Deep-HyROMnet: A Deep Learning-Based Operator Approximation for Hyper-Reduction of Nonlinear Parametrized PDEs

To speed-up the solution of parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as surrogate models obtained through machine learning techniques. Thanks to its physics-based structure, ensured by the use of a Galerkin projection of the full order model (FOM) onto a linear low-dimensional subspace, the Galerkin-RB method yields approximations that fulfill the differential problem at hand. However, to make the assembling of the ROM independent of the FOM dimension, intrusive and expensive hyper-reduction techniques, such as the discrete empirical interpolation method (DEIM), are usually required, thus making this strategy less feasible for problems characterized by (high-order polynomial or nonpolynomial) nonlinearities. To overcome this bottleneck, we propose a novel strategy for learning nonlinear ROM operators using deep neural networks (DNNs). The resulting hyper-reduced order model enhanced by DNNs, to which we refer to as Deep-HyROMnet, is then a physics-based model, still relying on the RB method approach, however employing a DNN architecture to approximate reduced residual vectors and Jacobian matrices once a Galerkin projection has been performed. Numerical results dealing with fast simulations in nonlinear structural mechanics show that Deep-HyROMnets are orders of magnitude faster than POD-Galerkin-DEIM ROMs, still ensuring the same level of accuracy

Sensitivity analysis of a multi-physics model for the vascular microenvironment

The vascular microenvironment is the scale at which microvascular transport, interstitial tissue properties and cell metabolism interact. The vascular microenvironment has been widely studied by means of quantitative approaches, including multi-physics mathematical models as it is a central system for the pathophysiology of many diseases, such as cancer. The microvascular architecture is a key factor for fluid balance and mass transfer in the vascular microenvironment, together with the physical parameters characterizing the vascular wall and the interstitial tissue. The scientific literature of this field has witnessed a long debate about which factor of this multifaceted system is the most relevant. The purpose of this work is to combine the interpretative power of an advanced multi-physics model of the vascular microenvironment with state of the art and robust sensitivity analysis methods, in order to determine the factors that most significantly impact quantities of interest, related in particular to cancer treatment. We are particularly interested in comparing the factors related to the microvascular architecture with the ones affecting the physics of microvascular transport. Ultimately, this work will provide further insight into how the vascular microenvironment affects cancer therapies, such as chemotherapy, radiotherapy or immunotherapy

Uncertainty quantification for nonlinear solid mechanics using reduced order models with Gaussian process regression

Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving the solution of nonlinear differential problems, because of the need to query expensive numerical solvers repeatedly. Projection-based reduced order models (ROMs), such as the Galerkin-reduced basis (RB) method, have been extensively developed in the last decades to overcome the computational complexity of high fidelity full order models (FOMs), providing remarkable speed-ups when addressing UQ tasks related with parameterized differential problems. Nonetheless, constructing a projection-based ROM that can be efficiently queried usually requires extensive modifications to the original code, a task which is non-trivial for nonlinear problems, or even not possible at all when proprietary software is used. Non-intrusive ROMs – which rely on the FOM as a black box – have been recently developed to overcome this issue. In this work, we consider ROMs exploiting proper orthogonal decomposition to construct a reduced basis from a set of FOM snapshots, and Gaussian process regression (GPR) to approximate the RB projection coefficients. Two different approaches, namely a global GPR and a tensor-decomposition-based GPR, are explored on a set of 3D time-dependent solid mechanics examples. Finally, the non-intrusive ROM is exploited to perform global sensitivity analysis (relying on both screening and variance-based methods) and parameter estimation (through Markov chain Monte Carlo methods), showing remarkable computational speed-ups and very good accuracy compared to high-fidelity FOMs

Use of a porcine collagen matrix as an alternative to autogenous tissue for grafting oral soft tissue defects

Purpose: Soft tissue grafting is often required to correct intraoral mucosal deficiencies. Autogenous grafts have disadvantages including an additional harvest site with its associated pain and morbidity and, sometimes, poor quality and limited amount of the graft. Porcine collagen matrices have the potential to be helpful for grafting of soft tissue defects. Patients and Methods: Thirty consecutive patients underwent intraoral grafting to re-create missing soft tissue. Defects ranged in size from 50 to 900 mm2. Porcine collagen matrices were used to reconstruct missing tissue. Indications included preprosthetic (22), followed by tumor removal (5), trauma (2), and release of cheek ankylosis (1). Results: The primary efficacy parameters evaluated were the degree of lateral and/or alveolar extension and the evaluation of re-epithelialization and shrinkage of the grafted area. Overall, the percentage of shrinkage of the graft was 14% (range, 5%-20%). The amount of soft tissue extension averaged 3.4 mm (range, 2-10 mm). The secondary efficacy parameters included hemostatic effect, pain evaluation, pain and discomfort, and clinical evaluation of the grafted site. All patients reported minimal pain and swelling associated with the grafted area. No infections were noted. Conclusion: This porcine collagen matrix provides a biocompatible surgical material as an alternative to an autogenous transplant, thus obviating the need to harvest soft tissue autogenous grafts from other areas of the oral cavity

Extraction of anthocyanins from grape (Vitis vinifera) skins employing natural deep eutectic solvents (NaDES)

In the last years, the possibility to exploit the high added value bioactive compounds obtained by the solid residues of the winemaking process in cosmetic, food supply and pharmaceutical field was explored. To enhance the biocompatibility of the final products and reduce the environmental impact of traditional extraction routes, researchers attempted at developing sustainable and green extraction processes. In the present work, the feasibility of employing NaDES (Natural Deep Eutectic Solvents) as a cheap and non-toxic alternative to traditional solvents for the extraction of bioactive compounds from winery wastes of Merlot marc was studied. Furthermore, a two-level factorial design was used to study the single and combined effect of process variables, namely, solid to liquid ratio dry grinding time and extraction time, on the extraction yield. Experimental show that, in the range studied, solid to liquid ratio has a predominant effect and both grinding and extraction times have a slightly appreciable effect on the extraction yield

Changes of Occlusal Plane in Growing Patients with Increased Vertical Dimension during Class II Correction by Using Cervical Headgear

This retrospective research aimed to highlight the changes of occlusal plane in Class II hyperdivergent subjects that received cervical headgear treatment and compared them to untreated controls in order to evaluate the occlusal changes that might be connected to a potential mandibular rotation.The sample of this investigation was represented by 20 hyperdivergent Class II subjects (10 males, 10 females; mean age 8.54) corrected by using cervical headgear (treated group) and 21 Class II patients (11 males, 10 females; mean age 8.41) hyperdivergent who had no therapy (control group). Lateral head films were studied for all the patients before treatment (T1) and after therapy (T2) for both groups; cephalometric analysis was used in order to seek the modifications between time points and between groups.Means and standard deviation have been computed for both groups. In order to confront the modification between the time points within the same group the Wilcoxon test was applied. The Mann-Whitney U test was applied to confront the dissimilarities between groups at T2.As a result of the Class II correction by using the cervical headgear treatment the occlusal plane was lowered and flattened compared to T1 and to the control group; the upper molars showed extrusion to the palatal plane, there was a significant forward rotation of mandible and the vertical dimension was not significantly modified. Downward and backward displacement of the upper jaw occurred

Self-Reported oral hygiene habits among dental patients in Italy

Objective: The objective of this survey was to assess oral hygiene habits andcompliance with guidelines for good oral health set forth by the Italian Ministry of Health (IMH). Subjects and Methods: A sample of 2,200 self-administered questionnaires was sent to four dental clinics across Italy to assess sociodemographic information, oral hygiene habits, frequency of dental visits and services received at previous visits among a population of adult patients. Results: Of the 2,200 questionnaires, 1,201 (54.6%) were returned. Findings showed that full compliance with the IMH recommendations was low (12%): a small number of patients (n = 223, 18.6%) visited a dentist every 6 months and only 256 (23.5%) brushed their teeth at least twice a day. Conclusion: Our data showed that regular attendance (at least 1 visit/year) at dental clinics for routine check-up and brushing teeth at least twice a day were poor. Therefore, we recommend that clinicians educate and motivate their patients about the benefits of healthy oral hygiene practice