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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7

Scalable phononic metamaterials: Tunable bandgap design and multi-scale experimental validation

Phononic metamaterials offer unprecedented control over wave propagation, making them essential for applications such as vibration isolation, waveguiding, and acoustic filtering. However, achieving scalable and precisely tunable bandgap properties across different length scales remains challenging. This study presents a user-friendly design framework for phononic metamaterials, enabling ultra-wide bandgap tunability (B/ω c ratios up to 172 %) across multiple frequency ranges and scales. Using finite element simulations of a Yablonovite-inspired unit cell, we establish a comprehensive parametric design space that illustrates how geometric parameters, such as sphere size and beam diameter, controls bandgap width and frequency. The scalability and robustness of the framework are validated through experimental testing on additively manufactured structures at both macro (10 mm) and micro (80 µm) scales, fabricated using Stereolithography and Two-Photon Polymerization. Transmission loss measurements, conducted with piezoelectric transducers and laser vibrometry, closely match simulations in the kHz and MHz frequency ranges, confirming the reliability and consistency of the bandgap behavior across scales. This work bridges theory and experiments at multiple scales, offering a practical methodology for the rapid design of phononic metamaterials and expanding their potential for diverse applications across a broad range of frequencies.

36 MATERIALS SCIENCE↗

Characterizing leaf-scale fluorescence with spectral invariants

Sun-induced chlorophyll fluorescence (SIF) is increasingly recognized as a non-destructive probe for tracking terrestrial photosynthesis. Emerging developments in spectral invariants theory provide an innovative and efficient approach for representing SIF radiative transfer processes at the canopy scale. However, modeling leaf-scale fluorescence based on the spectral invariants properties (SIP) remains underexplored. In this study, the spectral invariants theory is employed for the first time to model the leaf-scale total, backward and forward fluorescence (leaf-SIP SIF). The leaf-SIP SIF model separates the leaf-scale radiative transfer process into two distinct components: the wavelength-dependent one associated with leaf biochemical properties, and the wavelength-independent component linked to leaf structural characteristics. The leaf structure-related effects are characterized by two spectrally invariant parameters: the photon recollision probability (p) and the scattering asymmetry parameter (q), which are parameterized using the directly measurable leaf dry matter. Evaluation against field measurements shows that the proposed leaf-SIP SIF model has a good performance, with coefficient of determination (R 2 ) of 0.89, 0.89, 0.90 and root mean squared errors (RMSE) of 1.28, 0.69, 0.74 Wm -2 µm -1 sr -1 , respectively for the total, backward, and forward fluorescence (660–800 nm). The leaf-SIP SIF model with a more concise formulation demonstrates comparable performance with the widely used Fluspect model. Further, the leaf-SIP SIF model provides a simple and efficient approach for simulating leaf-scale fluorescence, with the potential to be integrated into a unified SIP-based model framework for simulating the radiative transfer processes across the soil-leaf-canopy-atmosphere continuum.

59 BASIC BIOLOGICAL SCIENCES↗

Mechanisms of electromagnetic field control on mineral scaling in brackish water reverse osmosis: Combined homogenous and heterogeneous nucleation

Electromagnetic field (EMF) treatment has emerged as a promising approach for scaling control due to its cost-effectiveness, simplicity, and low energy consumption. However, there is a limited understanding of the mechanisms by which applied EMF impacts mineral scaling in reverse osmosis (RO) systems. This has led to inconclusive and varied results and uncertainties regarding its effectiveness. This study elucidates the impacts of EMF on homogenous and heterogeneous nucleation and membrane performance during RO desalination of different feedwaters. Our results reveal that EMF exhibits greater efficacy in treating near-saturated water (SI∼0), especially when coupled with extended hydraulic flushing (HF). For saturated brackish water desalination, heterogeneous scaling predominantly occurs on membrane surfaces, with the effectiveness of EMF in inhibiting scaling primarily attributed to the hydration effect. In supersaturated solutions, EMF promotes bulk precipitation due to the magnetohydrodynamic effect, quickly blocking membrane pores. Thus, when the saturation reaches a certain high level during RO desalination, magnetohydrodynamic EMF effects can accelerate flux decline caused by homogeneous scaling. In conclusion, this work provides an efficient method for predicting EMF efficiency, emphasizing the importance of saturation conditions and HF cleaning duration in determining membrane performance, suggesting these show promise for improving undersaturated or near-saturated feedwater desalination via RO.

42 ENGINEERING↗

Mineral Scale Formation during Crossflow Reverse Osmosis at Constant Flux and Constant Transmembrane Pressure Conditions

Mineral scale formation on membrane surfaces is a significant challenge in reverse osmosis water purification. Laboratory fouling experiments are typically run such that the transmembrane pressure (TMP) is fixed, and the permeate flux decreases over time as scales accumulate on the membrane surface. However, this change in flux means that the hydrodynamic conditions at the membrane surface are continuously changing, which could affect crystallization and foulant deposition processes. Operating under constant permeate flux conditions, in contrast, is advantageous because it keeps the hydrodynamic conditions relatively consistent, making it possible to compare how membrane properties (e.g., surface chemistry) affect fouling propensity. Industrial reverse osmosis operations are not run strictly in either constant TMP or constant flux mode; while they may start at a constant TMP, feed pressure may be periodically adjusted to maintain permeate water production within a specified range. Here, the scarcity of constant permeate flux reverse osmosis scaling experiments reported in the literature frustrates efforts to compare membrane fouling processes under constant TMP and constant flux conditions. For the first time, the evolution of the fouling layer resistance was compared as a function of cumulative permeate volume per membrane area during constant TMP and constant flux reverse osmosis filtrations. Scaling experiments were conducted by challenging commercial reverse osmosis membranes with a model feed solution nearly saturated with calcium sulfate dihydrate (gypsum). At low fluxes, the increase in fouling layer resistance was quantitatively similar for the two operational modes. In contrast, at high fluxes, the fouling layer resistance increased more rapidly in constant flux filtration than in constant TMP filtration. The mechanism of scale formation in constant TMP and constant flux operation was self-limiting and self-reinforcing, respectively.

36 MATERIALS SCIENCE↗

Toward an Understanding of Linear Scaling Relations through Energy Decomposition Analysis

The discovery of linear scaling relations has fundamentally changed the field of heterogeneous catalysis. The scaling relations have been rationalized based on the d-band theory, specifically a separation of sp and d electron contributions to adsorption energies. Within the framework of energy decomposition analysis, a full understanding of such a separation would require one to further break down the adsorption energy into distinct energy components such as electrostatics, polarization, charge transfer, and van der Waals interactions, and to examine the sp and d contributions to each of them. As a step in this direction, we analyzed the interaction energy between CH x (x = 1–4) adsorbates and fcc(100) transition metal surfaces (M = Cu, Ag, Au, Rh, and Pt), with the surfaces represented both as slabs in plane-wave density functional theory (pw-DFT) calculations and as atomic clusters in atomic-orbital basis density functional theory (ao-DFT) calculations. Through an absolutely localized molecular orbital (ALMO) based energy decomposition analysis of the ao-DFT adsorption energy, each of the interaction energy components (electrostatics, polarization, van der Waals, and charge transfer) was found to follow its own scaling relations, with an intricate interplay among these energy components yielding the overall scaling relations for the total adsorption energies. Using the recently introduced ALMO-based polarization and charge-transfer analysis schemes, we further dissected polarization into metal surface and adsorbate contributions, and charge transfer into metal → adsorbate and adsorbate → metal contributions. The contributions from the sp and d electrons of the metal to these terms were further quantified, and the dominant role of the metal d electrons was reaffirmed. These results shed light on how CHx adsorbates interact with metal surfaces and further reveal the physical origin of the scaling relations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Microstructure Scale Lithium-Ion Battery Modeling: Part II. On In-Plane Heterogeneities and the Mechanisms that Regulate Them

Li-ion batteries performance and degradation are typically modeled at the macroscopic scale, that is neglecting in-plane heterogeneities that can arise from non-uniform electrode microstructures. Herein, a microstructure scale electrochemical model is used to quantify the impact of microstructure heterogeneity on cell performance during fast charging. The model predicts the electrolyte and solid concentration in-plane standard deviation can reach, respectively, ≈200 mol·m −3 and 6–7 kmol·m −3 locally. Further, the intercalation current density in-plane relative standard deviation can reach extremely high values, around 100% in the cathode and well above 100% in the anode graphite. These denote highly non-uniform lithiation rates and material utilization within each slice of the microstructure along the cell thickness. Non-uniform curvatures, at the particle scale (surface roughness) and between particles (size distribution), were found to initiate these in-plane heterogeneities, while an OCP-induced mechanism subsequently regulates them. The present model provides new insights into small length scale heterogeneity impact on battery performance not available with standard macro-scale/P2D modeling.

25 ENERGY STORAGE↗

Managing Subsurface Pressure Buildup and Interference in Commercial-Scale CO 2 Storage Project with Proximal Injection Wells

Large-scale decarbonization using carbon capture and storage (CCS) is likely to involve many commercial-scale CO 2 storage projects located in close proximity to each other. This close proximity raises concerns over pressure interference among the storage projects. Pressure interference between injection and storage efforts can reduce the practicable CO 2 storage resource and force wells to inject CO 2 at a lower rate to avoid the fracture pressure thresholds per United States Environmental Protection Agency (EPA) Class VI well regulations to preserve injection and confining zone integrity and potentially mitigate against inducing seismic activity. These analyses employ numerical full-physics reservoir modeling to evaluate how pressure buildup fronts and CO 2 plumes evolve under commercial-scale injection volumes of CO 2 in which multiple storage sites located in close proximity occur in tandem. The simulation models mimic injection at pseudo basin-scale and assume homogeneous saline formation(s) as storage targets with a pair of upper and lower homogeneous seal layer/s. These analyses specifically investigate the efficacy of two basin-wide reservoir pressure management strategies in addressing the technical challenges associated with pressure buildup and CO 2 plume commingling. The strategies explored include: 1) enlarging the area of injection well spacing (WS) and 2) storing CO 2 in a stacked sequence (SSS) of saline formations compared to a single formation. The storage and confining zones properties assumed were held common across the scenarios, unless specified otherwise. Analyses results show that after injecting 4 million tons per year for 30 years using 4 separate wells (each injecting 1 million metric tons per year), the radius of CO 2 plume extends to a mere 3 km or less from injection wells. Meanwhile, the radius of pressure buildup ranges on the order of tens to a few hundreds of kilometers, depending on the magnitude of pressure buildup threshold that one would use to define the front. CO 2 plume commingling from different injection wells appears to occur 50 years post-injection, especially under scenarios with narrowly spaced (i.e., < 5 km apart) injection well locations. Findings from sensitivity cases on the well spacing suggest that storage formations modeled would require different well spacing to avoid fracture pressure thresholds. For instance, modeled storage formations with high fracture gradients (i.e., 0.8 psi/ft) would need less than 5–km well spacing, whereas those with lower fracture gradients (i.e., 0.7 psi/ft) would need approximately 20–km well spacing, based on assumed modeling parameters. Under stacked injection, the pressure challenges (described above) still exist but are more alleviated due to distributing the same injection volume across more available reservoir volume. These analyses demonstrate that stacked-sequence storage can effectively address the challenges, while still providing the same target CO 2 storage volumes and allowing a large number of storage projects to be deployed in the same basin by better utilizing the available storage resource across different reservoir depths. Among cases modeled, the resulting pressure buildup front is most suppressed when each storage project distributes injection volumes over several wells, each of which injects a portion of the total CO 2 across the stacked sequence. This strategy results in the smallest CO 2 aerial footprint amongst scenarios evaluated but also shows the largest reduction in the pressure buildup at the top of perforation at the injection wells (upwards of approximately 42 percent compared to the commercial-scale single-formation storage), the result of which is crucial to maintain caprock integrity. The findings presented by this research draw attention to the importance of greater coordination among storage operators and regulatory stakeholders to foster the upscaling and deployment of CCS. These analyses provide insights into required decision-making when considering multi-project deployment in a shared basin. Because these analyses evaluate a very specific geologic situation, they bear further investigations across other geologic situations.

42 ENGINEERING↗

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗

2024 Electric Vehicles at Scale Semiannual Stakeholder Meeting

The U.S. Department of Energy (DOE) Electric Vehicles at Scale Lab Consortium (EVs@Scale Lab Consortium) is accelerating research to support the establishment of a secure and scalable national network of charging infrastructure. This network will be critical to support tens of millions of light-, medium-, and heavy-duty EVs on American roads by 2030. The EVs@Scale Lab Consortium brings together national laboratories and key stakeholders to conduct infrastructure research and development (R&D) that advances innovations in, and sets unified standards for, high-power and wireless charging. The effort will also develop technologies to integrate vehicle charging with the power grid, and develop cybersecurity measures to protect drivers, vehicles, equipment, and the grid. The first hybrid EVs@Scale Lab Consortium Semiannual Stakeholder Meeting was held at ANL on September 27-28, 2023, to identify research, development, and deployment needs to accelerate technology development for electric vehicles at scale and explore opportunities for collaboration across government, academia, and industry.

advanced charging and grid interface technologies↗

Spaced out: An economic framework to explore the impacts of PV panel spacing on large-scale farming in Colorado

CONTEXT Agrivoltaic systems co-locate solar technologies with agricultural operations on an integrated plot of land and potentially provide benefits to both energy and agricultural systems. To date, large-scale (>5-MW) agrivoltaic projects in the United States have been limited to grazing and ecovoltaic applications, raising questions about the impact and scalability of agrivoltaic crop systems. Many agrivoltaic designs raise the height of the solar panels to accommodate agricultural practices while keeping energy density high. However, raising the panels results in increased photovoltaic (PV) development costs, which often are higher than the economic returns of crop production underneath the panels. This leads to unfavorable project economics and the need for other agrivoltaic solutions than raising panels. OBJECTIVE To explore other solutions, we perform an initial feasibility analysis for an agrivoltaic solution that can integrate with large-scale farming practices by increasing the row spacing in between panels. Increased PV row spacing is a low-cost approach for scaling agrivoltaics to accommodate crop production and this spacing can be tailored to required crop equipment for different regions. Increasing row spacing will reduce the power density (PV installed per acre), but in areas that are not land limited, these agrivoltaic designs could be economically feasible. Our analysis establishes a framework for a feasibility analysis for where and with what crops spaced out panel agrivoltaic solutions might be economical. METHODS Using a case study for large-scale agriculture crops in Colorado, we establish a framework for wide-row agrivoltaic economic feasibility analysis. We utilized the System Advisor Model to calculate technoeconomic metrics to compare different row spacing solutions and capture tradeoffs of these system designs. RESULTS AND CONCLUSIONS We find that, in some circumstances, wider row agrivoltaic solutions that allow for continued mechanized crop production can provide economic benefits over a traditional utility-scale PV system. For most crops examined in this analysis, roughly $\$$200/acre in agricultural profit justified spacing out the panels to at least 31.7 ft. to accommodate agrivoltaic configurations versus PV only configurations. Additionally, opportunities for increased agricultural revenue with agrivoltaic systems allow PV project economics to tolerate a larger range of CAPEX variability while remaining economically viable relative to the PV only configurations. SIGNIFICANCE This framework can be adapted for a wide variety of crops and regions and allows for examination of economically favorable sites for future agrivoltaic systems that utilize different configuration and expand opportunities for agrivoltaics.

14 SOLAR ENERGY↗

A multiscale design method using interpretable machine learning for phononic materials with closely interacting scales

Manipulating the dispersive characteristics of vibrational waves is beneficial for many applications, e.g., high-precision instruments. architected hierarchical phononic materials have sparked promise tunability of elastodynamic waves and vibrations over multiple frequency ranges. In this article, hierarchical unit-cells are obtained, where features at each length scale result in a band gap within a targeted frequency range. Our novel approach, the ‘‘hierarchical unit-cell template method,’’ is an interpretable machine-learning approach that uncovers global unit-cell shape/topology patterns corresponding to predefined band-gap objectives. A scale-separation effect is observed where the coarse-scale band-gap objective is mostly unaffected by the fine-scale features despite the closeness of their length scales, thus enabling an efficient hierarchical algorithm. Moreover, the hierarchical patterns revealed are not predefined or self-similar hierarchies as common in current hierarchical phononic materials. Furthermore, our approach offers a flexible and efficient method for the exploration of new regions in the hierarchical design space, extracting minimal effective patterns for inverse design in applications targeting multiple frequency ranges.

Architected materials↗

Large-Scale Compatibilization of Postconsumer Polyolefins in the Presence of Paraffin Wax as a Rheology Modifier

Postconsumer polyolefins (r-POs) are leading plastic waste contributors today. This study reports, for the first time, the compatibilization of r-POs at a 50 kilogram (kg) scale with a styrene block copolymer compatibilizer in the presence of paraffin waxes as rheology modifiers (RMs). The addition of the rheological modifier (RM) and compatibilizer enhances the melt flow indices (MFIs) and mechanical properties, respectively. One aspect of this study is to compare the effectiveness of low-cost paraffin wax to that of specialized and expensive RMs in r-POs. The mechanical and rheological properties such as the melt flow index (MFI) of r-POs were compared in the presence of two types of RMs. Next, the study explores the challenges encountered when scaling the compatibilization of r-POs in the presence of paraffin wax from a 10-g to a 50-kg scale. The mechanical properties were determined and compared for samples at different scales. The study further investigated the effect of the method used for blending paraffin wax with r-PO and its impact on the value of their MFI and mechanical properties. This at-scale validation could pave the way for the commercialization of r-POs.

crystallinity↗

Air‐Ice‐Ocean Coupling During a Strong Mid‐Winter Cyclone: Observing Coupled Dynamic Interactions Across Scales

Abstract Arctic cyclones are key drivers of sea ice and ocean variability. During the 2019–2020 Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition, joint observations of the coupled air‐ice‐ocean system were collected at multiple spatial scales. Here, we present observations of a strong mid‐winter cyclone that impacted the MOSAiC site as it drifted in the central Arctic pack ice. The sea ice dynamical response showed spatial structure at the scale of the evolving and translating cyclonic wind field. Internal ice stress and ocean stress play significant roles, resulting in timing offsets between the atmospheric forcing and the ice response and post‐cyclone inertial ringing in the ice and ocean. Ice motion in response to the wind field then forces the upper ocean currents through frictional drag. The strongest impacts to the sea ice and ocean from the passing cyclone occur as a result of the surface impacts of a strong atmospheric low‐level jet (LLJ) behind the trailing cold front and changing wind directions between the warm‐sector LLJ and post cold‐frontal LLJ. Impacts of the cyclone are prolonged through the coupled ice‐ocean inertial response. Local impacts of the approximately 120 km wide LLJ occur over a 12 hr period or less and at scales of a kilometer to a few tens of kilometers, meaning that these impacts occur at combined smaller spatial scales and faster time scales than most satellite observations and coupled Earth system models can resolve.

Meteorology & Atmospheric Sciences↗

Non-equilibrium critical scaling and universality in a quantum simulator

Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e. a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Cross-scale covariance for material property prediction

A simulation can stand its ground against an experiment only if its prediction uncertainty is known. The unknown accuracy of interatomic potentials (IPs) is a major source of prediction uncertainty, severely limiting the use of large-scale classical atomistic simulations in a wide range of scientific and engineering applications. Here we explore covariance between predictions of metal plasticity, from 178 large-scale (~10 8 atoms) molecular dynamics (MD) simulations, and a variety of indicator properties computed at small-scales (≤10 2 atoms). All simulations use the same 178 IPs. In a manner similar to statistical studies in public health, we analyze correlations of strength with indicators, identify the best predictor properties, and build a cross-scale “strength-on-predictors” regression model. This model is then used to estimate regression error over the statistical pool of IPs. Small-scale predictors found to be highly covariant with strength are computed using expensive quantum-accurate calculations and used to predict flow strength, within the statistical error bounds established in our study.

36 MATERIALS SCIENCE↗

Locating the missing large-scale emission in the jet of M87* with short EHT baselines

In very-long baseline interferometric arrays, nearly co-located stations probe the largest scales and typically cannot resolve the observed source. In the absence of a large-scale structure, closure phases constructed with these stations are zero and, since they are independent of station-based errors, they can be used to probe data issues. Here, we show how these trivial closure phases become nonzero with a brightness distribution on smaller scales than their short baseline would suggest. When applied to sources that are made up of a bright compact and large-scale diffuse component, the trivial closure phases directly measure the centroid relative to the compact source and higher-order image moments. We present a technique to measure these image moments with minimal model assumptions and validate it on synthetic Event Horizon Telescope (EHT) data. We then apply this technique to 2017 and 2018 EHT observations of M87* and find a weak preference for extended emission in the direction of the large-scale jet. We also apply it to 2021 EHT data and measure the source centroid about 1 mas northwest of the compact ring, which is consistent with the jet observed at lower frequencies.

79 ASTRONOMY AND ASTROPHYSICS↗

Small-Scale Irrigation: Improving Food Security under Changing Climate and Water Resource Conditions in Ethiopia

We develop a new systems modeling tool that integrates knowledge from hydrology, agriculture, and economics to understand the effect of small-scale irrigation on food security and groundwater sustainability in Ethiopia. Irrigation is an effective tool to mitigate climate impacts and improve agricultural yields. Small-scale irrigation, such as decentralized groundwater irrigation, is well suited for developing countries where smallholder farming communities are widely dispersed and can only afford small infrastructure investment. We study the underlying interdependencies between food and water systems in Ethiopia, where small-holder agriculture is the foundation of the nation’s economy and climate variability has led to great challenges to its food security. Our coupled market and crop model with groundwater module captures the interdependencies of climate, water availability (including irrigation), crop yield, farmland allocation, crop production, transport and consumption based on a system approach across multiple spatial scales. We study the implication of small-scale irrigation to Ethiopia’s food security and water resource conditions as a “what-if” question by comparing an irrigation scenario to the calibrated baseline in 2015, a year of significant drought and crop failure over a large portion of Ethiopia. Our model offers fresh insights into geographic disparities in outcomes that are driven by baseline climate variability, soil fertility, and market conditions. In general, we find that small-scale irrigation can potentially improve food security through increases in food consumption, but it requires policy support to direct the increases of production to domestic consumption while maintaining a sustainable groundwater condition. By using Ethiopia as an example, we show the strength of our model to study how water infrastructure resources support critical functions and service in water and food systems.

Zhang, Ying↗

Invariant discovery of features across multiple length scales: Applications in microscopy and autonomous materials characterization

Physical imaging is a foundational characterization method in areas from condensed matter physics and chemistry to astronomy and spans length scales from atomic to universe. Images encapsulate crucial data regarding atomic bonding, materials microstructures, and dynamic phenomena such as microstructural evolution and turbulence, among other phenomena. The challenge lies in effectively extracting and interpreting this information. Variational Autoencoders (VAEs) have emerged as powerful tools for identifying the underlying factors of variation in image data, providing a systematic approach to distilling meaningful patterns from complex data sets. However, a significant hurdle in their application is the definition and selection of appropriate descriptors reflecting local structures. Here, we introduce the scale-invariant VAE approach (SI-VAE) based on the progressive training of the VAE with the descriptors sampled at different length scales. The SI-VAE allows the discovery of the length scale-dependent factors of variation in the system. Here, we illustrate this approach using the ferroelectric domain images and generalize it to the movies of the electron-beam induced phenomena in graphene and topography evolution across combinatorial libraries. This approach can further be used to initialize the decision making in automated experiments including structure–property discovery and can be applied across a broad range of imaging methods. This approach is universal and can be applied to any spatially resolved data including both experimental imaging studies and simulations, and can be particularly useful for exploration of phenomena such as turbulence and scale-invariant transformation fronts.

36 MATERIALS SCIENCE↗