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Chapter 4 - Recent Advances in Identification of Differential Equations from Noisy Data: IDENT Review

Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of time-dependent data. If we assume that the differential equation is a linear combination of various linear and nonlinear differential terms, then the identification problem can be formulated as solving a linear system. The goal then reduces to finding the optimal coefficient vector that best represents the time derivative of the given data. We review some recent works on the identification of differential equations. We find some common themes for the improved accuracy: (i) The formulation of linear system with proper denoising is important, (ii) how to utilize sparsity and model selection to find the correct coefficient support needs careful attention, and (iii) there are ways to improve the coefficient recovery. We present an overview and analysis of recent developments on the topic.

97 MATHEMATICS AND COMPUTING↗

Biocatalytic system for comparatively assessing the functional association of monolignol cytochrome P450 monooxygenases with their redox partners

Lignin is a complex heterogenous polymer derived from oxidative radical polymerization of three monolignols, i.e., p-coumaryl alcohol, coniferyl alcohol and sinapyl alcohol. These lignin monomeric precursors structurally differ in their methoxy groups of the benzene rings. In phenylpropanoid-monolignol biosynthetic pathway, the endoplasmic reticulum (ER)-resident cytochrome P450 monooxygenases, cinnamate 4-hydroxylase, coumaroyl ester 3´-hydroxylase and ferulate 5-hydroxylase, establish the key structural characteristics of monolignols. The catalysis of cytochrome P450 monooxygenase requires reducing power, which is supplied by the ER electron transfer chains, composed of cytochrome P450 oxidoreductase (CPR), cytochrome b5 reductase (CBR) and/or cytochrome b5 protein (CB5), from cofactor NADPH or NADH. While NADPH-dependent CPR serves as the typical electron donor for most P450 enzymes, in some cases, the CBR-CB5 or CPR-CB5 electron transfer system also transfers electrons to the terminal P450 enzymes. There are tremendous studies focusing on the discovery and characterization of cytochrome P450 monooxygenases. However, very limited attention has been paid to the versatility and the roles of electron transfer components in the P450 catalytic system. Due to the membrane-residence property of both P450 enzymes and electron transfer components, it is challenging to establish an effective experimental system to evaluate the functional association of P450s with their redox partners. This chapter describes a yeast cell biocatalytic system and the related experimental procedures for comparatively assessing the functional relationship of monolignol biosynthetic P450 enzymes and different redox partners in their catalysis.

59 BASIC BIOLOGICAL SCIENCES↗

Chemical and structural origin of hole states in yttria-stabilized zirconia

Yttria-stabilized zirconia (YSZ) has important electrochemical applications as a fast oxygen ion conductor and is the state-of-the-art electrolyte material for solid oxide fuel/electrolyzer cells. While much attention has been paid to the fast oxygen ion conduction, the electronic conductivity and especially hole carriers are not well understood, yet essential for the electrochemical stability, conduction kinetics and microstructural evolution in YSZ. The present work uses first-principles calculations to illustrate the chemical nature and local structural features of hole states in oxidized YSZ. Three types of hole states have been identified, including delocalized hole states on normal oxygen ions, localized hole states on special oxygen ions with extreme local structures, and peroxide-like groups. In conclusion, the implications on various experimental observations are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Elemental segregation to lattice defects in the CrMnFeCoNi high-entropy alloy during high temperature exposures

The influence of small plastic pre-strains on the elevated-temperature stability and microstructure of the equiatomic CrMnFeCoNi FCC solid solution is investigated. Particular attention is given to whether any of the alloy elements segregate to individual dislocations. To that end, CrMnFeCoNi samples were first deformed in tension at room temperature to plastic strains of 0.2 and 2.3%, and subsequently annealed at 973 K for 800 hours. The pre-strains activated planar slip of 1/2<110>-type dislocations on {111}-type glide planes. Interactions of this planar slip with special Σ3 grain boundaries formed a large number of dislocation segments with a <110>-type crystallographic orientation suitable for a credible end-on analysis of dislocation cores in HR-STEM. The cores of the 1/2<110> dislocations pushed up against the investigated grain boundaries were found to be close to the compact configuration. Within the sensitivity of the Super-X EDS mapping, no concentration gradient was detected near dislocations that would indicate enrichment at dislocation cores of any of the elemental constituents of the alloy after the pre-deformation and annealing. However, a Cr-rich tetragonal sigma phase nucleated and grew at grain boundary triple junctions during this anneal, processes that were not accelerated by the enhanced dislocation density present after pre-strain. A clear chromium gradient was observed in the Cr-depleted zones near grain boundaries suggesting that Cr transport occurred by relatively slow diffusion from the bulk to the grain boundaries and then by relatively fast diffusion along the grain boundaries to the precipitates. Accompanying the Cr depletion near grain boundaries is a simultaneous Ni and Mn enrichment, which promotes formation of the L1 0 NiMn phase that is observed on the grain boundaries after prolonged annealing.

36 MATERIALS SCIENCE↗

Vacancy formation energies and migration barriers in multi-principal element alloys

Multi-principal element alloys (MPEAs) continue to garner interest as structural and plasma-facing materials due to their structural (phase) stability and increased resistance to radiation damage. Despite sensitivity of mechanical behavior to irradiation and point-defect formation, there has been scant attention on understanding vacancy stability and diffusion in refractory-based MPEAs. Using density-functional theory, we examine vacancy stability and diffusion barriers in body-centered cubic (Mo 0.95 W 0.05 ) 0.85 Ta 0.10 (TiZr) 0.05 . The results in this MPEA show strong dependence on environment, originating from local lattice distortion associated with charge-transfer between neighboring atoms that vary with different chemical environments. We find a correlation between degree of lattice distortion and migration barrier: (Ti, Zr) with less distortion have lower barriers, while (Mo, W) with larger distortion have higher barriers, depending up local environments. Under irradiation, our findings suggest that (Ti, Zr) are significantly more likely to diffuse than (Mo, W) while Ta shows intermediate effect. Finally, material degradation caused by vacancy diffusion can be controlled by tuning composition of alloying elements to enhance creep strength at extreme operating temperatures and harsh conditions.

36 MATERIALS SCIENCE↗

Oxidation mechanism in a refractory multiple-principal-element alloy at high temperature

Refractory multiple-principal-element alloys (RMPEAs) are promising structural materials to enable increased power efficiency in high-temperature oxidation environments, but the oxidation behavior and microstructures of the oxides, especially at the beginning of the oxidation, have received limited attention. Here, the oxidation mechanism in an equimolar W-Mo-Ta-Nb-V was investigated at 1300 °C and compared with the equimolar W-Mo-Ta-Nb alloy without V. The oxide scale on WMoTaNbV after 1 min exposure is shown to be composed of a degradation layer at the interface of the alloy/oxide, an initial oxide transition layer, followed by the main phase aggregate oxide layer, and an outermost oxide layer. At the early stage of oxidation, the absorption of oxygen by the RMPEA substrate forms a solid solution. Vanadium accelerates the initial degradation process as it forms VO. The initial oxidation-induced degradation of RMPEA follows a sequence governed by the free energy change accompanied by local element segregation. Liquid V-Mo oxides aggregate in the intermediate oxide layer. The inward growth of the oxide scale is controlled by the local composition changes, the orientation of the substrate, the crystal structure, and physical properties such as melting points of the oxides.

36 MATERIALS SCIENCE↗

Robust deep learning framework for constitutive relations modeling

Modeling the full-range deformation behaviors of materials under complex loading and materials conditions is a significant challenge for constitutive relations (CRs) modeling. Here, we propose a general encoder-decoder deep learning framework that can model high-dimensional stress-strain data and complex loading histories with robustness and universal capability. The framework employs an encoder to project high-dimensional input information (e.g., loading history, loading conditions, and materials information) to a lower-dimensional hidden space and a decoder to map the hidden representation to the stress of interest. We evaluated various encoder architectures, including gated recurrent unit (GRU), GRU with attention, temporal convolutional network (TCN), and the Transformer encoder, on two complex stress-strain datasets that were designed to include a wide range of complex loading histories and loading conditions. All architectures achieved excellent test results with an root-mean-square error (RMSE) below 1 MPa. Additionally, we analyzed the capability of the different architectures to make predictions on out-of-domain applications, with an uncertainty estimation based on deep ensembles. The proposed approach provides a robust alternative to empirical/semi-empirical models for CRs modeling, offering the potential for more accurate and efficient materials design and optimization.

36 MATERIALS SCIENCE↗

Controlling solute channel formation using magnetic fields

Solute channel formation introduces compositional and microstructural variations in a range of processes, from metallic alloy solidification, to salt fingers in ocean and water reservoir flows. Applying an external magnetic field interacts with thermoelectric currents at solid/liquid interfaces generating additional flow fields. This thermoelectric (TE) magnetohydrodynamic (TEMHD) effect can impact on solute channel formation, via a mechanism recently drawing increasing attention. To investigate this phenomenon, we combined in situ synchrotron X-ray imaging and Parallel-Cellular-Automata-Lattice-Boltzmann based numerical simulations to study the characteristics of flow and solute transport under TEMHD. Observations suggest the macroscopic TEMHD flow appearing ahead of the solidification front, coupled with the microscopic TEMHD flow arising within the mushy zone are the primary mechanisms controlling plume migration and channel bias. Two TE regimes were revealed, each with distinctive mechanisms that dominate the flow. Further, we show that grain orientation modifies solute flow through anisotropic permeability. These insights led to a proposed strategy for producing solute channel-free solidification using a time-modulated magnetic field.

36 MATERIALS SCIENCE↗

Grain boundary solute segregation across the 5D space of crystallographic character

Solute segregation in materials with grain boundaries (GBs) has emerged as a popular method to thermodynamically stabilize nanocrystalline structures. However, the impact of varied GB crystallographic character on solute segregation has never been thoroughly examined. Here, this work examines Co solute segregation in a dataset of 7272 Al bicrystal GBs that span the 5D space of GB crystallographic character. Considerable attention is paid to verification of the calculations in the diverse and large set of GBs. In addition, the results of this work are favorably validated against similar bicrystal and polycrystal simulations. As with other work, we show that Co atoms exhibit strong segregation to sites in Al GBs and that segregation correlates strongly with GB energy and GB excess volume. Segregation varies smoothly in the 5D crystallographic space but has a complex landscape without an obvious functional form.

36 MATERIALS SCIENCE↗

Hierarchical domain structures in buckled ferroelectric free sheets

Flat elastic sheets tend to display wrinkles and folds. From pieces of clothing down to two-dimensional crystals, these corrugations appear in response to strain generated by sheet compression or stretching, thermal or mechanical mismatch with other elastic layers, or surface tension. Extensively studied in metals, polymers and, — more recently — in van der Waals exfoliated layers, with the advent of thin single crystal freestanding films of complex oxides, researchers are now paying attention to novel microstructural effects induced by bending ferroelectric-ferroelastics, where polarization is strongly coupled to lattice deformation. Here we show that wrinkle undulations in BaTiO3 sheets bonded to a viscoelastic substrate transform into a buckle delamination geometry when transferred onto a rigid substrate. Using spatially resolved techniques at different scales (Raman, scanning probe and electron microscopy), we show how these delaminations in the free BaTiO3 sheets display a self-organization of ferroelastic domains along the buckle profile that strongly differs from the more studied sinusoidal wrinkle geometry. Moreover, we disclose the hierarchical distribution of a secondary set of domains induced by the misalignment of these folding structures from the preferred in-plane crystallographic orientations. Our results disclose the relevance of the morphology and orientation of buckling instabilities in ferroelectric free sheets, for the stabilization of different domain structures, pointing to new routes for domain engineering of ferroelectrics in flexible oxide sheets.

36 MATERIALS SCIENCE↗

Energetics of the nucleation and glide of disconnection modes in symmetric tilt grain boundaries

Grain boundaries (GBs) evolve by the nucleation and glide of disconnections, which are dislocations with a step character. In this work, motivated by recent success in predicting GB properties such as the shear coupling factor and mobility from the intrinsic properties of disconnections, we develop a systematic method to calculate the energy barriers for the nucleation and glide of individual disconnection modes under arbitrary driving forces and a quasi-2D setting. This method combines tools from bicrystallography to enumerate disconnection modes and the Nudged elastic band (NEB) method to calculate their energetics, yielding minimum energy paths and atomistic mechanisms for the nucleation and glide of each disconnection mode. We apply the method to accurately predict shear coupling factors of $[001]$ symmetric tilt grain boundaries in Cu. Particular attention is paid to the boundaries where the dislocation-based disconnection nucleation model produces incorrect nucleation barriers. We demonstrate that the method can accurately compute energy barriers and predict shear-coupling factors in the low-temperature regime. For certain disconnection modes in which the assumptions underlying our method do not hold, we report upper bounds on the energy barriers for disconnection nucleation and glide. In addition, the NEB trajectories reveal interesting phenomena such as the dissociation of a higher energy mode into lower energy modes, and in some cases, shear coupling being mediated by partial disconnections, wherein the GB structure temporarily changes to a metastable state before reverting back to its original structure. Graphical abstract

36 MATERIALS SCIENCE↗

Defining and applying an electricity demand flexibility benchmarking metrics framework for grid-interactive efficient commercial buildings

Building demand flexibility (DF) research has recently gained attention. To unlock building DF as a predictable grid resource, we must establish a quantitative understanding of the resource size, performance variability, and predictability based on large empirical datasets. Researchers have proposed various sets of theoretical metrics to measure this performance. Some metrics have been applied to simulation results, but most fall short of exploring the complexities in real building applications. There are practical metrics used in individual demand response field studies but they alone cannot fulfil the job of DF benchmarking across a diverse group of buildings. The electrical grid's geographically diverse and changing nature presents challenges to comparing building DF performance measured under different conditions (i.e., benchmarking DF). To address this challenge, a novel DF benchmarking framework focused on load shedding and shifting is presented; the foundation is a set of simple, proven single-event metrics with attributes describing event conditions. These enable benchmarking and visualization in different dimensions for identifying trends that represent how these attributes influence DF. To test its feasibility and scalability, the DF framework was applied to two case studies of 11 office buildings and 121 big-box retail buildings with demand response participation data. Furthermore, these examples provided a pathway for using both building level benchmarking and aggregation to extract insights into building DF about magnitude, consistency, and influential factors. Potential applications of the framework and real-world values have been identified for grid and building stakeholders.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Physics-informed machine learning for building performance simulation-A review of a nascent field

Building performance simulation (BPS) is critical for understanding building dynamics and behavior, analyzing the performance of the built environment, optimizing energy efficiency, improving demand flexibility, and enhancing building resilience. However, conducting BPS is not trivial. Traditional BPS relies on accurate building energy models, which are primarily physics-based and heavily dependent on detailed building information, expert knowledge, and case-by-case model calibrations, significantly limiting their scalability. With the development of sensing technology and the increased availability of data, there is growing attention and interest in data-driven BPS. However, purely data-driven models often suffer from limited generalization ability and a lack of physical consistency, resulting in poor performance in real-world applications. To address these limitations, recent studies have begun integrating physics priors into data-driven models, a methodology known as physics-informed machine learning (PIML). PIML is an emerging field where its definitions, methodologies, evaluation criteria, application scenarios, and future directions remain open. To bridge those gaps, this study systematically reviews the state-of-the-art PIML for BPS, offering a comprehensive definition of PIML and comparing it to traditional BPS approaches regarding data requirements, modeling effort, performance, and computational cost. We also summarize the commonly used methodologies, validation approaches, application domains, available data sources, open-source packages, and testbeds. In addition, this study provides a general guideline for selecting appropriate PIML models based on BPS applications. Finally, this study identifies key challenges and outlines future research directions, providing a solid foundation and valuable insights to advance R&D of PIML in BPS.

Jiang, Zixin↗

Thermal characterization of the build chamber in electron beam melting

Electron beam powder bed fusion, commonly termed electron beam melting (EBM), offers great versatility in multiple-part processes and can produce high quality as-built components due to low residual stresses. The EBM process is complex and requires careful thermal management, including uniform and consistent preheating of the powder bed, in order to ensure quality and consistency of the product. However, most of the simulations in the literature focus on the selective melting stage of the process. As of today, optimal conditions for initial pre-heating temperatures are only available for specific materials. Thus, in order to extend the EBM technology to other desired build materials, a much better understanding of the pre-heating stages is required. In this work, numerical and experimental approaches are combined in order to investigate the effects and sensitivities of heat removal from the build plate during EBM pre-heating stages. For this purpose, a carefully reconstructed numerical model of the build chamber of an ARCAM Q20 + machine is developed. It includes all main parts of the chamber and all relevant heat transfer mechanisms, whereas special attention is paid to radiation heat exchange between various bodies. In order to validate the model, dedicated experiments are performed, in which a system of thermocouples is installed in the build chamber, allowing direct measurement of the local temperatures of the start-plate and heat shields. A good agreement between the simulation and experimental findings is achieved, leading to a better understanding of the thermal processes characteristic to the pre-heating stages. This basic analysis is followed by a representative pre-heating case, where a powder bed is also considered. The energy required to obtain the desired pre-heating temperatures is evaluated, and the role of the powder bed in heat transfer within the chamber is assessed. The pre-heating stage, simulated in the present work, is supposed to create proper conditions for sintering and consequent melting of the powder, which are highly dependent on the local temperatures and heat transfer features. Thus, the findings of the reported work present a step towards a better understanding of the thermal processes that characterize EBM. The reported model can be further used to provide realistic boundary condition inputs for other meso- or macro-scale models as a function of time and geometry. The model can serve also for verification of machine settings, i.e., jump-safe and melt-safe ones which actually provide desired preheat, and for development of settings for new powders.

36 MATERIALS SCIENCE↗

Microstructure and high temperature tensile properties of 316L fabricated by laser powder-bed fusion

316L stainless steel fabricated by laser powder-bed fusion (LPBF) has attracted significant attention due to a unique combination of strength and ductility at room temperature. Understanding of high temperature tensile properties of LPBF fabricated 316L is, however, limited. In the present investigation, tensile testing was conducted at 20–700ºC on LPBF 316L in as printed condition and after annealing for 5 h at 500–800ºC. Room temperature data confirmed the excellent ductility of the LPBF-processed 316L steel due to the cellular structure with high dislocation density. However, a significant decrease in ductility was observed at temperatures above 200ºC. These results are consistent with a change of deformation mechanisms observed in wrought 316L, with twinning playing a key role at room temperature. Finally, microstructure characterization and tensile testing revealed that the cellular structure is stable up to 500ºC, but a decrease of yield strength was observed at temperatures above 600ºC likely due to a decrease in dislocation density via annealing.

36 MATERIALS SCIENCE↗

Integrating helicoid channels for passive control of fiber alignment in direct-write 3D printing

3D printing of fiber-reinforced composites has been receiving increasing attention as an efficient additive approach enabling lightweight, functional, and high-performance components required for industrial applications. The properties of fiber composites significantly depend on internal microstructures, including fiber orientation, distribution, and degree of alignment. Although multiple strategies have been introduced for controlling the fiber composites microstructures, these strategies are mostly active approaches relying on additional control of mechatronics parts, external forces, or intentionally introduced unstable flows inside narrow nozzles. These methods suffer from higher risk of nozzle clogging and requiring extra parts in 3D printing. Here, we introduce helicoid channels into extrusion system as a passive approach to control the fiber alignment without any additional moving parts in direct-write 3D printing. The helicoid channels automatically guide the composite inks and align fibers before flowing into narrow nozzle space, avoiding clogging and improving printability. The analyses indicate that both helicoid surface to volume ratio and helix angle affect the pre-alignment of fibers, leading to tunable mechanical properties of printed fiber-reinforced composites with increased stiffness and strength up to 77.6% and 47.8%, respectively.

36 MATERIALS SCIENCE↗

Mica filled polyetherketoneketones for material extrusion 3D printing

Polyetherketoneketone (PEKK) has superior physical properties to most available thermoplastics compatible with material extrusion-based 3D printing, including analogs in the polyaryletherketone (PAEK) family. To date, the performance of fused filament fabrication (FFF) compatible PEKK has been detailed primarily as a function of varying the isomer ratios composing the co-polymer structure. The strategy to form blends or composites with PEKK for FFF is attractive for further tailoring of performance in application, yet has received limited attention. Here, we report the integration of three grades of mica platelets into PEKK at 10% and 30% mass loadings to generate an array of filament feedstocks that were then used to print objects with a simple FFF machine. The effects of mica coating chemistry and surface treatment on the compatibility with PEKK and resulting properties are described. Mica fillers at both loadings have only subtle influence on the FFF relevant melt rheological properties inherent to PEKK. Pigment micas at high loadings can lower the melting temperature of PEKK (up to 19 ºC) without shifting its glass transition temperature and inhibit much of the undesirable crystallization occurring during processing with unfilled PEKK. The printed composites were effectively cold crystallized post-printing, affording crystalline fractions up to 90% relative to unfilled PEKK with increased dimensional stabilities. All micas, when used as fillers in low and high relative PEKK crystallinities, significantly increased the tensile modulus (as high as 126% or to 7.31 GPa) of parts in correlation to the loading. Furthermore, the underlying microstructural features of a printed composite were compared to unfilled PEKK by use of a high-resolution helical micro-computed tomography instrument. Practically, pigment micas can confer a wide range of rich colors to 3D-printed PEKK.

36 MATERIALS SCIENCE↗

ThermoPore: Predicting part porosity based on thermal images using deep learning

Part qualification is often a critical and labor-intensive process in additive manufacturing, particularly in the detection of defects such as porosity, which stands to benefit significantly from advancements in machine learning. We present a deep learning approach for quantifying and localizing ex-situ porosity within Laser Powder Bed Fusion fabricated samples utilizing in-situ thermal image monitoring data. Our goal is to build the real time porosity map of parts based on thermal images acquired during the build. The quantification task builds upon the established Convolutional Neural Network model architecture to predict pore count and the localization task leverages the spatial and temporal attention mechanisms of the novel Video Vision Transformer model to indicate areas of expected porosity. Our model for porosity quantification achieved a R 2 score of 0.57 and our model for porosity localization produced an average Intersection over Union (IoU) score of 0.32 and a maximum of 1.0. This work is setting the foundations of part porosity “Digital Twins” based on additive manufacturing monitoring data and can be applied downstream to reduce time-intensive post-inspection and testing activities during part qualification and certification. In addition, we seek to accelerate the acquisition of crucial insights normally only available through ex-situ part evaluation by means of machine learning analysis of in-situ process monitoring data.

Deep learning↗