Abstract : Control problems, including optimization problems with PDE constraints, have numerous applications across science and engineering, including chemical processes, mathematical biology, fluid flow control, imaging problems, and mean-field games. Of crucial importance is to develop efficient and robust numerical schemes which can solve mathematical models for such problems and the large-scale optimality systems. This can involve accurate and stable discretization schemes, modern linear algebra to solve systems of equations resulting from such problems, and, increasingly, technologies from parallel computing. This session will cover the state-of-the-art in the design of numerical methods for such problems, arising from a range of scientific applications.
[03637] Recent Developments in Preconditioning for PDE-Constrained Optimization
Format : Talk at Waseda University
Author(s) :
John Pearson (University of Edinburgh)
Abstract : In this talk, we survey some recent research into numerical linear algebra for PDE-constrained optimization problems. In particular, we consider preconditioned iterative methods for the robust solution of resulting linear(ized) systems. Having provided some motivation for the construction of effective preconditioners, we briefly summarise some solution strategies devised by the speaker along with collaborators, for time-dependent problems, fluid flow control systems, and multiple saddle-point systems arising from PDE-constrained optimization.
[01670] GKBO method for global optimization of non-convex high dimensional functions.
Format : Talk at Waseda University
Author(s) :
Federica Ferrarese (University of Verona and Trento)
Abstract : The study of numerical methods for global optimization of non-convex high dimensional functions has attracted a lot of attention in recent years. In this talk, a new efficient numerical method for global optimization inspired to classical
algorithms will be presented. Different theoretical and numerical results will be shown comparing this algorithm to the
classical ones. Finally, further extensions to localized versions of this algorithm, useful to minimize functions with
multiple global minima, will be introduced.
[01649] Online identification and control of PDEs via RL methods
Format : Talk at Waseda University
Author(s) :
Alessandro Alla
Michele Palladino (Università degli studi dell'Aquila)
Agnese Pacifico (Sapienza, Università di Roma)
Andrea Pesare (Bending Spoons)
Abstract : In this talk we focus on the control of unknown Partial Differential Equations. Our approach is based on the idea to control and identify on the fly. The control, in this work, is computed using the State Dependent Riccati approach whereas the identification of the model on bayesian linear regression. At each iteration we obtain an estimation of the a-priori unknown coefficients of the PDEs based on the observed data and then we compute the control of the correspondent model. We show by numerical evidence the convergence of the method for infinite horizon problems.
[03371] A statistical POD approach for feedback boundary optimal control in fluid dynamics
Format : Talk at Waseda University
Author(s) :
Luca Saluzzi (Scuola Normale Superiore di Pisa)
Sergey Dolgov (University of Bath)
Dante Kalise (Imperial College London)
Abstract : I consider feedback boundary optimal control problems and their reduction by the means of a Statistical Proper Orthogonal Decomposition, method characterized by the introduction of stochastic terms in the model to enrich the knowledge of the Full Order Model and in the collection of optimal trajectories as snapshots. The HJB equation is then solved by a data-driven Tensor Train Cross and applied to the control of the incompressible Navier-Stokes equation in a backward-step domain.
Abstract : Partial differential equations (PDEs) with nonlocal effects pose various
challenges in the analysis as well as the numerical solution. This is all the
more true for optimal control problems involving nonlocal PDEs. In this
presentation, we will discuss examples of optimal control problems for nonlocal
PDEs and exhibit the numerical challenges posed by the associated blocks in the
optimality systems.
[01642] Decentralized strategies for coupled shape and parameter inverse problems
Abstract : We present a novel family of algorithms framed within game theory setting and dedicated to solve ill-posed
inverse problems, where unknown shapes -obstacles or inclusions- or sources are to be reconstructed
as well as missing boundary conditions, for steady Stokes fluids.
Some theoretical results and several numerical experiments are provided that corroborate the ability
of the approch to tackle harsh problems.
[04057] Stability-exploiting adaptive finite elements for optimal control
Format : Talk at Waseda University
Author(s) :
Manuel Schaller (Technische Universität Ilmenau)
Abstract : Optimal control problems often exhibit a particular stability property which, for time-dependent problems, manifests itself, e.g., by means of a turnpike property. The latter states that optimal solutions to dynamic problems reside close to a particular steady state for the majority of the time. Such a stable behavior can be shown under stabilizability and detectability-like assumptions and in particular also can be shown to hold when the uncontrolled equations are unstable. In this talk, we will show how this stability leads to locality of discretization errors which can be exploited by means of adaptive finite-element methods, leading to a significant reduction in computational expenses, e.g., in a Model Predictive Controller.
