Validity Of Solution Research Articles

Toward robust scalar-based gradient plasticity modeling and simulation at finite deformations

Strain gradient plasticity has been the subject of extensive research in the past 40 years in order to model size effects in metal plasticity, on the one hand, and provide finite width shear bands in the simulation of localization phenomena, on the other hand. However, the use of the emerging models is still limited to academic applications and has not yet been adopted by industry practitioners. The present paper systematically reviews the pros and the cons of gradient plasticity at finite strains based on the gradient of scalar plastic variables, in particular the gradient of the cumulative plastic strain. It proposes benchmark tests addressing both size effect modeling and plastic strain localization simulation. It includes new analytical solutions for validation of FE implementation. It focuses on the micromorphic approach to gradient plasticity, as a convenient method for implementation in FE codes. New features of the analysis include the comparison of three distinct formulations of rate-independent gradient plasticity at finite deformations, based on the multiplicative decomposition of the deformation gradient and on quadratic potentials with respect to gradient terms. The performance of micromorphic and Lagrange-multiplier-based strain gradient plasticity models is evaluated for various monotonic and cyclic loading conditions including confined plasticity in simple glide and tension, bending and torsion at large deformations. Limitations are pointed out in the case of bending and torsion, which can be overcome for instance by the use of the gradient of equivalent plastic strain model.

Robust deep learning-based forward dose calculations for VMAT on the 1.5T MR-linac

In this work we present a framework for robust deep learning-based VMAT forward dose calculations for the 1.5T MR-linac. A convolutional neural network was trained on the dose of individual multi-leaf-collimator VMAT segments and was used to predict the dose per segment for a set of MR-linac-deliverable VMAT test plans. The training set consisted of prostate, rectal, lung and esophageal tumour data. All patients were previously treated in our clinic with VMAT on a conventional linac. The clinical data were converted to an MR-linac environment prior to training. During training time, gantry and collimator angles were randomized for each training sample, while the multi-leaf-collimator shapes were rigidly shifted to ensure robust learning. A Monte Carlo dose engine was used for the generation of the ground truth data at 1% statistical uncertainty per control point. For a set of 17 MR-linac-deliverable VMAT test plans, generated on a research treatment planning system, our method predicted highly accurate dose distributions, reporting 99.7% ± 0.5% for the full plan prediction at the 3%/3 mm gamma criterion. Additional evaluation on previously unseen IMRT patients passed all clinical requirements resulting in 99.0% ± 0.6% for the 3%/3 mm analysis. The overall performance of our method makes it a promising plan validation solution for IMRT and VMAT workflows, robust to tumour anatomies and tissue density variations.

Unsteady Water-Based Ternary Hybrid Nanofluids on Wedges by Bioconvection and Wall Stretching Velocity: Thermal Analysis and Scrutinization of Small and Larger Magnitudes of the Thermal Conductivity of Nanoparticles

The uniqueness of nanofluids in the field of thermal analysis and engineering is associated with their thermal conductivity and thermodynamics. The dynamics of water made up of (i) single-walled carbon nanotubes with larger magnitudes of thermal conductivity of different shapes (i.e., platelet, cylindrical, and spherical) and (ii) moderately small magnitudes of thermal conductivity (i.e., platelet magnesium oxide, cylindrical aluminum oxide, spherical silicon dioxide) were explored in order to address some scientific questions. In continuation of the exploration and usefulness of ternary hybrid nanofluid in hydrodynamics and geothermal systems, nothing is known on the comparative analysis between the two dynamics outlined above due to the bioconvection of static wedges and wedges with stretching at the wall. Reliable and valid numerical solutions of the governing equation that models the transport phenomena mentioned above are presented in this report. The heat transfer through the wall increased with the wall stretching velocity at a smaller rate of 0.52 and a higher rate of 0.59 when the larger and smaller thermal conductivity of nanoparticles were used, respectively. Larger or smaller magnitudes of the thermal conductivity of nanoparticles were used; the wall stretching velocity had no significant effects on the mass transfer rate but the distribution of the gyrotactic microorganism was strongly affected. Increasing the stretching at the wedge’s wall in the same direction as the transport phenomenon is suitable for decreasing the distribution of temperature owing to the higher velocity of ternary hybrid nanofluids either parallel or perpendicular to the wedge.

Effect of density change during solidification using variable time step method

A numerical solution has been developed for variable density phase change with shrinkage or expansion using the variable time step method, where the grid spacing is kept constant while the time step is kept as a variable. The temperature distribution has been studied as a function of position and time for different partition coefficient, initial and boundary temperatures. The key effect that has been investigated is the effect of the density variation due to phase change during solidification. The numerical solution obtained has been compared with that of the analytical solution for validation. It is found that with increase in density ratio, the interface moves slower for undercooled initial temperature and vice versa for superheated initial temperature. It is also seen that with a decrease in initial and boundary temperature, the interface moves faster.

What Does It Take to Solve the 3D Ising Model? Minimal Necessary Conditions for a Valid Solution.

An exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough, fomenting great prospects for further application, similarly to what happened when Lars Onsager solved the two-dimensional model eighty years ago. Hence, there have been many attempts to find analytic expressions for the exact partition function Z, but all such attempts have failed due to unavoidable conceptual or mathematical obstructions. Given the importance of this simple yet paradigmatic model, here we set out clear-cut criteria for any claimed exact expression for Z to be minimally plausible. Specifically, we present six necessary-but not sufficient-conditions that Z must satisfy. These criteria will allow very quick plausibility checks of future claims. As illustrative examples, we discuss previous mistaken "solutions", unveiling their shortcomings.

Hybrid 802.11p‐cellular architecture for NDN‐based VANET

SummaryVehicular network communications (VANET) face multiple challenges due to their intermittent connections and the rapid changes in their topologies. In recent years, several research efforts have explored the use of content‐centric approaches to alleviate some of these challenges. One of these promising network designs is Named Data Networking (NDN), which has become a valid solution to support VANET applications. However, in the NDN architecture, the main forwarding mechanism for the interest packets is flooding. This forwarding mechanism will result in excessive collisions, which will lead to the broadcast storm problem. In this paper, we propose VC‐NDN: a hybrid and hierarchical Named Data Networking architecture for VANETs. VC‐NDN improves content retrieval efficiency through an adapted NDN‐based communication model. VC‐NDN includes a new interest forwarding scheme to reduce packet collision in the network and an efficient mechanism to support push‐based traffic. Furthermore, to reduce communication costs, VC‐NDN uses two communication technologies in parallel, namely, IEEE 802.11p and cellular communications, while keeping the usage of the cellular network at a minimum level. Finally, to reduce the impact on vehicle mobility, VC‐NDN follows a hierarchical clustering architecture. Specifically, a density‐based clustering algorithm is designed to create and maintain stable clusters with multihop communication capability. Our performance study shows that VC‐NDN outperforms the basic VNDN solutions in terms of data retrieval delay and packet delivery ratio while minimizing the usage of the cellular network.

Treatment of skin defects with PRP enriched with hyaluronic acid - histological aspects in rat model.

Tissue healing is a complex, dynamic process, characterized by the replacement of devitalized and absent cell and tissue structures. This can be obtained by different methods, these being found in the "reconstructive scale", which although it is very rich does not offer a universally valid solution for closing skin wounds. In plastic surgery, platelet-rich plasma (PRP) has proven effective in the treatment of skin graft donor areas, burn wounds, skin grafts, tendons, or varicose ulcers. Also, hyaluronic acid (HA) has found its utility in different areas of medicine, other than the esthetics field, with satisfactory results after its use in various lesions. The aim of our study was to find a method of healing wounds with skin defect that shortens the time of complete epithelialization compared to native healing, which is accessible to any patient both by its simplicity and by the lowest possible costs. So, we decided to test a preparation consisting of PRP and granular HA in this type of wounds on a group of 30 Wistar rats. Corroborating the macroscopic data with the microscopic ones, an important similarity can be observed between the healing of the adjuvant-treated lesion at 14 days postoperatively and the healing of the lesion left to natural healing at 21 days, thus shortening the healing period by seven days.

Impossibility results about inheritance and order of death.

If several relatives died with no will, the order of their deaths could affect the inheritance result. When the order of death is unknown, there are three approaches to determine the inheritance result in this simultaneous death situation: apply an inheritance method that is not affected by the order of death; artificially assign the order of death; stipulate that persons with unknown orders do not inherit each other. The last approach is adopted by the current French Civil Code (denoted as the French Approach). We prove that under some basic requirements, the French Approach is the only valid solution to the order of death problem. Therefore, the inheritance law of a country that does not adopt the French Approach either has unsolvable inheritance problems or violates basic requirements. In the appendix, we study the existence and uniqueness of inheritance methods that are invariant for different orders of death and only violate one requirement, such as gender equality.

Gasification of Solid Recovered Fuels with Variable Fractions of Polymeric Materials

Gasification is a promising thermochemical technology used to convert waste materials into energy with the introduction of low amounts of an oxidant agent, therefore producing an environmental impact that is lower when compared to incineration and landfilling. Moreover, gasification allows a sustainable management of wastes and reduces the use of fossil fuels responsible for the increment of greenhouse gases. This work aimed to perform gasification tests with solid recovered fuels (SRF) containing organic fractions mainly retrieved from construction and demolition wastes to assess the potential for energy conversion. Tests were conducted in a pilot-scale downdraft gasifier (maximum feedstock input of 22 kg/h) at c.a. 800 °C, using SRF samples containing different proportions of polymeric wastes ranging between 0 and 20 wt %. Gas and chars obtained as by-products were analysed to evaluate their properties and to establish valid pathways for their valorisation. The addition of polymeric wastes reduced char production but rose both tar and HCl concentrations in the gas. The SRF with 10 wt % of polymeric wastes generated the best results, producing the highest calorific value for the gas (3.5 MJ/Nm3) and the highest cold-gas efficiency (45%). Possible char applications include their use as catalysts for tar decomposition, or as an additive in construction materials. Gasification can therefore be considered a valid solution for the energetic valorisation of these SRFs.

Two-piece zirconia implants in the posterior mandible and maxilla: A cohort study with a follow-up period of 9 years.

Long-term follow-up observations of zirconia implants are rare. This study aimed at evaluating the clinical performance of two-piece zirconia implants in the posterior jaws over 9 years. Sixty partially edentulous patients were treated with two-piece zirconia implants. In eight no primary stability could be achieved. Fifty-two patients received the final restoration (i.e., cemented fibreglass abutments and all-ceramic crowns). After 2 years, 2 implants failed and 4 dropouts were recorded. The remaining 46 patients with one target implant each were recalled at 9 years. Besides implant survival, clinical parameters at the implant level (plaque index-PI, bleeding on probing-BOP, probing depth-PD, mucosal recession-MR) were recorded and compared with previously collected data. Mechanical and technical complications were assessed. Thirty patients responded. The mean observation period was of 111.1 ± 2.2months. One implant was lost. Data recorded from the remaining 29 implants were analysed. PI values increased overtime. Mean BOP and PD remained unchanged during follow-up. No additional cases of peri-implantitis were recorded over the 10 diagnosed during the first 2 years of follow-up. No significant changes in mean MR values were detected over time, with 65% of the all included implants exhibiting no recession at 9 years and all the others, but one, a maximum MR of 1 mm. Three technical and 6 mechanical complications occurred in 7 patients between 2- and 9-years (6.9% and 20.7%, respectively, at patient level). Within the limitations of the present study, a high survival rate was registered. Albeit frequent mechanical and technical complications, two-piece zirconia implants could represent a valid solution for the replacement of single teeth in the posterior jaws.

Lung donation after circulatory death: A single-centre experience with uncontrolled donors with some considerations

IntroductionOrgan shortage represents one of the main issues associated with lung transplantation (LTx). Over the years, in an attempt to increase the donor pool, the use of donors after cardiac death (DCDs) has gradually increased, with good results that bode well for their wider use in the future. MethodsIn this work, our experience with DCDs is presented. In addition, a brief literature review on controlled (c) and uncontrolled (u) DCDs was performed on the studies published in the last four years. ResultsFrom 2018 to 2022 our center performed three LTx with DCDs. All the donors were uDCDs (Maastricht class II). The median warm ischemic time of the graft was 160 min. In all the three LTx, lungs were reconditioned using portable Ex-Vivo-Lung-Perfusion (EVLP) system (Organ Care System, OCS, TransMedics) for a median time of 535 min. All the three LTx were performed with an intraoperative veno-arterial extra-corporeal membrane oxygenation (V-A ECMO), which was prolonged postoperatively in one patient.Grade 3 primary graft disfunction (PGD) at 72 h was observed in one patient. No signs of acute rejection were observed in any patient at the surveillance transbronchial biopsies. One patient died 317 after LTx for consequences of a lung adenocarcinoma diagnosed in the native lung, while the other two are still alive with a preserved graft function. SummaryThe most recent studies confirm similar results between DCDs and DBDs in terms of survival and graft function. Good results can also be achieved in uDCDs if standardized protocols are followed and graft function is monitored by EVLP.Hence, the use of DCDs represents a valid solution to expand the donor pool.

SLICE - Solar Lightweight Intelligent Component for Envelopes: application for the ICARO pavilion

In the ongoing race to reduce polluting emissions, a significant contribution is made by the introduction of intelligent building management systems. The European directive 2002/91 on energy performance in buildings already invited us to look at a new generation of almost zero energy buildings. Research in the field of multifunctional facades offers the opportunity to provide an immediate response to improving air quality and, at the same time, optimizing the use of resources. In fact, adaptive facades can be traced to one of the most effective strategies to efficiently manage the interactions between external and internal environments to maximize winter heating, summer shading and natural ventilation, sound insulation, daylight transfer, glare-free, and interior comfort for the occupants. Nowadays, adaptive enclosures are not only able to interact with the environment and the user but allow the energy needs of buildings to be reduced by integrating technologies to produce energy from renewable sources. The contribution will present the latest developments of an innovative kinetic device for architecture, carried out by the University of Catania; it is the result of a multidisciplinary research project involving important local industrial companies. The component consists of a composite material substrate with integrated high-efficiency photovoltaic technology. The results shown below made it possible to evaluate the use of the designed component in light and stand-alone architectures, representing a valid solution to reduce the impact on the territory even in fragile contexts.

Stability of principal components under normal and non-normal parent populations and different covariance structures scenarios

Principal Component Analysis (PCA) is one of the most used multivariate techniques for dimension reduction assuming nowadays a particular relevance due to the increasingly common large datasets. Being mainly used as a descriptive/exploratory tool it does not require any explicit a priori assumption. However, regardless the parent population miss/unknown characterization, sample principal components are often used to characterize the parent population structure, as these are frequently targeted to visualize multivariate datasets on a 2D graphical display or to infer the first two latent dimensions. In this context, although the main goal might not be inferential, sample principal components may fail to provide a valid solution as principal components may vary considerably, depending on the extracted sample. The stability of the PCA solution is here studied considering normal and non-normal parent populations and three covariance structures scenarios. In addition, the effects of the covariance parameter, the dimension and the size of the sample are also investigated via Monte Carlo simulations. This study aims to understand how stability varies with the population and sample features, characterize the conditions under which PCA results are expected to be stable, and study a sample criterion for PCA stability.

How Does the Modeling Strategy Influence Design Optimization and the Automatic Generation of Parametric Geometry Variations?

The robustness and flexibility of a feature-based parametric CAD model determines the extent to which the geometry can be modified and reused in other design scenarios. The ability of a model to successfully adapt to changes depends on the type and sequence of the modeling operations selected to build the geometry, the parent–child dependencies defined during the modeling process, and the type and scope of the desired geometric change. Several formal modeling methodologies have been proposed to maximize model reusability, which have been shown to outperform unstructured approaches when designers need to manually modify the geometry. However, the effect of these parametric model strategies on the generation of valid solutions in heavily automated tasks has not yet been investigated. In this paper, we compare and analyze the performance of three well-established parametric modeling methodologies in various design optimization scenarios that involve the automatic generation of a large number of geometric variations. We discuss the results of a study with four parametric models of varying complexity and identify the limitations of each strategy in relation to the internal structure of the model. Our results show that explicit references and resilient modeling strategies are relatively robust for simple parts, but their effectiveness decreases significantly as the complexity of the model increases. In addition, we introduce the concept of intrinsic variability, which impacts the effectiveness of the methodology, and thus the quality of the parametric model, based on how the methodology is interpreted and executed. • The effect of formal parametric model strategies on the automatic generation of geometric variations is investigated. • A study with three formal methodologies and four parametric feature-based models of varying complexity is presented. • The horizontal modeling methodology is not an efficient strategy for automated environments. • The resilient methodology is most effective for simple parts and scenarios that involve manual changes. • Explicit reference modeling is effective for complex models and yields faster model regeneration times.

Performance of a multi-sensor wearable system for validating gait assessment: preliminary results on patients and healthy

Real-world (RW) gait analysis is becoming increasingly important since in these conditions an individual’s mobility performance can be measured, in addition to what happens in a standardised lab environment, where mobility capacity is assessed. This is even more relevant in the presence of a motor disability, when continuous daily-life monitoring can unveil limitations in movement, better stratify disease progression and the efficacy of medical treatments [1]. Wearable inertial measurement units (IMUs) represent the most valid solution to tackle this challenge, but their validation requires RW gait data from a reliable Gold Standard (GS). This study evaluates the performance of a wearable multi- sensor system (INDIP) which was specifically conceived to be used as a RW GS [2]. In particular, the INDIP performance in estimating digital mobility outcomes (DMOs) was assessed against a stereophotogrammetric (SP) system, on healthy older adults and patients from five different cohorts, following a purposely designed experimental protocol [3]. The INDIP system includes three IMUs (sampling frequency (fs) =100 Hz) positioned on lower back and feet, two pressure insoles (16 sensing elements, fs=100 Hz) and two time-of-flight distance sensors (fs=50 Hz, range=0.2 m) [2]. Experiments were carried out on 107 participants from six different cohorts (Healthy Adults (HA), Parkinson’s Disease (PD), Multiple Sclerosis (MS), Chronic Obstructive Pulmonary Disease (COPD), Congestive Heart Failure (CHF), Proximal Femoral Fracture (PFF)) while performing a complex eleven-task protocol [3]. Walking bouts (WBs) were obtained from the INDIP data, according to the flowchart described in [2]. Then, for each WB, relevant DMOs were computed. Accuracy of the estimated DMOs was evaluated at cohort level in terms of median relative error (%). For sake of brevity, here we only report walking speed results. A total of 103 subjects were considered for the analysis (1234 WBs in total). Results at cohort level for WB walking speed are presented in Table 1. Median relative errors ranged from 2.02% to 2.58%. Results reported for the WB walking speed showed very low median relative errors across all cohorts. For each cohort, the distributions of values from the INDIP and SP were very similar as shown by the means and standard deviations in Table 1 . Such low differences are excellent, especially when considering the complexity of the tasks included in the experimental protocol. In conclusion, the INDIP system is an accurate reference system for RW gait analysis.

Mastication Wear of Two Low Profile Attachment Systems for Overdenture: An In Vitro Study.

Edentulism is still a major problem in the world's population today. Implant-retained overdenture has proven to be a valid therapeutic solution in the mandible. This type of rehabilitation requires replacement of the matrices when those reach inadequate retention due to wearing processes. This study is aimed at evaluating the drop in retention of low-profile precision attachments following the application of vertical chewing forces. Two different attachment designs were compared. This in vitro study simulated an implant-retained overdenture on an edentulous mandible. Two low-profile attachments were compared. Loaded and unloaded sides were considered. Tests were performed by exerting a vertical cyclic force on the prosthesis at the level of the first molar of a hemiarch. Retention tests were performed before and after 400.000 chewing cycles, comparable to one year of use. The presence of vertical load wear was identified and characterized. Retention never fell below the values indicated by the manufacturer. Furthermore, significant differences were identified between the two retention systems. Loss of occlusal load retention is a component that must be evaluated by the clinician during the design of implant-prosthetic rehabilitation, particularly in those cases where elevated occlusal forces or parafunctions are present.

Formulation and importance of conservative transport in non-premixed flamelet models

The flamelet approach is widely used to model non-premixed turbulent combustion. In this model, chemistry is solved in mixture fraction space and the mixture fraction field is solved in physical space. Transport of reactive scalars in mixture fraction space is governed by two flow parameters: the scalar dissipation rate and the curvature of the mixture fraction field. While these two flow parameters can be easily evaluated if all scales are resolved, models are required if turbulence modeling is applied. However, conventional flow parameter models, which presume the shape of the flow parameters in mixture fraction space, do not consider that mixing in physical and mixture fraction space need to be modeled consistently, which can cause leading order errors. In this study, a consistent formulation of the governing equations and the flow parameters is derived, which is then applied within the Representative Interactive Flamelet (RIF) model to an auto-igniting, sooting, temporal n-dodecane jet under engine-relevant conditions. A Direct Numerical Simulation (DNS) is carried out and serves as reference solution for model validation. It is shown that the revised flow parameters yield superior model predictions of all investigated quantities in comparison to conventional models. Although the auto-ignition process is captured reasonably well by the conventional model, the modeling error in soot quantities is not tolerable. The revised model shows much better agreement with the DNS data and demonstrates that the RIF model is generally able to predict pollutants under the considered conditions. An analysis of the temporal soot mass evolution shows that an accurate description of both species and particle transport in mixture fraction space is essential for predicting soot formation.

Towards sustainable aquaculture systems: Biological and environmental impact of replacing fishmeal with Arthrospira platensis(Nordstedt) (spirulina)

Sustainable fish food production is crucial for aquaculture. Microalgae, such as spirulina (Arthrospira platensis), can supplement diet antioxidants or replace expensive fishmeal with high-quality proteins. In this study, we tested fish growth and wellbeing by feeding fish on a diet in which 5% of fishmeal was replaced by spirulina (SP5 diet). The low level of spirulina in the diet was intended as supplementation and was effective in ameliorating the redox state of a model fish species (juvenile Koi Carp, Cyprinus carpio L.) in a preliminary lab protocol in a six-week trial. When compared with both the control diet (no Spirulina) and a diet containing 30% spirulina replacing fishmeal (SP30 diet), SP5 was able to reduce the muscle levels of reactive oxygen species (ROS), oxidative damage, and susceptibility to oxidative stress, while increasing glutathione reductase and peroxidase activity. However, high production costs and impacts still limit the use of spirulina in fish diet. Recent studies focused on growing spirulina on urban or agro-industrial wastewater, with appropriate profiles for the alga growth. Therefore, in a circular economy context, a possibility still to be tested and exploited is feeding farmed fish with spirulina produced on output wastewater recirculated back from the same farming plant. Life Cycle Assessment (LCA) was applied to estimate the sustainability of such “circular” fish farming. The LCA ReCiPe Midpoint (H) impact assessment method was used. Firstly, the LCA environmental impacts associated with the production of spirulina grown on aquaculture wastewater as well as on the standard culture medium (Zarrouk medium) were assessed and compared by means of a “gate to gate” analysis. Then, the LCA impacts of an SP5 diet for fish, in which spirulina grown on aquaculture wastewater was used to replace 5% fishmeal (SP5ww), were compared to the diet containing spirulina grown on a standard medium (SP5st) and that one without spirulina (control diet). Results indicated that SP5ww was significantly less impacting, by avoiding the treatment and disposal of wastewater and the need for the highly impacting standard culture medium. In conclusion, the proposed approach for using spirulina in aquaculture represents a valid solution for aquaculture circular economy scenario while at the same time improving fish welfare.

Investigating Stroke Effects on Respiratory Parameters Using a Wearable Device: A Pilot Study on Hemiplegic Patients.

Quantitatively assessing personal health status is gaining increasing attention due to the improvement of diagnostic technology and the increasing occurrence of chronic pathologies. Monitoring physiological parameters allows for retrieving a general overview of the personal health status. Respiratory activity can provide relevant information, especially when pathologies affect the muscles and organs involved in breathing. Among many technologies, wearables may represent a valid solution for continuous and remote monitoring of respiratory activity, thus reducing healthcare costs. The most popular wearables used in this arena are based on detecting the breathing-induced movement of the chest wall. Therefore, their use in patients with impaired chest wall motion and abnormal respiratory kinematics can be challenging, but literature is still in its infancy. This study investigates the performance of a custom wearable device for respiratory monitoring in post-stroke patients. We tested the device on six hemiplegic patients under different respiratory regimes. The estimated respiratory parameters (i.e., respiratory frequency and the timing of the respiratory phase) demonstrated good agreement with the ones provided by a gold standard device. The promising results of this pilot study encourage the exploitation of wearables on these patients that may strongly impact the treatment of chronic diseases, such as hemiplegia.

Shape-supervised Dimension Reduction: Extracting Geometry and Physics Associated Features with Geometric Moments

In shape optimisation problems, subspaces generated with conventional dimension reduction approaches often fail to extract the intrinsic geometric features of the shape that would allow the exploration of diverse but valid candidate solutions. More importantly, they also lack incorporation of any notion of physics against which shape is optimised. This work proposes a shape-supervised dimension reduction approach. To simultaneously tackle these deficiencies, it uses higher-level information about the shape in terms of its geometric integral properties, such as geometric moments and their invariants. Their usage is based on the fact that moments of a shape are intrinsic features of its geometry, and they provide a unifying medium between geometry and physics. To enrich the subspace with latent features associated with shape’s geometrical features and physics, we also evaluate a set of composite geometric moments, using the divergence theorem, for appropriate shape decomposition. These moments are combined with the shape modification function to form a Shape Signature Vector (SSV) uniquely representing a shape. Afterwards, the generalised Karhunen–Loève expansion is applied to SSV, embedded in a generalised (disjoint) Hilbert space, which results in a basis of the shape-supervised subspace retaining the highest geometric and physical variance. Validation experiments are performed for a three-dimensional wing and a ship hull model. Our results demonstrate a significant reduction of the original design space’s dimensionality for both test cases while maintaining a high representation capacity and a large percentage of valid geometries that facilitate fast convergence to the optimal solution. The code developed to implement this approach is available at https://github.com/shahrozkhan66/SSDR.git . • Shape signature vector (SSV) comprises a shape modification vector and geometric moments (GM). • Karhunen–Loève expansion of SSV results in a shape-supervised space (SSS). • GM can induce the notion of physics resulting in a physics-informed SSS. • SSS retains higher geometric variance with fewer latent variables. • SSS is robust and compact, providing accelerated optimisation convergence.