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1,197 records · Page 14

Entanglement properties of SU(2) gauge theory

Understanding how isolated quantum systems thermalize is central to both fundamental physics and the development of quantum technologies. In this Perspective, we present recent and new results on thermalization in nonabelian gauge theory from exact real-time simulations of two-dimensional lattice models. We discuss tests of the eigenstate thermalization hypothesis, entanglement entropy dynamics, the absence of persistent non-thermal states, spectral signatures, and measures of quantum complexity. Our new results include a two-step thermalization process in localized regions and the role of higher gauge field representations. These findings suggest that thermalization in gauge theories may offer a test case for quantum advantage.

information theory and computation

Laser Beam Welding Benchmark Experiments Performed in Reduced Gravity and Vacuum

Laser beam welding (LBW) is affected by the extreme temperatures, reduced pressure, and reduced gravity present in space environments. Gravity and pressure especially influence its melt pool and solidification dynamics. A compact, modular vacuum chamber adaptable to flight platforms from parabolic to orbital currently hosts an experiment to investigate the combined influence of reduced gravity and pressure on LBW. A swappable cartridge contains a rotating platen on which customizable workpieces can be welded under vacuum, greatly increasing experimental throughput. Instrumentation includes weld and thermal cameras observing the process, thermocouples placed on workpieces, accelerometers, and vacuum sensors. Experimental data gathered during the welding process will be combined with post-flight nondestructive evaluation, metallography, and mechanical testing to provide validation datasets for computational modeling. Phase I of this effort involves a parabolic flight campaign in low gravity while an anticipated Phase II would proceed to in-space demonstration to access extended duration microgravity.

in-space welding

Should I stay or should I flow? An exploration of phase‐separated metallosupramolecular liquid crystal polymers

Abstract Dynamic liquid crystalline polymers (dLCPs) incorporate both liquid crystalline mesogens and dynamic bonds into a single polymeric material. These dual functionalities impart order‐dependent thermo‐responsive mechano‐optical properties and enhanced reprocessability/programmability enabling their use as soft actuators, adaptive adhesives, and damping materials. While many previous works studying dynamic LCPs utilize dynamic covalent bonds, metallosupramolecular bonds provide a modular platform where a series of materials can be accessed from a single polymeric feedstock through the variation of the metal ion used. A series of dLCPs were prepared by the addition of metal salts to a telechelic 2,6‐bisbenzimidazolylpyridine (Bip) ligand endcapped LCP to form metallosupramolecular liquid crystal polymers (MSLCPs). The resulting MSLCPs were found to phase separate into hard and soft phases which aids in their mechanical robustness. Variations of the metal salts used to access these materials allowed for control of the thermomechanical, viscoelastic, and adhesive properties with relaxations that can be tailored independently of the mesogenic transition. This work demonstrates that by accessing phase separation through the incorporation of metallosupramolecular moieties, highly processable yet robust MSLCP materials can be realized. This class of materials opens the door to LCPs with bulk flow behavior that can also be utilized as multi‐level adhesives.

Chemistry

Fabrication of Large-Area Metal-on-Carbon Catalytic Condensers for Programmable Catalysis

Catalytic condensers stabilize charge on either side of a high-k dielectric film to modulate the electronic states of a catalytic layer for the electronic control of surface reactions. Here, carbon sputtering provided for fast, large-scale fabrication of metal–carbon catalytic condensers required for industrial application. Carbon films were sputtered on HfO 2 dielectric/p-type Si with different thicknesses (1, 3, 6, and 10 nm), and the enhancement of conductance and capacitance of carbon films was observed upon increasing the carbon thickness following thermal treatment at 400 °C. After Pt deposition on the carbon films, the Pt catalytic condenser exhibited a high capacitance of ∼210 nF/cm 2 that was maintained at a frequency ∼1000 Hz, satisfying the requirement for a dynamic catalyst to implement catalytic resonance. Temperature-programmed desorption of carbon monoxide yielded CO desorption peaks that shifted in temperature with the varying potential applied to the condenser (−6 or +6 V), indicating a shift in the binding energy of carbon monoxide on the Pt condenser surface. A substantial increase in capacitance (∼2000 nF/cm 2 ) of the Pt-on-carbon devices was observed at elevated temperatures of 400 °C that can modulate ∼10% of charge per metal atom when 10 V potential was applied. A large catalytic condenser of 42 cm 2 area Pt/C/HfO 2 /Si exhibited a high capacitance of 9393 nF with a low leakage current/capacitive current ratio (<0.1), demonstrating the practicality and versatility of the facile, large-scale fabrication method for metal–carbon catalytic condensers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

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

Computational simulation of asymmetric phase transformation in cracked Li₇La₃Zr₂O₁₂: Variant selection and chemo-mechanical implications

Coupling between microcracks and phase transformation in ion-conducting ceramics can jointly affect mechanical responses and ion transport. In this work we investigate the cubic-to-tetragonal phase transformation in Li₇La₃Zr₂O₁₂ in the presence of a microcrack under hydrostatic loading and quantify its implications for crack-tip stress concentration and Li-ion transport using phase-field and molecular dynamics simulations. The phase transformation exhibits a strong asymmetry between hydrostatic tension and compression. Under tension, the crack edge nucleates one tetragonal variant that amplifies the crack-tip stress intensity and promotes crack opening. Under compression, the crack tip nucleates a different tetragonal variant that enhances the stress-induced crack-closure tendency. Effective Li diffusivity analysis shows faster transport degradation under compression due to accelerated transformation kinetics, exposing a trade-off between mechanical stability and ionic conductivity. These results highlight the intertwined nature of cracking, phase transformation, and ionic transport in ion-conducting oxides and provide mechanistic insights into chemo-mechanical degradation of solid electrolytes.

36 MATERIALS SCIENCE

Machine Learning for Predicting Team Functioning in HERA Missions

Team functioning is integral to success in future long term space exploration missions. Proactively detecting declines in team functioning can mitigate conflict and ensure mission success. This project developed a speech-based artificial intelligence (AI) system that unobtrusively predicts degradation in team functioning, including performance and cohesion, in the Human Exploration Research Analog (HERA) Campaigns 4 and 5. The AI system conducted automated analysis of the prosodic (tone of voice) and linguistic (language content) components of speech, modeling interpersonal dynamics at both the turn-taking and day-wide levels. We investigated team functioning via observing structured interactions (i.e., multi-mission space exploration vehicle-extra vehicular activity [MMSEV-EVA], team interaction battery [TIB]) and unstructured interactions before the MMSEV-EVA task. We developed machine learning models to predict team functioning (objective task accuracy, self reported team efficacy and self reported team cohesion) by analyzing OpenSmile acoustic features, linguistic descriptors extracted via the linguistic inquiry and word count (LIWC) dictionary, and semantic embeddings. In the TIB, static models using logistic regression and random forests were not able to predict task accuracy, but predicted team efficacy and cohesion during both the decision making and relational tasks to a moderate level (60-70%). Majority voting on the individual turns to predict day long team efficacy further increased accuracies (70-80%). Finally, long short-term memory (LSTM) models showed the best performance across all variables (80-91%), including task performance. In the MMSEV-EVA, static models achieved an accuracy of 60% with majority voting, which increased to 80% through the incorporation of mission day as a variable, accounting for the learning effect. A key finding across both tasks was the "team-dependent" nature of these interactions; models achieved much higher accuracy when trained on prior days of the same team's data rather than attempting to generalize across entirely different teams, with even 1-2 days of prior data per team achieving 5-15% improvement over team-independent models. In addition, the incorporation of pre-task data from the same team also improves model performance, e.g., incorporating data from the decision-making task of the TIB, which preceded the relational task, improved the prediction of team efficacy and cohesion during the latter. We compared model performance when trained on machine-generated data compared to data that had been further corrected by human annotators. Overall, models trained on human-corrected data exhibited a modest improvement in performance, particularly when acoustic features were used. We found no significant correlation between word error rate (WER) and model accuracy (r(55) = -0.08, p = 0.51), but model’s accuracy was significantly higher for medium/high quality transcription (0.74 (SD = 0.48)) compared to the low-quality group (0.64 (SD = 0.36)) (t(63)=2.82, p = 0.006). Based on these, several design recommendation emerge, that could inform Standards at NASA. Models predicting team functioning should incorporate at least one to two days of historical interaction data, include brief pre-task discussions, and explicitly model temporal learning effects, especially for longer operational tasks. Minimum quality standards for automated speech-processing pipelines are needed, given the performance gains observed with manually corrected acoustic data. Finally, systems should leverage both acoustic features and language embeddings in complementary ways, with modality choices and fusion strategies tailored to mission context, task demands, and data quality requirements.

Shrivatsa Mishra

Analysis of Impact Induced Damage and its Effect on Structural Integrity of Space Flight Composite Overwrapped Pressure Vessels

The objective of this research work has been to provide analytical background and support to the ongoing experimental program at NASA, White Sands Test Facility, involving testing composite overwrapped pressure vessels (COPV) for impact damage and cyclic pressurization. Preliminary theoretical basis, including the governing equations for a shallow shell subjected to internal pressure, has been established. Effects of the Griffith type cracks on the structural integrity of the cylindrical vessel were evaluated by methods of Fracture Mechanics. The results indicate that the effective mass of the pressure vessel is an important factor influencing the response to impact events. We also have found that the material properties of the target, contained in the constitutive equations of the composite attached to the Aluminum liner, dominate the impact event in the low velocity range, the material properties become less important, while the target mass distribution and the impactor mass become more significant as the velocity of the impactor increases. Therefore, at high-velocity impact it is not only the kinetic energy of the impactor but also its mass which has a significant effect on the dynamics of the event, and consequently on the induced damage. This work also suggests a methodology for an assessment of the rate of loading effects on the degradation of the material toughness associated with a high-velocity impact where the rate effects become significant. To model the rate dependence of the material response a viscoelastic-plastic constitutive equations were assumed, and on this basis predictions are made regarding the rate dependent material resistance curve. Other dynamic phenomena associated with the impact event have been treated in the framework of the Computational Mechanics using the courtesy of Prof. P. Guebelle and his graduate student at University of Illinois at Urbana-Champaign who have an access to a super-fast computer located on their campus. Finally, the guidelines for a follow-up research program are provided in the body of this report. They address three major areas: theoretical research, numerical studies, and further experimental work.

Michael P Wnuk

Optical transparency of LiF (100) shock compressed to ∼360 GPa

High-purity [100] lithium fluoride (LiF) is the most widely used optical window in dynamic compression experiments due to its wide bandgap and well-characterized mechanical response. Recent plate-impact experiments established the [100] LiF Hugoniot to ∼230 GPa and demonstrated shock-induced melting onset at 182 GPa with complete melting by 195 GPa; theoretical models predict LiF optical transparency to nearly 900 GPa. To experimentally examine the optical transparency of [100] LiF at higher pressures and in the liquid state, laser-driven shock experiments were performed at peak stresses ranging from 223 to 363 GPa. Optical response was examined by measuring the particle velocity histories at the Kapton/LiF interface using laser interferometry at 532 and 1550 nm wavelengths; in-material particle velocities were obtained using established refractive-index corrections. Continuous photonic Doppler velocimetry fringes were observed across the entire stress range, demonstrating that LiF remains transparent to 1550 nm light throughout the multi-megabar regime investigated. At 532 nm, fringe visibility depended on the reflector coating: aluminum mirrors provided signals to ∼235 GPa, while gold mirrors extended this limit to 270.5 GPa, indicating that the shorter-wavelength response is likely sensitive to experimental configuration rather than to the loss of LiF transparency. Continued optical transparency to at least 360 GPa indicates that shock-melted LiF does not display bandgap closure over the stress range explored. Furthermore, these results provide direct experimental constraints on the high-pressure optical response and establish LiF (100) as a robust optical window material for laser-driven dynamic compression experiments approaching 400 GPa.

Renganathan, P. [Argonne National Laboratory (ANL)

Explainable machine learning reveals that local structural motifs encode the thermodynamic state across the CuZr metallic glass-forming range

Metallic glasses derive their properties from the statistics of local atomic motifs rather than from long-range order, yet a quantitative, chemistry-specific link between motif populations and the underlying glassy state has remained elusive. In this work we combine large-scale molecular dynamics, Voronoi tessellation, deep neural networks, and SHapley Additive exPlanations (SHAP) to identify which local structural motifs define the glassy state of Cu—Zr metallic glasses. A dataset of 17,180 atomistic configurations spanning ten compositions (Cu 20 Zr 80 –Cu 80 Zr 20 ) and four quench rates (10 9 –10 12 K/s) is used to train a feed-forward neural network that regresses temperature across the 50–2000 K liquid–supercooled–glass range, achieving a mean absolute error of 19.89 K and R 2 = 0.9974, confirming that the local structural state is faithfully encoded in motif-level structure. SHAP analysis then reveals that a tightly coupled near-icosahedral family of motifs (coordination numbers (CN) 11–13, including the full icosahedron 001200 and its single-atom-perturbation sibling 10930) collectively encodes the thermodynamic state of the system across the full glass-forming range. The CN = 11–13 ordered members carry negative SHAP values at high populations, tracking the most deeply-quenched configurations, while 10930 shows the reversed signature consistent with its role as a soft-spot host whose population shrinks as the icosahedral network deepens. The analysis demonstrates that explainable machine learning can isolate the minimal motif vocabulary defining the glassy state and recovers the near-icosahedral building blocks previously identified by data-driven analyses of Cu—Zr. The approach provides a general, chemistry-specific route for characterizing the structural state of disordered materials.

36 MATERIALS SCIENCE

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

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.

Secondary Flows

Riddles About the Origin and Thermal History of the Moon

Analyses of lunar rocks have confirmed that the interior of the Moon has been subjected to magmatic differentiation, as has been determined by calculation of the thermal history of the Moon. However, it appears that differentiation occurred so early that it could not have been related to heating by long-lived radioactive elements, but rather indicates a high initial temperature of the Moon. The reasons for the high initial temperature remain unknown. The presence of a central, partially melted area revealed by seismic observations forces us to reject convective models of the Moon, while the dimensions of this area, together with the measured heat fluxes from the interior, serve as "boundary conditions" for any new calculations of the thermal history for a two-layered differentiated model of the Moon operative over the past 3.5 billion years. If we start with the early differentiation of the Moon and the high content of long-lived radioactive elements in it, explanation of its current thermal properties represents no difficulty. But these prerequisites themselves remain unexplained. Due to the continuing controversy concerning the true nature of the process of magmatic differentiation of the Moon, estimation of the composition of the entire Moon on the basis of analyses of surface rock remains unreliable, and use of these estimates to clarify the origin of the Moon is premature. Existing hypotheses concerning the origin of the Moon encounter dynamic difficulties, as well as difficulties with explanation of the high initial temperature, to say nothing of the difficulty involved in explaining the proposed differences in the composition of the Earth and Moon.

B Yu Levin

Development of a Digital Twin for Electrified Aircraft Powertrain Health Management

The augmentation of aircraft powertrains with electrical power systems is a promising path to reducing aircraft fuel consumption, emissions, and noise. Like conventional propulsion systems, electrified aircraft propulsion (EAP) systems will be subject to wear and tear throughout their lifecycles. System health management for EAP will enable efficient flight and maintenance scheduling, realizing economic, safety, and reliability benefits. A digital twin is, broadly, a dynamically updated virtual representation of an individual physical asset. This paper presents a Kalman filter-based approach for the development of a digital twin for an electrified powertrain and applies the approach to an EAP controls testbed. Measurements from nominal testbed operations are used to update a nonlinear model of the testbed. A Kalman filter is then created and used to identify and isolate anomalous testbed behavior based on measurements from off- nominal operations. Results show that the Kalman filter-based digital twin can monitor individual powertrain components’ health for degradation or other changes in performance. The applicability of the presented digital twin approach to any hybrid- or fully-electrified powertrain is emphasized.

Electrified Aircraft Propulsion

Oceanic fronts shape hemispheric contrasts in polar stratospheric extremes

Sudden Stratospheric Warmings (SSWs) and Polar Stratospheric Clouds (PSCs) exhibit striking inter-hemispheric asymmetries: SSWs are frequent in the Arctic but rare in the Antarctic, while PSCs are more persistent in the Antarctic. Although land–sea thermal contrast and orography (LSCO) have been traditionally invoked to explain these asymmetries, here we show using semi-idealized model experiments that even though LSCO strongly impacts the mean state of SSWs and PSCs, it alone cannot fully account for the observed differences. Using model experiments, we reveal that midlatitude oceanic sea surface temperature (SST) fronts represent a crucial supporting additional driver of the hemispheric stratospheric differences. Like LSCO, SST fronts enhance stratospheric convergence of resolved waves, strengthening the Brewer–Dobson Circulation and inducing high-latitude adiabatic warming. This warming significantly enhances Arctic SSW frequency and strongly suppresses PSC formation. Sub-grid-scale non–resolved wave forcing modulates the stratospheric resolved waves effect. The oceanic impact is dominated by North Pacific SST fronts. Our results highlight the indispensable role of SST fronts in shaping Arctic–Antarctic asymmetries in stratospheric dynamics and associated extremes.

Omrani, Nour-Eddine [Univ. of Bergen (Norway)] (OR

Capturing Secondary Kinetic Instabilities in Three‐Dimensional Dayside Reconnection Using an Improved Gradient‐Based Closure

Magnetic reconnection is a highly dynamic process that excites a wide variety of kinetic waves and instabilities. Transverse current sheet instabilities such as the lower-hybrid drift and secondary drift-kink instabilities in particular have been shown by kinetic simulations to modify the reconnection and introduce significant turbulence and mixing to the reconnection layer. Past studies using the ten-moment fluid model to capture important kinetic physics such as the electron inertia and full representation of the pressure tensor proved advantageous to a two-fluid representation of reconnection, but the model struggled when using a local relaxation closure for the heat flux to replicate the current sheet instabilities and subsequent mixing seen in kinetic simulations. This work uses the Gkeyll software framework to perform simulations of asymmetric reconnection based on the 16 October 2015 MMS crossing of a diffusion region, the Burch event. An improved gradient-based heat flux closure is implemented, showing significant improvement in secondary kinetic instabilities that grow in the current sheet. These instabilities generate turbulence which leads to growth of secondary magnetic islands and flux ropes.

Bradshaw, K. [Princeton University, NJ (United Sta

Sierra/SD - Users Manual - 5.32

Sierra/SD provides a massively parallel implementation of structural dynamics finite element analysis, required for high-fidelity, validated models used in modal, vibration, static and shock analysis. This document provides a user's guide to the input for Sierra/SD. Details of input specifications for the different solution types, output options, element types and parameters are included.

Beale, Dagny Marie [Sandia National Laboratories (

Quantifying System Strength From Grid-Forming Resources Using Frequency Scan Approach: Preprint

Current industry practices for quantifying the system strength contribution from grid-forming (GFM) resources to ensure stability of power systems dominated by inverter-based resources (IBRs) are primarily based on iterative electromagnetic transient (EMT) time-domain simulation studies. While feasible, these approaches are resource-intensive, lack scalability and intuition, and might not evaluate the system strength contribution over the entire frequency range of interest. This paper introduces a novel, frequency-domain approach to quantify system strength support provided by a GFM resource using frequency scans. The proposed method uses transfer functions from the grid voltage magnitude (V) and phase (?), respectively, to the reactive (Q) and active power (P) output of a GFM resource for quantifying its contribution to system strength. These transfer functions provide a direct measure of the ability of a GFM resource to behave as a stiff voltage source behind a reactance over a specified frequency range, enabling robust quantification of its system strength contribution. The key innovation of this work is the development of a frequency domain system strength metric called the dynamic short-circuit ratio (dSCR) that is suitable for IBR-dominated power systems and is directly related with the familiar short circuit ratio (SCR) metric. The new metric, dSCR, enables the assessment of system strength contributions from both synchronous machines and converter-based GFM resources using a unified benchmark, which is not possible with the traditional SCR metric. The paper also demonstrates how impedance scans could identify if an unstable condition observed during weak grid conditions is a result of the lack active or reactive power support or both. By leveraging the proposed frequency-domain dSCR metric for quantifying system strength contribution from GFM IBRs, the paper demonstrates targeted mitigation strategies for weak grid instabilities without resorting to repeated, time-consuming time-domain simulations. The result is a scalable and efficient approach to remediate stability challenges in power systems with high shares of IBRs and accelerating the integration of GFM technologies for system strength support in power systems.

24 POWER TRANSMISSION AND DISTRIBUTION

Machine learning the electric field response of condensed phase systems using perturbed neural network potentials

Abstract The interaction of condensed phase systems with external electric fields is of major importance in a myriad of processes in nature and technology, ranging from the field-directed motion of cells (galvanotaxis), to geochemistry and the formation of ice phases on planets, to field-directed chemical catalysis and energy storage and conversion systems including supercapacitors, batteries and solar cells. Molecular simulation in the presence of electric fields would give important atomistic insight into these processes but applications of the most accurate methods such as ab-initio molecular dynamics (AIMD) are limited in scope by their computational expense. Here we introduce Perturbed Neural Network Potential Molecular Dynamics (PNNP MD) to push back the accessible time and length scales of such simulations. We demonstrate that important dielectric properties of liquid water including the field-induced relaxation dynamics, the dielectric constant and the field-dependent IR spectrum can be machine learned up to surprisingly high field strengths of about 0.2 V Å −1 without loss in accuracy when compared to ab-initio molecular dynamics. This is remarkable because, in contrast to most previous approaches, the two neural networks on which PNNP MD is based are exclusively trained on molecular configurations sampled from zero-field MD simulations, demonstrating that the networks not only interpolate but also reliably extrapolate the field response. PNNP MD is based on rigorous theory yet it is simple, general, modular, and systematically improvable allowing us to obtain atomistic insight into the interaction of a wide range of condensed phase systems with external electric fields.

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