POD-based reduced order methods for optimal control problems governed by parametric partial differential equation with varying boundary control

In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the boundary control acts on the system. This peculiar formulation might benefit from model order reduction. Indeed, fast and reliable simulations of this model can be of utmost usefulness in many applied fields, such as geophysics and energy engineering. However, varying boundary control features very complicated and diversified parametric behaviour for the state and adjoint variables. The state solution, for example, changing the boundary control parameter, might feature transport phenomena. Moreover, the problem loses its affine structure. It is well known that classical model order reduction techniques fail in this setting, both in accuracy and in efficiency. Thus, we propose reduced approaches inspired by the ones used when dealing with wave-like phenomena. Indeed, we compare standard proper orthogonal decomposition with two tailored strategies: geometric recasting and local proper orthogonal decomposition. Geometric recasting solves the optimization system in a reference domain simplifying the problem at hand avoiding hyper-reduction, while local proper orthogonal decomposition builds local bases to increase the accuracy of the reduced solution in very general settings (where geometric recasting is unfeasible). We compare the various approaches on two different numerical experiments based on geometries of increasing complexity

Space-time POD-Galerkin approach for parametric flow control

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time evolution of several nonlinear optimality systems in many-query context, where a system must be analysed for various physical and geometrical features. Optimal control can be used in order to fill the gap between collected data and mathematical model and it is usually related to very time consuming activities: inverse problems, statistics, etc. Standard discretization techniques may lead to unbearable simulations for real applications. We aim at showing how reduced order modelling can solve this issue. We rely on a space-time POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space in a fast way for several parametric instances. The proposed algorithm is validated with a numerical test based on environmental sciences: a reduced optimal control problem governed by viscous Shallow Waters Equations parametrized not only in the physics features, but also in the geometrical ones. We will show how the reduced model can be useful in order to recover desired velocity and height profiles more rapidly with respect to the standard simulation, not losing accuracy

Model Order Reduction for Nonlinear and Time-Dependent Parametric Optimal Flow Control Problems

The goal of this thesis is to provide an overview of the latest advances on reduced order methods for parametric optimal control governed by partial differential equations. Historically, parametric optimal control problems are a powerful and elegant mathematical framework to fill the gap between collected data and model equations to make numerical simulations more reliable and accurate for forecasting purposes. For this reason, parametric optimal control problems are widespread in many research and industrial fields. However, their computational complexity limits their actual applicability, most of all in a parametric nonlinear and time-dependent framework. Moreover, in the forecasting setting, many simulations are required to have a more comprehensive knowledge of very complex systems and this should happen in a small amount of time. In this context, reduced order methods might represent an asset to tackle this issue. Thus, we employed space-time reduced techniques to deal with a wide range of equations. We propose a space-time proper orthogonal decomposition for nonlinear (and linear) time-dependent (and steady) problems and a space-time Greedy with a new error estimation for parabolic governing equations. First of all, we validate the proposed techniques through many examples, from the more academic ones to a test case of interest in coastal management exploiting the Shallow Waters Equations model. Then, we will focus on the great potential of optimal control techniques in several advanced applications. As a first example, we will show some deterministic and stochastic environmental applications, adapting the reduced model to the latter case to reach even faster numerical simulations. Another application concerns the role of optimal control in steering bifurcating phenomena arising in nonlinear governing equations. Finally, we propose a neural network-based paradigm to deal with the optimality system for parametric prediction

Model Reduction for Parametrized Optimal Control Problems in Environmental Marine Sciences and Engineering

We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental parametrized optimal control problems are usually studied for different configurations described by several physical and/or geometrical parameters representing different phenomena and structures. The solution of parametrized problems requires a demanding computational effort. In order to save com- putational time, we rely on reduced basis techniques as a reliable and rapid tool to solve parametrized problems. We introduce general parametrized linear quadratic optimal control problems, and the saddle-point structure of their optimality system. Then, we propose a POD-Galerkin reduction of the optimality system. Finally, we test the resulting method on two environmental applications: a pollutant control in the Gulf of Trieste, Italy and a solution tracking governed by quasi-geostrophic equations, in its linear and nonlinear version, describing North Atlantic Ocean dynamic. The two experiments underline how reduced order methods are a reliable and convenient tool to manage several environmental optimal control problems, for different mathematical models, geographical scale as well as physical meaning

Consistency of the full and reduced order models for evolve-filter-relax regularization of convection-dominated, marginally-resolved flows

Numerical stabilization is often used to eliminate (alleviate) the spurious oscillations generally produced by full order models (FOMs) in under-resolved or marginally-resolved simulations of convection-dominated flows. In this article, we investigate the role of numerical stabilization in reduced order models (ROMs) of marginally-resolved, convection-dominated incompressible flows. Specifically, we investigate the FOM–ROM consistency, that is, whether the numerical stabilization is beneficial both at the FOM and the ROM level. As a numerical stabilization strategy, we focus on the evolve-filter-relax (EFR) regularization algorithm, which centers around spatial filtering. To investigate the FOM-ROM consistency, we consider two ROM strategies: (i) the EFR-noEFR, in which the EFR stabilization is used at the FOM level, but not at the ROM level; and (ii) the EFR-EFR, in which the EFR stabilization is used both at the FOM and at the ROM level. We compare the EFR-noEFR with the EFR-EFR in the numerical simulation of a 2D incompressible flow past a circular cylinder in the convection-dominated, marginally-resolved regime. We also perform model reduction with respect to both time and Reynolds number. Our numerical investigation shows that the EFR-EFR is more accurate than the EFR-noEFR, which suggests that FOM-ROM consistency is beneficial in convection-dominated, marginally-resolved flows

DNMT3B Functions: Novel Insights From Human Disease

DNA methylation plays important roles in gene expression regulation and chromatin structure. Its proper establishment and maintenance are essential for mammalian development and cellular differentiation. DNMT3B is the major de novo DNA methyltransferase expressed and active during the early stage of embryonic development, including implantation. In addition to its well-known role to methylate centromeric, pericentromeric, and subtelomeric repeats, recent observations suggest that DNMT3B acts as the main enzyme methylating intragenic regions of active genes. Although largely studied, much remains unknown regarding how these specific patterns of de novo CpG methylation are established in mammalian cells, and which are the rules governing DNMT3B recruitment and activity. Latest evidence indicates that DNMT3B recruitment is regulated by numerous mechanisms including chromatin modifications, transcription levels, non-coding RNAs, and the presence of DNA-binding factors. DNA methylation abnormalities are a common mark of human diseases involving chromosomal and genomic instabilities, such as inherited disease and cancer. The autosomal recessive Immunodeficiency, Centromeric instability and Facial anomalies syndrome, type I (ICF-1), is associated to hypomorphic mutations in DNMT3B gene, while its altered expression has been correlated with the development of tumors. In both cases, this implies that abnormal DNA hypomethylation and hypermethylation patterns affect gene expression and genomic architecture contributing to the pathological states. We will provide an overview of the most recent research aimed at deciphering the molecular mechanisms by which DNMT3B abnormalities are associated with the onset and progression of these pathologies

Molecular and epigenetic analysis of the fragile histidine triad tumour suppressor gene in equine sarcoids

<p>Abstract</p> <p>Background</p> <p>Sarcoids are peculiar equine benign tumours. Their onset is associated with Bovine Papillomavirus type -1 or -2 (BPV-1/2) infection. Little is known about the molecular interplay between viral infection and neoplastic transformation. The data regarding papillomavirus infections in human species show the inactivation of a number of tumour suppressor genes as basic mechanism of transformation. In this study the putative role of the tumour suppressor gene Fragile Histidine Triad (FHIT) in sarcoid tumour was investigated in different experimental models. The expression of the oncosuppressor protein was assessed in normal and sarcoid cells and tissue.</p> <p>Results</p> <p>Nine paraffin embedded sarcoids and sarcoid derived cell lines were analysed for the expression of FHIT protein by immunohistochemistry, immunofluorescence techniques and western blotting. These analyses revealed the absence of signal in seven out of nine sarcoids. The two sarcoid derived cell lines too showed a reduced signal of the protein. To investigate the causes of the altered protein expression, the samples were analysed for the DNA methylation profile of the CpG island associated with the FHIT promoter. The analysis of the 32 CpGs encompassing the region of interest showed no significative differential methylation profile between pathological tissues and cell lines and their normal counterparts.</p> <p>Conclusion</p> <p>This study represent a further evidence of the role of a tumour suppressor gene in equine sarcoids and approaches the epigenetic regulation in this well known equine neoplasm. The data obtained in sarcoid tissues and sarcoid derived cell lines suggest that also in horse, as in humans, there is a possible involvement of the tumour suppressor FHIT gene in BPV induced tumours. DNA methylation seems not to be involved in the gene expression alteration. Further studies are needed to understand the basic molecular mechanisms involved in reduced FHIT expression.</p