A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems

In this work, we present an extension of genetic algorithm (GA) which exploits the supervised learning technique called active subspaces (AS) to evolve the individuals on a lower-dimensional space. In many cases, GA requires in fact more function evaluations than other optimization methods to converge to the global optimum. Thus, complex and high-dimensional functions can end up extremely demanding (from the computational point of view) to be optimized with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower-dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions-Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov-and finally we apply it to an aeronautical shape optimization problem

Basic ideas and tools for projection-based model reduction of parametric partial differential equations

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions, offline-online decomposition and error estimation is introduced. Several tools for geometry parametrizations, such as free form deformation, radial basis function interpolation and inverse distance weighting interpolation are explained. The empirical interpolation method is introduced as a general tool to deal with non-affine parameter dependency and non-linear problems. The discrete and matrix versions of the empirical interpolation are considered as well. Active subspaces properties are discussed to reduce high-dimensional parameter spaces as a pre-processing step. Several examples illustrate the methodologies

Enhancing CFD predictions in shape design problems by model and parameter space reduction

In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD

Reduced order isogeometric analysis approach for PDEs in parametrized domains

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to obtain the parametric formulation of the domain and proper orthogonal decomposition with interpolation for the computational reduction of the model. This technique provides a real-time solution for any parameter by combining several solutions, in this case computed using isogeometric analysis on different geometrical configurations of the domain, properly mapped into a reference configuration. We underline that this reduced order model requires only the full-order solutions, making this approach non-intrusive. We present in this work the results of the application of this methodology to a heat conduction problem inside a deformable collector pipe

Enhancing CFD predictions in shape design problems by model and parameter space reduction

In this work we present an advanced computational pipeline for the approximation and prediction of the lift coefficient of a parametrized airfoil profile. The non-intrusive reduced order method is based on dynamic mode decomposition (DMD) and it is coupled with dynamic active subspaces (DyAS) to enhance the future state prediction of the target function and reduce the parameter space dimensionality. The pipeline is based on high-fidelity simulations carried out by the application of finite volume method for turbulent flows, and automatic mesh morphing through radial basis functions interpolation technique. The proposed pipeline is able to save 1/3 of the overall computational resources thanks to the application of DMD. Moreover exploiting DyAS and performing the regression on a lower dimensional space results in the reduction of the relative error in the approximation of the time-varying lift coefficient by a factor 2 with respect to using only the DMD

Advances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: Overview and perspectives

Several problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments

Omics sciences and precision medicine in melanoma

Background: This article provides an overview of the application of omics sciences in melanoma research. The name omics sciences refers to the large-scale analysis of biological molecules like DNA, RNA, proteins, and metabolites. Methods: In the course of this review, we have adopted a focu-sed research strategy, meticulously selecting the most pertinent and emblematic articles related to the topic. Our methodology included a systematic examination of the scientific literature to guarantee a thorough and precise synthesis of the existing sources. Results: With the advent of high-throughput technologies, omics have become an essential tool for understanding the complexity of melanoma. In this article, we discuss the different omics approaches used in melanoma research, including genomics, transcriptomics, proteomics, and metabolomics. We also highlight the major findings and insights gained from these studies, including the identification of new therapeutic targets and the development of biomarkers for diagnosis and prognosis. Finally, we discuss the challenges and future directions in omics-based melanoma research, including the integration of multiple omics data and the development of personalized medicine approaches. Conclusions: Overall, this article emphasizes the importance of omics science in advancing our understanding of melanoma and its potential for improving patient outcomes

On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis

In this work, Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) methodologies are applied to hydroacoustic dataset computed using Large Eddy Simulation (LES) coupled with Ffowcs Williams and Hawkings (FWH) analogy. First, a low-dimensional description of the flow fields is presented with modal decomposition analysis. Sensitivity towards the DMD and POD bases truncation rank is discussed, and extensive dataset is provided to demonstrate the ability of both algorithms to reconstruct the flow fields with all the spatial and temporal frequencies necessary to support accurate noise evaluation. Results show that while DMD is capable to capture finer coherent structures in the wake region for the same amount of employed modes, reconstructed flow fields using POD exhibit smaller magnitudes of global spatiotemporal errors compared with DMD counterparts. Second, a separate set of DMD and POD modes generated using half the snapshots is employed into two data-driven reduced models respectively, based on DMD mid cast and POD with Interpolation (PODI). In that regard, results confirm that the predictive character of both reduced approaches on the flow fields is sufficiently accurate, with a relative superiority of PODI results over DMD ones. This infers that, discrepancies induced due to interpolation errors in PODI is relatively low compared with errors induced by integration and linear regression operations in DMD, for the present setup. Finally, a post processing analysis on the evaluation of FWH acoustic signals utilizing reduced fluid dynamic fields as input demonstrates that both DMD and PODI data-driven reduced models are efficient and sufficiently accurate in predicting acoustic noises

Genetic Screening in a Large Cohort of Italian Patients Affected by Primary Lymphedema Using a Next Generation Sequencing (NGS) Approach

Primary lymphedema is a rare inherited condition characterized by swelling of body tissues caused by accumulation of fluid, especially in the lower limbs. In many patients, primary lymphedema has been associated with variations in a number of genes involved in the development and maintenance of the lymphatic system. In this study, we performed a genetic screening in patients affected by primary lymphedema using a next generation sequencing (NGS) approach. With this technology, based on a custom-made oligonucleotide probe library, we were able to analyze simultaneously in each patient all the coding exons of 10 genes (FLT4, FOXC2, CCBE1, GJC2, MET, HGF, GATA2, SOX18, VEGFC, KIF11) associated with primary lymphedema. In the study population, composed of 45 familial and 71 sporadic cases, we identified the presence of rare variants with a potential pathogenic effect in 33% of subjects. Overall, we found a total of 36 different rare nucleotidic alterations, 30 of which had not been previously described. Among these, we identified 23 mutations that we considered most likely to be disease causing. Patients with an FLT4 or FOXC2 alteration accounted for the largest percentage of the sample, followed by MET, HGF, KIK11, GJC2 and GATA2. No alterations were identified in SOX18, VEGFC, and CCBE1 genes. In conclusion, we showed that NGS technology can be successfully applied to perform molecular screening of lymphedema-associated genes in large cohort of patients with a reasonable effort in terms of cost, work, and time