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High-Throughput Screening of Strong Electron–Phonon Couplings in Ternary Metal Diborides

Here, we perform a high-throughput screening on phonon-mediated superconductivity in a ternary metal diboride structure with alkali, alkaline earth, and transition metals. We find 17 ground states and 78 low-energy metastable phases. From fast calculations of zone-center electron–phonon coupling, 43 compounds are revealed to show electron–phonon coupling strength higher than that of MgB 2 . An anticorrelation between the energetic stability and electron–phonon coupling strength is identified. We suggest two phases, i.e., Li 3 ZrB 8 and Ca 3 YB 8 , to be synthesized, which show reasonable energetic stability and superconducting critical temperature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

L-phase variants of Agromyces ramosus

Earlier results suggested that Agromyces ramosus possibly might exist naturally in soil as a cell-wall-defective form. The purpose of the present study was to test this hypothesis by determining whether the laboratory-adapted strains of A. ramosus could be artificially induced into the L-phase and, if so, to examine some parameters affecting induction and the stability of the L-forms. The hypothesis was also tested by attempting to revert the laboratory L-phase strains by subjecting them to the technique originally used for isolation of the bacterial form from soil. It is shown that A. ramosus is easily induced into the L-phase by growing it on an agar media containing low levels of penicillin or glycine. The L-forms are found to be stable after initial contact with the inducing agent and to be unable to be reverted to the bacterial form. However, this lack of reversion does not completely negate the hypothesis that L-forms might occur in nature, because it is possible that L-forms existing in the natural state are less stable than those found in the laboratory where there is little selective pressure toward reversion.

Horwitz, A. H.↗

Benchmark microgravity experiments and computations for 3D dendritic-array stability in directional solidification

In this study, we present a comprehensive quantitative analysis of stability bands for dendritic arrays during directional solidification of a transparent succinonitrile-0.46 wt % camphor alloy, spanning a broad range of pulling velocities. Taking advantage of the microgravity environment aboard the International Space Station where most convection effects are suppressed, we obtain unique measurements that quantify the stable primary spacing range of spatially extended three-dimensional dendritic array structures under purely diffusive growth conditions. Through carefully designed velocity jump experiments and detailed examination of sub-grain boundary dynamics, we characterize key instabilities, including elimination and tertiary branching, shedding new light on the mechanisms governing dynamic dendritic spacing selection in extended 3D arrays. Phase field simulations are performed to characterize the stability limits of dendritic array structures for quantitative comparison with the flight experiments. Although the simulations capture general trends, significant deviations are noted at the upper stability boundary, indicating the influence of additional, unexplored factors. These findings contribute to a deeper understanding of dendritic growth dynamics and offer valuable benchmark data that could aid in refining predictive models and improving control of dendritic microstructures in metallurgical applications.

36 MATERIALS SCIENCE↗

Flight Test of an Intelligent Flight-Control System

The F-15 Advanced Controls Technology for Integrated Vehicles (ACTIVE) airplane (see figure) was the test bed for a flight test of an intelligent flight control system (IFCS). This IFCS utilizes a neural network to determine critical stability and control derivatives for a control law, the real-time gains of which are computed by an algorithm that solves the Riccati equation. These derivatives are also used to identify the parameters of a dynamic model of the airplane. The model is used in a model-following portion of the control law, in order to provide specific vehicle handling characteristics. The flight test of the IFCS marks the initiation of the Intelligent Flight Control System Advanced Concept Program (IFCS ACP), which is a collaboration between NASA and Boeing Phantom Works. The goals of the IFCS ACP are to (1) develop the concept of a flight-control system that uses neural-network technology to identify aircraft characteristics to provide optimal aircraft performance, (2) develop a self-training neural network to update estimates of aircraft properties in flight, and (3) demonstrate the aforementioned concepts on the F-15 ACTIVE airplane in flight. The activities of the initial IFCS ACP were divided into three Phases, each devoted to the attainment of a different objective. The objective of Phase I was to develop a pre-trained neural network to store and recall the wind-tunnel-based stability and control derivatives of the vehicle. The objective of Phase II was to develop a neural network that can learn how to adjust the stability and control derivatives to account for failures or modeling deficiencies. The objective of Phase III was to develop a flight control system that uses the neural network outputs as a basis for controlling the aircraft. The flight test of the IFCS was performed in stages. In the first stage, the Phase I version of the pre-trained neural network was flown in a passive mode. The neural network software was running using flight data inputs with the outputs provided to instrumentation only. The IFCS was not used to control the airplane. In another stage of the flight test, the Phase I pre-trained neural network was integrated into a Phase III version of the flight control system. The Phase I pretrained neural network provided realtime stability and control derivatives to a Phase III controller that was based on a stochastic optimal feedforward and feedback technique (SOFFT). This combined Phase I/III system was operated together with the research flight-control system (RFCS) of the F-15 ACTIVE during the flight test. The RFCS enables the pilot to switch quickly from the experimental- research flight mode back to the safe conventional mode. These initial IFCS ACP flight tests were completed in April 1999. The Phase I/III flight test milestone was to demonstrate, across a range of subsonic and supersonic flight conditions, that the pre-trained neural network could be used to supply real-time aerodynamic stability and control derivatives to the closed-loop optimal SOFFT flight controller. Additional objectives attained in the flight test included (1) flight qualification of a neural-network-based control system; (2) the use of a combined neural-network/closed-loop optimal flight-control system to obtain level-one handling qualities; and (3) demonstration, through variation of control gains, that different handling qualities can be achieved by setting new target parameters. In addition, data for the Phase-II (on-line-learning) neural network were collected, during the use of stacked-frequency- sweep excitation, for post-flight analysis. Initial analysis of these data showed the potential for future flight tests that will incorporate the real-time identification and on-line learning aspects of the IFCS.

Davidson, Ron↗

Durability of YSZ Coated Ti2AlC in 1300 °C Mach 0.3 Burner Rig Tests

A thermal barrier coating system survived burner rig testing at 1300 °C for 500 h. A 160 µm thick yttria stabilized zirconia (YSZ) coating was applied to a Ti2AlC MAX phase bar sample by plasma spray physical vapor deposition (PS-PVD) and tested face-on in an atmospheric Mach 0.3 jet fuel burner, using 5-h thermal cycles. No thermal barrier coating (TBC) spallation or recession was observed, only a 2.4 mg/cm2 mass gain. The modest weight gain precluded severe volatility losses under high velocity burner conditions. The coating surface exhibited colonies of (111)flourite fiber-textured columns separated by craze patterns, with no visible moisture attack. The metastable tetragonal t' YSZ phase was obtained initially, transitioning to equilibrium teq and cubic YSZ, but with little detrimental monoclinic. The thickness of the alumina TGO was ~21 to 23 μm under the heated YSZ face and ~13 to 15 μm on the uncoated, cooler backside. The backside exhibited removal of initial transient TiO2 nodules and partial etching of the underlying Al2O3 scale by volatile hydroxides formed in high temperature, high velocity water vapor. Aerodynamic forces produced some bending of the cantilevered sample via creep. The test indicated exceptional stability of YSZ coatings on Ti2AlC under turbine conditions, with thermal expansion matching playing a key role. The purpose of this study was to demonstrate long term durability of YSZ/MAX phase system in aggressive high temperature burner rig testing. MAX phases have been keenly studied because of their unique crystal structure and intriguing properties (Refs. 1 and 2). Having Mn+1(Al,Si)(C,N)n general composition, they are defined as ceramics, but possess unusual desirable attributes such as high conductivity, thermal shock resistance, easy machinability, and deformation tolerance. The mechanical properties derive from weak M-(Al,Si) bonding in the basal plane that leads to sliding and kinking in preference to catastrophic crack growth. Like most ceramics they are phase stable at high temperatures, generally up to 1500 °C. High temperature oxidation resistance is excellent for alumina-forming Ti3AlC2, Ti2AlC, and Cr2AlC, as reviewed by Tallman, et al. (Ref. 3). Compatibility with α-Al2O3 scales is further enhanced in cyclic exposures by a close matching of thermal expansion coefficients, (Ref. 4) i.e., (~9.3, 10.2, 11.3×10–6/K for Al2O3, Ti2AlC, and YSZ, to be discussed). Turbine environments generally contain 10 percent water vapor in the combustion gases, therefore moisture effects can be a concern for some materials (Ref. 5). Furnace tests of MAX phases in high temperature steam generally showed little effect on Al2O3 scale growth (Ref. 6). However, high velocity and high pressure gas can influence scale losses by the formation of volatile reaction products, such as TiO(OH)2 and Al(OH)3 (Refs. 7 to 10). This phenomenon had been discussed for 1100 to 1300 °C high pressure burner rig tests of Ti2AlC (Ref. 11). A single cubic growth rate parameter kcubic was measurably lower than comparable furnace TGA data, but it could be matched reasonably well if corrected for a slight volatility term. In general, a two-parameter cubic-linear growth-volatility law was believed to apply. Corresponding scale volatility loss rates, directly measured at 1300 °C on a pre-oxidized sample, were moderate (0.012 mg/cm2/h) and largely attributed to removal of the initial TiO2 transient scale. A related CH4 burner study of high purity Cr2AlC MAX phase demonstrated 1200 °C durability after 500 rapid (5 min. heat and 2 min. cool) thermal shock cycling (29 h hot time) (Ref. 12). Heating and cooling rates were ~1000 and 500 °C per minute, with a gas velocity of 5 m/s, producing a 75 °C/mm gradient. A 7 μm Al2O3 surface scale and a 13 μm Cr7C3 depletion zone formed with no signs of failure. No evidence of scale volatility was evident, although weight change was not provided, the velocity was moderate, and the total hot time was not extensive. The same high gradient BRT was used to produce 1400 °C surface temperatures for a YSZ/Cr2AlC/IN738 system in the first study of MAX phases used as bond coats for thermal barrier coatings (TBC) (Ref. 25). Here TBC failure was reported after 745 cycles, with only a 1.5 μm Al2O3 scale entrained within a porous, Cr7C3 bondcoat depletion phase. YSZ thermal barrier coatings have been considered to be a compatible complement to Al-MAX phases because of thermal expansion matching and extremely low volatility in water vapor. Initial studies showed superior oxidative stability up to 1300 °C, for long times (at least 500 h) for Ti2AlC substrates and less (268 h) for Cr2AlC, while withstanding large alumina TGO scale thickness (~35 to 40 μm) (Refs. 13 and 14). By comparison, typical superalloy systems can only survive 1150 °C maximum interface temperatures for extended periods, with a maximum sustained TGO below 10 μm (Ref. 15). High temperature SiC based systems are known to form slow-growing SiO2 scales. But these are subject to rate enhancement and volatile Si(OH)4 products in the presence of water vapor, as described comprehensively by Opila, et al. (Refs. 5, 16 to 19). Net weight losses are generally observed in high velocity, high pressure burner rig studies (e.g., 0.084 mg/cm2/h at 1300 °C) (Ref. 20). Furthermore, the loss rates have been shown from chemical physics to scale with v1/2 and pH2O 2 (Ref. 16). Low activity, moisture-resistant environmental barrier coatings (EBC), such as rare earth silicates, are needed to prevent substrate recession under turbine conditions (Refs. 21 to 23).

Smialek, James L.↗

Surface Stabilization with Fluorine of Layered Ultrahigh-Nickel Oxide Cathodes for Lithium-Ion Batteries

High-nickel layered oxide cathodes are key to meet the demands of the electric vehicle industry because of their high specific capacity. However, commercialization of these materials is hindered by critical challenges, such as phase transitions, particle cracking, aggressive surface reactivity, and thermal instability. Cation doping along with surface coating has proven to be an effective way to circumvent some of these issues to a large extent. Herein, fluorine coating is employed on a high-nickel Li[Ni 0.95 Mn 0.015 Co 0.02 Al 0.01 Mg 0.005 ]O 2 (NMCAM) cathode via a solution route. Detailed structural and electrochemical analyses indicate fluorine largely decorates the surface at low enough calcination temperatures. The cathode with 1 mol % fluorine coating exhibits a capacity retention of 71% after 500 cycles as compared to 59% for the control sample when cycled to a high cutoff voltage of 4.3 V in a full cell configuration with graphite anode. Post-mortem analysis of cycled electrodes reveals that surface reactivity is a major contributor to capacity fade as compared to particle cracking. Fluorine coating reduces surface reactivity and the depth to which rock-salt phase is formed on the surface during cycling. The thermal stability is also enhanced after fluorine coating as the material shows less heat release at high states of charge. Furthermore, this work demonstrates an effective, economical, and scalable way to stabilize the surface with fluorine and enhance the electrochemical performance of high-nickel cathodes.

25 ENERGY STORAGE↗

Assessment of uranium nitride interatomic potentials

Uranium mononitride (UN) is a promising nuclear fuel due to its high fissile density, high thermal conductivity, and suitability for reprocessing. In this study, two uranium nitride interatomic potentials are assessed: Tseplyaev and Starikov's angular-dependent potential and Kocevski et al.'s embedded atom model potential. Predictions of the thermophysical and elastic properties of UN, UN 2 , and α- and β-U 2 N 3 computed using both potentials are assessed and compared to available experimental data. Notably, the Tseplyaev potential performs better with the energetic aspects of UN, e.g., specific heat capacity and point defect formation energies, whereas the Kocevski potential performs better with the structural aspects of UN, e.g., thermal expansion as well as with the elastic properties. The reasons why the Kocevski potential underestimates the UN specific heat are explained by examining the UN phonon properties modeled using both potentials. The Kocevski potential shows better identification of the mechanical stability ranges of UN, UN 2 , and α- and β-U 2 N 3 , reasonably predicting the melting point of UN and predicting stable structures for UN 2 and α- and β-U 2 N 3 . On the other hand, the Tseplyaev potential predicts a premature phase change of both UN and UN 2 and cannot stabilize α- nor β-U 2 N 3 . However, the Kocevski potential cannot predict a stable α-U phase and is thus not suitable for the calculation of formation energies for non-stoichiometric point defects.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Vertical Spin Tunnel Testing and Stability Analysis of Multi-Mission Earth Entry Vehicles

Multi-Mission Earth Entry Vehicles (MMEEVs) are blunt-body vehicles designed with the purpose of transporting payloads from space to the surface of the Earth. To achieve high reliability and minimum weight, MMEEVs avoid using limited-reliability systems, such as parachutes, retro-rockets, and reaction control systems and rely on the natural aerodynamic stability of the vehicle throughout the Entry, Descent, and Landing phases of flight. Testing in NASA Langley's 20-FT Vertical Spin Tunnel (20-FT VST), dynamically-scaled MMEEV models was conducted to improve subsonic aerodynamic models and validate stability criteria for this class of vehicle. This report documents the resulting data from VST testing for an array of 60-deg sphere-cone MMEEVs. Model configurations included were 1.2 meter, and 1.8 meter designs. The addition of a backshell extender, which provided a 150% increase in backshell diameter for the 1.2 meter design, provided a third test configuration. Center of Gravity limits were established for all MMEEV configurations. An application of System Identification (SID) techniques was performed to determine the aerodynamic coefficients in order to provide databases for subsequent 6-degree-of-freedom simulations.

Glaab, Louis J.↗

Active Learning Accelerated Discovery of Stable Iridium Oxide Polymorphs for the Oxygen Evolution Reaction

The discovery of high-performing and stable materials for sustainable energy applications is a pressing goal in catalysis and materials science. Understanding the relationship between a material’s structure and functionality is an important step in the process, such that viable polymorphs for a given chemical composition need to be identified. Machine-learning-based surrogate models have the potential to accelerate the search for polymorphs that target specific applications. Herein, we report a readily generalizable active-learning (AL) accelerated algorithm for identification of electrochemically stable iridium oxide polymorphs of IrO 2 and IrO 3 . The search is coupled to a subsequent analysis of the electrochemical stability of the discovered structures for the acidic oxygen evolution reaction (OER). Structural candidates are generated by identifying all 956 structurally unique AB2 and AB3 prototypes in existing materials databases (more than 38000). Next, using an active learning approach, we find 196 IrO 2 polymorphs within the thermodynamic amorphous synthesizability limit and reaffirm the global stability of the rutile structure. We find 75 synthesizable IrO 3 polymorphs and report a previously unknown FeF 3 -type structure as the most stable, termed α-IrO 3 . To test the algorithms performance, we compare to a random search of the candidate space and report at least a 2-fold increase in the rate of discovery. Additionally, the AL approach can acquire the most stable polymorphs of IrO 2 and IrO 3 with fewer than 30 density functional theory optimizations. Analysis of the structural properties of the discovered polymorphs reveals that octahedral local coordination environments are preferred for nearly all low-energy structures. Subsequent Pourbaix Ir–H 2 O analysis shows that α-IrO3 is the globally stable solid phase under acidic OER conditions and supersedes the stability of rutile IrO 2 . Calculation of theoretical OER surface activities reveal ideal weaker binding of the OER intermediates on α-IrO 3 than on any other considered iridium oxide. We emphasize that the proposed AL algorithm can be easily generalized to search for any binary metal oxide structure with a defined stoichiometry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Rheological Properties of Quasi-2D Fluids in Microgravity

Freely suspended smectic films of sub-micrometer thickness and lateral extensions of several millimeters are used to study thermally driven convection and diffusion in the film plane. The experiments were performed during a six minute microgravity phase of a TEXUS suborbital rocket flight (Texus 52, launched April 27, 2015). The project served as a preliminary test for a planned ISS Experiment with liquid crystal films (OASIS), and in addition it provided new experimental data on smectic films exposed to in-plane thermal gradients.We find an attraction of the smectic material towards the cold edge of the film in a temperature gradient, similar to a Soret effect. This process is reversed when this edge is heated up again. Thermal convection driven by two thermocontacts in the film is practically absent, even at temperature gradients up to 10 Kmm, thermally driven convection sets in when the hot post reaches the transition temperature to the nematic phase.An additional experiment was performed under microgravity conditions to test the stability of liquid crystal bridges in different smectic phases.

microgravity↗

Hole Trapping in Halide Perovskites Induces Phase Segregation

Metal halide perovskites have garnered a great deal of attention for their applications in photovoltaics, LEDs, and radiation detection. The ease of solution processing high-quality perovskite semiconductors with large absorption coefficients and tolerance to native defects is decidedly attractive. Additionally, the ability to precisely tune the band gap of halide perovskites through compositional alloying of the halide ion is of particular interest for a range of applications, especially for tandem solar cells. However, under steady state light irradiation, an initially homogeneous mixed halide perovskite (MHP) will form local domains that are rich in one halide ion (e.g., Br or I). This light-induced phase segregation in MHPs forms iodide-rich domains that act as charge carrier traps and lowers the efficiency of perovskite-based devices. Thus, phase segregation poses a serious challenge to the implementation of MHPs in real-world device settings. Interestingly, when a phase segregated MHP film is placed in the dark, entropic driving forces become dominant and the segregated perovskite remixes and returns to its initially homogeneous state. Several key mechanistic details of phase segregation have been elucidated over the years. However, there are still aspects of halide segregation that are not clear, and there is ongoing debate in the literature as to what are the key factors that contribute to the mechanism. This Account discusses recent results that point to the specific role of hole trapping in phase segregation. Interestingly, generation of holes through above-band-gap excitation or through electrochemical injection increases ion migration and leads to phase segregation. The thermodynamic and redox properties of halide perovskites provide a strong driving force for hole trapping and oxidation of iodide species in MHPs. However, mobile halide species within the perovskite lattice take time to migrate and generate halide-rich domains. When in contact with a nonpolar solvent, the migration of iodine species is further extended to expulsion of iodine from the perovskite film. Thus, the mobility of halides and their susceptibility to hole-induced oxidation play a crucial role in determining the long-term stability of metal halide perovskites. Strategies to gain kinetic control over ion migration to slow phase segregation are needed to overcome these hurdles and achieve stable mixed halide perovskites. Modification of the perovskite composition through introduction of different cations or halide ions, or introduction of low-dimensional perovskite phases may suppress phase segregation. Furthermore, in achieving stability and improving the efficiency of perovskite solar cells and light emitting devices with minimal impacts, suppression of segregation remains the key factor.

36 MATERIALS SCIENCE↗

Sustainable materials acceleration platform reveals stable and efficient wide-bandgap metal halide perovskite alloys

The vast chemical space of emerging semiconductors, like metal halide perovskites, and their varied requirements for semiconductor applications have rendered trial-and-error environmentally unsustainable. Here, in this work, we demonstrate RoboMapper, a materials acceleration platform (MAP), that achieves 10-fold research acceleration by formulating and palletizing semiconductors on a chip, thereby allowing high-throughput (HT) measurements to generate quantitative structure-property relationships (QSPRs) considerably more efficiently and sustainably. We leverage the RoboMapper to construct QSPR maps for the mixed ion FA 1-y Cs y Pb(I 1-x Br x ) 3 halide perovskite in terms of structure, bandgap, and photostability with respect to its composition. We identify wide-bandgap alloys suitable for perovskite-Si hybrid tandem solar cells exhibiting a pure cubic perovskite phase with favorable defect chemistry while achieving superior stability at the target bandgap of ~1.7 eV. RoboMapper’s palletization strategy reduces environmental impacts of data generation in materials research by more than an order of magnitude, paving the way for sustainable data-driven materials research.

36 MATERIALS SCIENCE↗

Quantum phases in the honeycomb-lattice J 1 – J 3 ferro-antiferromagnetic model

The significant role of quantum effects in magnets with competing interactions remains at the forefront of condensed matter physics for over 50 years, inspiring a multitude of quests for exotic states, models that can realize them, and real materials that can host them. The elusive spin-liquid states with strong entanglement are but one example; others include valence-bond phases with spatial symmetry breaking, quantum spin nematics that are quantum analogues of liquid crystals, and an especially extensive class of unconventional magnetically ordered phases that do not appear in the classical solutions of the underlying spin models. It is the latter group of phenomena that creates a broader context for the research effort in the present work concerning the search for and an identification of the novel ground states of quantum magnets. In this work, we have studied one of the paradigmatic models in quantum magnetism that is also attracting a significant recent interest because it appears to be providing a tantalizingly close description for many of the newly synthesized materials. We demonstrated that the phase diagram of the quantum ferro-antiferromagnetic model on the honeycomb lattice differs dramatically from the classical one. It hosts the double-zigzag and Ising-z phases as unexpected intermediaries between ferromagnetic and zigzag states that are also extended beyond their classical regions of stability. In broad agreement with quantum order-by-disorder arguments, these collinear phases completely supersede the classical spiral state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Protonation Stimulates the Layered to Rock Salt Phase Transition of Ni‐Rich Sodium Cathodes

Abstract Protonation of oxide cathodes triggers surface transition metal dissolution and accelerates the performance degradation of Li‐ion batteries. While strategies are developed to improve cathode material surface stability, little is known about the effects of protonation on bulk phase transitions in these cathode materials or their sodium‐ion battery counterparts. Here, using NaNiO 2 in electrolytes with different proton‐generating levels as model systems, a holistic picture of the effect of incorporated protons is presented. Protonation of lattice oxygens stimulate transition metal migration to the alkaline layer and accelerates layered‐rock‐salt phase transition, which leads to bulk structure disintegration and anisotropic surface reconstruction layers formation. A cathode that undergoes severe protonation reactions attains a porous architecture corresponding to its multifold performance fade. This work reveals that interactions between electrolyte and cathode that result in protonation can dominate the structural reversibility/stability of bulk cathodes, and the insight sheds light for the development of future batteries.

25 ENERGY STORAGE↗

Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations. Phase 6-A: Effects of blade torsion, of blade flap bending flexibility and of rotor support flexibility on rotor stability and random response

The effects of lifting rotor blade torsion, blade flap bending flexibility and rotor support flexibility on rotor stability and random response are described. The subjects discussed are: (1) blade representation and method of analysis, (2) random gust response statistics for coupled torsion-flapping rotor blade vibrations, (3) flap bending corrections to the rigid blade analysis of lifting rotors, and (4) effects of rotor support flexibility. The response of linear periodically time varying systems to random excitation is examined.

Hohenemser, K. H.↗

Stability and synthesis across barium tin sulfide material space

The underexplored Ba–Sn–S phase space is explored at various temperatures and cation ratios with combinatorial sputtering, crystallizing rocksalt-derived phases, Ba 2 SnS 4 , and Ba 7 Sn 5 S 15 . These findings are supported by DFT computed phase diagrams.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗

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