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We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity) from surface-based geophysical measurements (e.g., seismic, electric/magnetic (EM) data). The problems are governed by partial…
We propose a novel inverse-modelling approach which estimates the parameters of a simple land-surface model (LSM) by assimilating data into a differentiable physics-based forward model. The governing equations are expressed within a…
We present a new method to invert variable stress changes of fractures from InSAR ground displacements. Fractures can be either faults or magma intrusions, embeded in a 3D heterogeneous crust with prominent topographies. The method is based…
The deployment of electromagnetic (EM) induction tools while drilling is one of the standard routines for assisting the geosteering decision-making process. The conductivity distribution obtained through the inversion of the EM induction…
Electrical Impedance Tomography (EIT) is a powerful imaging technique with diverse applications, e.g., medical diagnosis, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity…
This work focuses on estimating soil properties from water moisture measurements. We consider simulated data generated by solving the initial-boundary value problem governing vertical infiltration in a homogeneous, bounded soil profile,…
Estimating subsurface dielectric properties is essential for applications ranging from environmental surveys of soils to nondestructive evaluation of concrete in infrastructure. Conventional wave inversion methods typically assume few…
Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary…
The analysis of electromagnetic scattering has long been performed on a discrete representation of the geometry. This representation is typically continuous but {\em not} differentiable. The need to define physical quantities on this…
Electrical Resistivity Tomography (ERT) is increasingly used to study subsurface hydrological processes. It shows promising potential for estimating soil water content, a key but challenging property to quantify. However, converting the…
Precise magnetic field modeling is fundamental to the closed-loop control of electromagnetic navigation systems (eMNS) and the analytical Multipole Expansion Model (MPEM) is the current standard. However, the MPEM relies on strict physical…
In this paper we consider physics-informed detection of terrain material change in radar imagery (e.g., shifts in permittivity, roughness or moisture). We propose a lightweight electromagnetic (EM) forward model to simulate bi-temporal…
We extend density matrix embedding theory to periodic systems, resulting in an electronic band structure method for solid-state materials. The electron correlation can be captured by means of a local impurity model using various choices of…
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…
The interaction between the foundation structures and the soil has been developed for many engineering applications. For the determination of the stress in foundation structure it is needed to determine the influence of the stiffness of…
Full-waveform inversion (FWI) plays a vital role in geoscience to explore the subsurface. It utilizes the seismic wave to image the subsurface velocity map. As the machine learning (ML) technique evolves, the data-driven approaches using ML…
The excavation process in mechanized tunneling can be improved by reconnaissance of the geology ahead. A nondestructive exploration can be achieved in means of seismic imaging. A full waveform inversion approach, which works in the…
Full-Waveform Inversion (FWI) is a nonlinear iterative seismic imaging technique that, by reducing the misfit between recorded and predicted seismic waveforms, can produce detailed estimates of subsurface geophysical properties.…
The purpose of this article is to provide a perspective -- admittedly, a rather subjective one -- of recent developments at the interface of machine learning/data-driven methods and nonlinear wave studies. We review some recent pillars of…