1,109 research outputs found
Deep convolutional neural networks for estimating porous material parameters with ultrasound tomography
We study the feasibility of data based machine learning applied to ultrasound
tomography to estimate water-saturated porous material parameters. In this
work, the data to train the neural networks is simulated by solving wave
propagation in coupled poroviscoelastic-viscoelastic-acoustic media. As the
forward model, we consider a high-order discontinuous Galerkin method while
deep convolutional neural networks are used to solve the parameter estimation
problem. In the numerical experiment, we estimate the material porosity and
tortuosity while the remaining parameters which are of less interest are
successfully marginalized in the neural networks-based inversion. Computational
examples confirms the feasibility and accuracy of this approach
Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method
This paper discusses the computation of derivatives for optimization problems
governed by linear hyperbolic systems of partial differential equations (PDEs)
that are discretized by the discontinuous Galerkin (dG) method. An efficient
and accurate computation of these derivatives is important, for instance, in
inverse problems and optimal control problems. This computation is usually
based on an adjoint PDE system, and the question addressed in this paper is how
the discretization of this adjoint system should relate to the dG
discretization of the hyperbolic state equation. Adjoint-based derivatives can
either be computed before or after discretization; these two options are often
referred to as the optimize-then-discretize and discretize-then-optimize
approaches. We discuss the relation between these two options for dG
discretizations in space and Runge-Kutta time integration. Discretely exact
discretizations for several hyperbolic optimization problems are derived,
including the advection equation, Maxwell's equations and the coupled
elastic-acoustic wave equation. We find that the discrete adjoint equation
inherits a natural dG discretization from the discretization of the state
equation and that the expressions for the discretely exact gradient often have
to take into account contributions from element faces. For the coupled
elastic-acoustic wave equation, the correctness and accuracy of our derivative
expressions are illustrated by comparisons with finite difference gradients.
The results show that a straightforward discretization of the continuous
gradient differs from the discretely exact gradient, and thus is not consistent
with the discretized objective. This inconsistency may cause difficulties in
the convergence of gradient based algorithms for solving optimization problems
An Energy Based Discontinuous Galerkin Method for Coupled Elasto-Acoustic Wave Equations in Second Order Form
We consider wave propagation in a coupled fluid-solid region, separated by a
static but possibly curved interface. The wave propagation is modeled by the
acoustic wave equation in terms of a velocity potential in the fluid, and the
elastic wave equation for the displacement in the solid. At the fluid solid
interface, we impose suitable interface conditions to couple the two equations.
We use a recently developed, energy based discontinuous Galerkin method to
discretize the governing equations in space. Both energy conserving and upwind
numerical fluxes are derived to impose the interface conditions. The highlights
of the developed scheme include provable energy stability and high order
accuracy. We present numerical experiments to illustrate the accuracy property
and robustness of the developed scheme
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