A parameter identification problem for systems governed by first-order, linear hyperbolic partial differential equations subjected to periodic forcing is investigated. The problem is posed as a PDE constrained optimization problem with data of the problem given by the measured input and output variables at the boundary of the domain. By using the governing equations in the frequency domain, a s...

Abstract In this work and in the context of PDE constrained optimization problems, we are interested identification a parameter diffusion equation proposed [1]. We propose to identify automatically by gradient descent algorithm improve restoration noisy image. Finally, give numerical results illustrate performance automatic selection compare our with other image denoising approaches or algorith...

Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, residual form PDE interest and its boundary conditions are lumped into a composite objective function as soft penalties. Here, we show that this specific way formulating is source severe limitations in PINN approach when applied different kinds PDEs. To address th...

We present a framework for modeling gliomas growth and their mechanical impact on the surrounding brain tissue (the so-called, mass-effect). We employ an Eulerian continuum approach that results in a strongly coupled system of nonlinear Partial Differential Equations (PDEs): a reaction-diffusion model for the tumor growth and a piecewise linearly elastic material for the background tissue. To e...

While topological derivatives have proven useful in applications of topology optimization and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, particular the context nonlinear partial differential equation (PDE) constraints. We present a systematic yet formal approach for numerical computation large class PDE-constrained problems with respect to arbi...

We propose and compare methods for the analysis of extreme events in complex systems governed by PDEs that involve random parameters, situations where we are interested quantifying probability a scalar function system's solution is above threshold. If threshold large, this small its accurate estimation challenging. To tackle difficulty, blend theoretical results from large deviation theory (LDT...

Coupled 3D-1D problems arise in many practical applications, an attempt to reduce the computational burden simulations where cylindrical inclusions with a small section are embedded much larger domain. Nonetheless resolution of such can be non trivial, both from mathematical and geometrical standpoint. Indeed coupling requires operate standard function spaces, and, also, simulation geometries c...

We propose and analyze a Stein variational reduced basis method (SVRB) to solve large-scale PDE-constrained Bayesian inverse problems. To address the computational challenge of drawing numerous samples requiring expensive PDE solves from posterior distribution, we integrate an adaptive goal-oriented model reduction technique with optimization-based gradient descent method. present detailed anal...

We present a PDE-constrained optimization algorithm which is designed for parallel scalability on distributed-memory architectures with thousands of cores. The method is based on a linesearch interior-point algorithm for large-scale continuous optimization, it is matrix-free in that it does not require the factorization of derivative matrices. Instead, it uses a new parallel and robust iterativ...