Related papers: Waveform inversion with a data driven estimate of …
Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward…
This is a continuation of our study [Uhlmann-Zhai, JMPA, 2021] on an inverse boundary value problem for a nonlinear elastic wave equation. We prove that all the linear and nonlinear coefficients can be recovered from the…
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
We study a class of statistical inverse problems with non-linear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the non-linearity.…
We present a systematic derivation of the wave kinetic equation describing the dynamics of a statistically inhomogeneous incoherent wave field in a medium with a weak quadratic nonlinearity. The medium can be nonstationary and…
In this paper, we empirically reveal an invariance over images-images share a set of one-way wave equations with latent speeds. Each image is uniquely associated with a solution to these wave equations, allowing for its reconstruction with…
In this paper, we propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted…
Gravitational-wave data analysis is rapidly absorbing techniques from deep learning, with a focus on convolutional networks and related methods that treat noisy time series as images. We pursue an alternative approach, in which waveforms…
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…
We consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at receivers outside the object. The data is assumed to be generated by plane waves impinging on the obstacle…
We report numerical simulations of surface gravity waves forced at small scale and the subsequent inverse cascade of wave action. We combine the spectral approach to simulating weakly nonlinear waves with the capabilities of modern Graphics…
We study the fixed angle inverse scattering problem of determining a sound speed from scattering measurements corresponding to a single incident wave. The main result shows that a sound speed close to constant can be stably determined by…
We propose a coherent method for the detection and reconstruction of gravitational wave signals for a network of interferometric detectors. The method is derived using the likelihood functional for unknown signal waveforms. In the standard…
In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent's objective function that best…
Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating…
In hydrology, modeling streamflow remains a challenging task due to the limited availability of basin characteristics information such as soil geology and geomorphology. These characteristics may be noisy due to measurement errors or may be…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…
In micro-seismic event measurements, pinpointing the passive source's exact spatial and temporal location is paramount. This research advocates for the combined use of both P- and S-wave data, captured by geophone monitoring systems, to…