (MP2) for TPO foams Sustainably produces TPO foams using supercritical (ScF) N 2 with 20% lightweighting Shows enhanced paintability for TPO foam improved surface aesthetics Digital lifecycle (DLC) that predicts both foam microstructure and properties DLC maps process effects & microstructure onto FEA mesh for precise prediction

Engineering↗

DOE OSTI2026

Upper ocean mixing, surface heat fluxes, and heat content variability in the upper 150 m during Hurricane Laura (2020)

Observations (from thermistor sensors and a hurricane glider) and model-based temperature were used to answer questions including the following: 1) What physical and environmental conditions explain the rapid intensification of Hurricane Laura? 2) How did the pre-existing warm mixed layer at Stone mooring (StM) influence the degree of cooling in the mixed layer? 3) How did vertical mixing, surface heat fluxes, and advective processes collectively shape the mixed layer heat evolution at StM? Observations measured by thermistor sensors showed that Hurricane Laura induced a cooling of -1.2oC in the mixed layer when Hurricane Laura’s wind speed increased to 47 m/s on 26 August. This contrasts with the -1.04oC mixed layer temperature change estimated from model-based temperature. At StM, the presence of a 31oC warm mixed layer and elevated heat content (60-80kJ/cm2) effectively preconditioned the upper ocean ahead of Hurricane Laura’s passage. After Hurricane Laura passed, turbulent mixing associated with the storm transported the heat anomalies downward into subsurface layers. In addition, this study shows that a surface heat flux of 5.04 kJ/cm2 supported the intensity of Hurricane Laura as it traversed over the StM. Using a mixed layer heat balance model, this study shows that entrainment flux and surface flux mostly contributed to the observed change in the mixed layer temperature.

Tsai, Senam↗

DOE OSTI2024

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗