Microscopic Volume Research Articles

Multiscale contact homogenisation: A novel perspective through the method of multiscale virtual power

The interaction between deformable bodies and rigid foundations undergoing finite strains is explored in this work with the Method of Multiscale Virtual Power, unlocking novel insights into contact homogenisation theories. The focus lies in establishing the foundational kinematical links across scales and achieving seamless homogenisation of the traction vector through rigorous duality arguments. Two distinct families of contact homogenisation models are formulated: surface–surface and surface–volume models. These families emerge from the virtual power balance established between the target macroscopic surface and the corresponding microscopic contact surface or volume. They not only represent fundamental kinematical entities at each scale but also enable the replacement of the heterogeneous contact traction distribution with a smooth, homogenised version. Microscale equilibrium problems and homogenisation relations, along with the relevant macro- and microscale quantities, are derived by means of straightforward variational arguments. Furthermore, potential finite size effects are addressed in the homogenised response, enhancing the reliability and applicability of the strategy across diverse scenarios. Promising submodels have been identified within both families, broadening the understanding of multiscale contact phenomena and including existing models as particular cases. The proposed continuum-based variational families of models naturally lead to generic finite element-based frameworks for contact homogenisation of heterogeneous solids, as described in a forthcoming paper.

Water and brain function: effects of hydration status on neurostimulation with transcranial magnetic stimulation.

Neurostimulation/neurorecording are tools to study, diagnose, and treat neurological/psychiatric conditions. Both techniques depend on volume conduction between scalp and excitable brain tissue. Here, we examine how neurostimulation with transcranial magnetic stimulation (TMS) is affected by hydration status, a physiological variable that can influence the volume of fluid spaces/cells, excitability, and cellular/global brain functioning. Normal healthy adult participants (32, 9 males) had common motor TMS measures taken in a repeated-measures design from dehydrated (12-h overnight fast/thirst) and rehydrated (identical dehydration protocol followed by rehydration with 1 L water in 1 h) testing days. The target region was left primary motor cortex hand area. Response at the target muscle was recorded with electromyography. Urinalysis confirmed hydration status. Motor hotspot shifted in half of participants. Motor threshold decreased in rehydration, indicating increased excitability. Even after redosing/relocalizing TMS to the new threshold/hotspot, rehydration still showed evidence of increased excitability: recruitment curve measures generally shifted upward and the glutamate-dependent paired-pulse protocol, short intracortical facilitation (SICF), was increased. Short intracortical inhibition (SICI), long intracortical inhibition (LICI), long intracortical facilitation (LICF), and cortical silent period (CSP) were relatively unaffected. The hydration perturbations were mild/subclinical based on the magnitude/speed and urinalysis. Motor TMS measures showed evidence of expected physiological changes of osmotic challenges. Rehydration showed signs of macroscopic and microscopic volume changes including decreased scalp-cortex distance (brain closer to stimulator) and astrocyte swelling-induced glutamate release. Hydration may be a source of variability affecting any techniques dependent on brain volumes/volume conduction. These concepts are important for researchers/clinicians using such techniques or dealing with the wide variety of disease processes involving water balance.NEW & NOTEWORTHY Hydration status can affect brain volumes and excitability, which should affect techniques dependent on electrical volume conduction, including neurostimulation/recording. We test the previously unknown effects of hydration on neurostimulation with TMS and briefly review relevant physiology of hydration. Rehydration showed lower motor threshold, shifted motor hotspot, and generally larger responses even after compensating for threshold/hotspot changes. This is important for clinical and research applications of neurostimulation/neurorecording and the many clinical disorders related to water balance.

The Influence of the Interface on the Micromechanical Behavior of Unidirectional Fiber-Reinforced Ceramic Matrix Composites: An Analysis Based on the Periodic Symmetric Boundary Conditions

The long-term periodicity and uncontrollable interface properties during the preparation process for silicon carbide fiber reinforced silicon carbide-based composites (SiCf/SiC CMC) make it difficult to thoroughly investigate their mechanical damage behavior under complex loading conditions. To delve deeper into the influence of the interface strength and toughness on the mechanical response of microscopic representative volume element (RVE) models under complex loading conditions, in this work, based on numerical simulation methods, a microscale representative volume element (RVE) with periodic symmetric boundary conditions for the material is constructed. The phase-field fracture theory and cohesive zone model are coupled to capture the brittle cracking of the matrix and the debonding behavior at the fiber/matrix interface. Simulation analysis is conducted for tensile, compressive, and shear loading as well as combined loading, and the validity of the model is verified based on the Chamis theory. Further investigation is conducted into the mechanical response behavior of the microscale RVE model under complex loading conditions in relation to the interface strength and interface toughness. The results indicate that under uniaxial loading, increasing the interface strength leads to a tighter bond between the fiber and matrix, suppressing crack initiation and propagation, and significantly increasing the material’s fracture strength. However, compared to the transverse compressive strength, increasing the interface strength does not continuously enhance the strength under other loading conditions. Meanwhile, under the condition of strong interface strength of 400 MPa, an increase in the interface toughness significantly increases the transverse compressive strength of the material. When it increases from 2 J/m2 to 20 J/m2, the transverse compressive strength increases by 28.49%. Under biaxial combined loading, increasing the interface strength significantly widens the failure envelope space under σ2-τ23 combined loading; with the transition from transverse compressive stress to tensile stress, the transverse shear strength shows a trend of first increasing and then decreasing, and when the ratio of transverse shear displacement to transverse tensile/compressive displacement is −1, it reaches the maximum. This study provides strong numerical support for the investigation of the interface properties and mechanical behavior of SiCf/SiC composites under complex loading conditions, offering important references for engineering design and material performance optimization.

Multiscale modeling for the impact behavior of 3D angle-interlock woven composites

In this paper, a multiscale modeling framework predicting the impact response of three-dimensional angle-interlock woven composites (3DAWCs) is presented. Multiscale modeling is performed sequentially at the mirco, meso, and macroscales. A microscopic representative volume element (RVE) model is established to characterize the yarn's nonlinear mechanical properties and damage behavior at different strain rates. At the mesoscale, a novel subcell-based discretization scheme is proposed to discretize 3DAWCs, and developing six representative subcells (RSCs) that bridge the microscale and macroscale effective properties. Based on it, a ballistic impact model involving six kinds of homogeneous material bricks is established. Furthermore, elastic-viscoplastic damage constitutive models are developed for the epoxy matrix and the yarn, respectively, to enhance the predicted accuracy of the multiscale model. Ballistic impact tests of 3DAWCs are conducted, and X-ray micro-computed tomography is employed to evaluate the internal damage of the 3DAWC target after impact. Validation work is conducted by comparing the experimental and numerical results of the ballistic impact of the 3DAWC target, which indicates the effectiveness and efficiency of the developed multiscale framework in the impact damage prediction of 3DAWCs.

Octopaminergic descending neurons in Drosophila: Connectivity, tonic activity and relation to locomotion

Projection neurons that communicate between different brain regions and local neurons that shape computation within a brain region form the majority of all neurons in the brain. Another important class of neurons is neuromodulatory neurons; these neurons are in much smaller numbers than projection/local neurons but have a large influence on computations in the brain. Neuromodulatory neurons are classified by the neurotransmitters they carry, such as dopamine and serotonin. Much of our knowledge of the effect of neuromodulators comes from experiments in which either a large population of neuromodulatory neurons or the entire population is perturbed. Alternatively, a given neuromodulator is exogenously applied. While these experiments are informative of the general role of the neurotransmitter, one limitation of these experiments is that the role of individual neuromodulatory neurons remains unknown. In this study, we investigate the role of a class of octopaminergic (octopamine is the invertebrate equivalent of norepinephrine) neurons in Drosophila or fruit fly. Neuromodulation in Drosophila work along similar principles as humans; and the smaller number of neuromodulatory neurons allow us to assess the role of individual neurons. This study focuses on a subpopulation of octopaminergic descending neurons (OA-DNs) whose cell bodies are in the brain and project to the thoracic ganglia. Using in-vivo whole-cell patch-clamp recordings and anatomical analyses that allow us to compare light microscopy data to the electron microscopic volumes available in the fly, we find that neurons within each cluster have similar physiological properties, including their relation to locomotion. However, neurons in the same cluster with similar anatomy have very different connectivity. Our data is consistent with the hypothesis that each OA-DN is recruited individually and has a unique function within the fly's brain.

A constitutive model of solid propellants considering aging and confinement pressure

AbstractAging during storage and confinement pressure during launch are the two major loading conditions that affect the integrity of solid rocket motors. In comparison to other component materials, solid propellants, as highly filled composites, have a low modulus and fracture toughness and are therefore common sources of failure. The key to improving the integrity of the solid rocket motor is in assessing the health of the solid propellants during storage or launch. To address this issue, we revised the previous model for the progressive damage viscoelasticity of solid propellants to include the effect of chemical aging during storage and the influence of confinement pressure during launch. Specifically, the increase in relaxation time due to aging and the nonequilibrium volume dilatation characteristics under triaxial tension and compression of solid propellants have been considered. To validate the developed model, standard relaxation tests and uniaxial tensile tests on solid propellants without aging were used to calibrate the model parameters. Furthermore, the model was validated by comparison with uniaxial tensile tests under confined pressure after aging and well predicts the aging temperature/time‐dependent mechanical responses of solid propellants. After validation, the developed model was used to study the influence of confinement pressure on microscopic damage evolution and macroscopic volume expansion. Overall, the developed model can be used for the analysis of the integrity of the solid rocket motor after the aging process.

Identification and extraction of cementation patterns in sand modified by MICP: New insights at the pore scale.

Microbially induced calcium carbonate precipitation (MICP) is an environmentally friendly technology that improves soil permeability resistance through biocementation. In this study, 2D microscopic analysis and 3D volume reconstruction were performed on river sand after 24 cycles of bio-treatment based on stacked images and computed tomography (CT) scanning data, respectively, to extract biocementation patterns between particles. Based on the mutual validation findings of the two techniques, three patterns in the biocemented sand were identified as G-C-G, G-C, and G-G. Specifically, 2D microscopic analysis showed that G-C-G featured multi-particle encapsulation and bridging, with a pore filling ratio of 81.2%; G-C was characterized by locally coated particle layers, with a pore filling ratio of 19.7%; and the G-G was marked by sporadic filling of interparticle pores, with a pore filling ratio of 11.7%. G-C-G had the best cementation effect and permeability resistance (effective sealing rate of 68.5%), whereas G-C (effective sealing rate of 2.4%) had a relatively minor contribution to pore-filling and flow sealing. 3D volume reconstruction showed that G-C-G had the highest pore filling rate, followed by G-G and G-C. The average filling ratios of area and volume for G-C-G were 83.979% and 77.257%, respectively; for G-G 20.360% and 23.600%; and for G-C 11.545% and 11.250%. The analysis of the representative element volume (REV) was conducted, and the feasibility and reliability of the micro-scale pattern extraction results were confirmed to guide the analysis of macro-scale characteristics. The exploration of the effectiveness of cementation patterns in fluid sealing provides valuable insights into effective biocementation at the pore scale of porous media, which may inspire future research.

Proton-Assisted Assembly of Colloidal Nanoparticles into Wafer-Scale Monolayers in Seconds.

Underwater adhesion processes in nature promise controllable assembly of functional nanoparticles for industrial mass production; However, their artificial strategies have faced challenges to uniformly transfer nanoparticles into a monolayer, particularly those below 100nm in size, over large areas. Here a scalable "one-shot" self-limiting nanoparticle transfer technique is presented, enabling the efficient transport of nanoparticles from water in microscopic volumes to an entire 2-inch wafer in a remarkably short time of 10 seconds to reach near-maximal surface coverage (≈40%) in a 2D mono-layered fashion. Employing proton engineering in electrostatic assembly accelerates the diffusion of nanoparticles (over 50 µm2/s), resulting in a hundredfold faster coating speed than the previously reported results in the literature. This charge-sensitive process further enables "pick-and-place" nanoparticle patterning at the wafer scale, with large flexibility in surface materials, including flexible metal oxides and 3D-printed polymers. As a result, the fabrication of wafer-scale disordered plasmonic metasurfaces in seconds is successfully demonstrated. These metasurfaces exhibit consistent resonating colors across diverse material and geometrical platforms, showcasing their potential for applications in full-color painting and optical encryption devices.

Prediction and adjustment of elastic properties in three‐dimensional orthogonal woven composites through dual‐scale modeling

AbstractThree‐dimensional (3D) orthogonal woven composites can overcome the drawback of weak interlaminar strengths in traditional laminated composites and exhibit excellent resistance to out‐of‐plane impact, however, the significant difference in properties in the in‐plane orthogonal direction will limit the potential range of application thereof. Predicting elastic properties and exploring methods of adjustment are therefore of paramount importance. Using computed tomography (CT) scanning to obtain detailed parameter models, a corresponding dual‐scale model of microscopic representative volume element (RVE) and mesoscopic RVE was established, and the accuracy of the model was experimentally validated, which can predict the elastic properties of materials. In addition, the influences of the yarn fiber volume fraction and weaving distance on elastic properties were evaluated using the elastic modulus visualization method, and a formula integrating these two factors is provided for adjustment of the in‐plane orthogonal Young's modulus.Highlights Experimentally validated microscale and mesoscale RVE models were established. The influences of factors on elastic properties were visualized. The relationship between Young's modulus and influencing factors was derived. A reliable strategy for adjusting the in‐plane Young's modulus was proposed.

Accounting for mesoscale geometry and intra-yarn fiber volume fraction distribution on 3D angle-interlock fabric permeability

Understanding resin flows within 3D interlock fabrics involves addressing a dual-scale flow problem. Indeed, the fluid can flow through inter-yarn channels, characterized by a unit cell mesoscale morphology, but also within yarns considered as homogeneous equivalent porous media. The former is assumed to follow the Stokes’ law while the latter be related to the Darcy’s law, directly linked to the microscopic intra-yarn fiber volume fraction (FVF) field. In this work, a coupled Stokes–Darcy steady-state flow within a 3D woven textile, modeled at mesoscale, is solved through a finite element monolithic approach with a mixed velocity-pressure formulation, stabilized by the Variational MultiScale Method (VMS) and implemented in the Z-set software. The fabric permeability tensor is then computed without any assumptions on its nature and analyzed both through its diagonal components, its eigenvectors and eigenvalues. The main contribution of this study lies in examining the influence of variations of the inter-yarn porous medium morphology, through textile compaction and geometrical reduction to prevent edge flows, and the intra-yarn permeability (from complete field to unique value) on the overall fabric permeability.

Deep-learning-assisted snapshot optical tomography for microscopic volume prediction: a simulation study.

In this simulation study, we demonstrate fast-yet-accurate volume measurement of microscopic objects by combining snapshot optical tomography and deep learning. Snapshot optical tomography simultaneously collects a multitude of projection images and thus can perform 3D imaging in a single snapshot. However, as with other wide-field microscopy techniques, it suffers from the missing-cone problem, which can seriously degrade the quality of 3D reconstruction. We use deep learning to generate a volume prediction from 2D projection images bypassing the 3D reconstruction.

Grain shape-protrusion-based modeling and analysis of material removal in robotic belt grinding

The accurate prediction of material removal (MR) remains a persistent challenge in the field of robotic belt grinding, particularly with the consideration of the stochastic nature of abrasive grains. Starting from the characteristics that abrasive grains with different shapes participate in grinding, this work presents a novel MR model that extends from microscopic grain-workpiece interaction to macroscopic wheel-curved surface contact. Specifically, the irregular shapes of single abrasive grains are generalized into four typical types, namely, semi-sphere, cone, equilateral-triangular pyramid, and square pyramid. Based on the effective abrasive grains determined by stochastic grain protrusion heights, the microscopic contact force and material removal volume shared by different effective individual abrasive grains are modeled and analyzed subsequently. Together with the macroscopic contact pressure solved by the Hertzian contact theory, the material removal model is derived by considering the geometrical characteristics of different-shaped abrasive grains. Finally, the grinding experiments on the Ti–6Al–4V test block and aero-engine blade were conducted under controllable grinding parameters, through which the effectiveness and applicability of the proposed model were validated, and the material removal characteristics with different structured abrasive belts were investigated.

Across the stages: a multiscale extension of the generalized stochastic microdosimetric model (MS-GSM2) to include the ultra-high dose rate

Ultra-high dose rate (UHDR) irradiations with different types of radiation have shown a larger sparing of normal tissue and unchanged tumor control with respect to conventional delivery. In recent years, there has been an accumulation of experimental evidence related to the so-called FLASH effect. However, the underpinning mechanism remains, to date, extremely debated and largely unexplained, while the involvement of multiple scales of radiation damage has been suggested. Since it is believed that the chemical environment plays a crucial role in the FLASH effect, this work aims to develop a multi-stage tool, the multiscale generalized stochastic microdosimetric model (MS-GSM2), that can capture several possible effects on DNA damage at the UHDR regime, such as reduction of DNA damage yield due to organic radical recombination, damage fixation due to oxygenation, and spatial and temporal dose deposition effects, allowing us to explore most of the candidate mechanisms for explaining the FLASH effect. The generalized stochastic microdosimetric model (GSM2) is a probabilistic model that describes the time evolution of DNA damage in a cell nucleus using microdosimetric principles, accounting for different levels of spatio-temporal stochasticity. In particular, the GSM2 describes radiation-induced DNA damage formation and kinetic repair in the case of protracted irradiation without considering the Poissonian assumption to treat the number of radiation-induced DNA damage. In this work, we extend the GSM2, coupling the evolution of DNA damage to fast chemical reaction kinetics, described by a system of ordinary differential equations, accounting for an additional level of stochasticity, i.e., in chemistry. We simulate energy deposition by particles in a microscopic volume, which mimics the cell nucleus, in order to examine the combined effects of several chemical species and the time evolution of DNA damage. We assume that UHDR modifies the time evolution of the peroxyl radical concentration, with a consequent reduction in the yield of the indirect DNA damage. This damage reduction emerges only at UHDR and is more pronounced at high doses. Moreover, the indirect damage yield reduction depends on the radiation quality. We show that the MS-GSM2 can describe the empirical trend of dose- and dose rate-dependent cell sensitivity over a broad range, particularly the larger sparing of healthy tissue occurring at the FLASH regime. The complete generality of the MS-GSM2 also allows us to study the impact of different dose delivery time structures and radiation qualities, including high LET beams.

A two-scale numerical study on the mechanobiology of abdominal aortic aneurysms.

Abdominal aortic aneurysms (AAAs) are a serious condition whose pathophysiology is related to phenomena occurring at different length scales. To gain a better understanding of the disease, this work presents a multi-scale computational study that correlates AAA progression with microstructural and mechanical alterations in the tissue. Macro-scale geometries of a healthy aorta and idealized aneurysms with increasing diameter are developed on the basis of existing experimental data and subjected to physiological boundary conditions. Subsequently, microscopic representative volume elements of the abluminal side of each macro-model are employed to analyse the local kinematics at the cellular scale. The results suggest that the formation of the aneurysm disrupts the micromechanics of healthy tissue, which could trigger collagen growth and remodelling by mechanosensing cells. The resulting changes to the macro-mechanics and microstructure of the tissue seem to establish a new homeostatic state at the cellular scale, at least for the diameter range investigated.

Data‐driven finite element computation of microstructured materials

AbstractThis paper presents a model‐free data‐driven strategy for linear and non‐linear finite element computations of open‐cell foam. Employing sets of material data, the data‐driven problem is formulated as the minimization of a distance function subjected to the physical constraints from the kinematics and the balance laws of the mechanical problem.The material data sets of the foam are deduced here from representative microscopic material volumes. These volume elements capture the stochastic characteristics of the open‐cell microstructure and the properties of the polyurethane material. Their computation provides the required stress‐strain data used in the macroscopic finite element computations without postulating a specific constitutive model. The paper shows how to derive suitable material data sets for the different cases of (non‐)linear and (an‐)isotropic material behavior efficiently. The numerical example of a rubber sealing illustrates possible areas of application, and the proposed strategy's versatility.

Imaging local diffusion in microstructures using NV-based pulsed field gradient NMR.

Understanding diffusion in microstructures plays a crucial role in many scientific fields, including neuroscience, medicine, or energy research. While magnetic resonance (MR) methods are the gold standard for diffusion measurements, spatial encoding in MR imaging has limitations. Here, we introduce nitrogen-vacancy (NV) center-based nuclear MR (NMR) spectroscopy as a powerful tool to probe diffusion within microscopic sample volumes. We have developed an experimental scheme that combines pulsed gradient spin echo (PGSE) with optically detected NV-NMR spectroscopy, allowing local quantification of molecular diffusion and flow. We demonstrate correlated optical imaging with spatially resolved PGSE NV-NMR experiments probing anisotropic water diffusion within an individual model microstructure. Our optically detected PGSE NV-NMR technique opens up prospects for extending the current capabilities of investigating diffusion processes with the future potential of probing single cells, tissue microstructures, or ion mobility in thin film materials for battery applications.

Multiscale progressive damage model for plain woven composites

In this paper, a novel multiscale progressive damage model is proposed to study the complex mechanical behavior and damage mechanism of plain woven composites. In the macroscale, composites are treated as full-scale model with three-dimensional solid elements. The mechanical response of element integration points depends on the mesoscale constitutive relationship, including orthotropic undulating yarn and isotropic matrix. Based on the microscopic representative volume element (RVE), the stress amplification factor (SAF) database is introduced to characterize the microscale stress state of the fiber and matrix. SAF is used to realize the stress correlation calculation from the yarn level to the micro level, and a progressive damage model based on the micro-mechanics of failure (MMF) theory is developed. Quasi-static tension experiments are carried out to validate the accuracy of the model, and the influence of meso‑scale waviness and non-waviness constitutive models on the simulation results is compared. The results indicate the waviness constitutive model predicts are more consistent with the experimental results, and the prediction deviations about modulus, failure strength and failure strain are around 5%. The damage initiation of matrix in the yarn and pure matrix occurs successively, and finally the fiber failure is the main cause of catastrophic damage. Furthermore, the proposed multiscale method can be further used to predict the strength and damage of full-size woven composites under complicated loading.

Micromechanical deformation modeling and failure prediction of thermoplastic composites

Based on the multi-scale progressive homogenization theory, a micromechanical model is proposed that can predict the plastic deformation of thermoplastic fiber-reinforced composites. By developing microscopic representative volume elements (RVEs) that include three materials phases: fiber, matrix and fiber–matrix interface, the effect of elastic–plastic material behaviors and interface debonding on the mechanical properties of thermoplastic composites can be considered. Employing this model, the deformation and failure process of carbon fiber reinforced PEEK composite is studied, considering the effects of random size and distribution of carbon fiber, as well as the ratio of interface debonding. It can be found that the yielding strength is most sensitive to the proportion of interface debonding compared to Young’s modulus and ultimate strength. Interface debonding has the most significant impact on the mechanical performances of thermoplastic composites by introducing a higher degree of plastic deformation into the polymer matrix and changing the evolution path of material damage.

Erosion evolution and mass loss of polyimide in AO environment using 3D Monte Carlo method

Polyimide films coated on the surface of satellites are exposed to atomic oxygen (AO) environment during service. This will suffer variation of microscopic structure and morphology, leading to corrosion and mass loss in macroscopic. In this work, a 3D undercutting model based on Monte Carlo method (MC) and Ray Tracing method was constructed, with which the AO related erosion feature of polyimide film was evaluated. Then, we predicted the evolution of erosion cross-section of the coated material with defect of different sizes and shapes exposed in higher AO fluence. The macroscopic mass loss was derived by the eroded microscopic volume and material density, during which the actual roughness was considered in our proposed undercutting model. This work provides insights into the study of microscopic 3D erosion morphology and connects with macroscopic mass loss in experiment at higher fluences.

Reduced order homogenization of thermoelastic materials with strong temperature dependence and comparison to a machine-learned model

In this work, an approach for strongly temperature-dependent thermoelastic homogenization is presented. It is based on computational homogenization paired with reduced order models (ROMs) that allow for full temperature dependence of material parameters in all phases. In order to keep the model accurate and computationally efficient at the same time, we suggest the use of different ROMs at few discrete temperatures. Then, for intermediate temperatures, we derive an energy optimal basis emerging from the available ones. The resulting reduced homogenization problem can be solved in real time. Unlike classical homogenization where only the effective behavior, i.e., the effective stiffness and the effective thermal expansion, of the microscopic reference volume element are of interest, our ROM delivers also accurate full-field reconstructions of all mechanical fields within the microstructure. We show that the proposed method referred to as optimal field interpolation is computationally as efficient as simplistic linear interpolation. However, our method yields an accuracy that matches direct numerical simulation in many cases, i.e., very accurate real-time predictions are achieved. Additionally, we propose a greedy sampling procedure yielding a minimal number of direct numerical simulations as inputs (two to six discrete temperatures are used over a range of around 1000 K). Further, we pick up a black box machine-learned model as an alternative route and show its limitations in view of the limited amount of training data. Using our new method to generate an abundance of data, we demonstrate that a highly accurate tabular interpolator can be gained easily.