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Accelerating the discovery of structural materials is essential for applications in hard and refractory alloys, hypersonic platforms, nuclear systems, and other extreme environment technologies. Progress is often constrained by slow…
We study the inverse medium scattering problem to reconstruct the unknown inhomogeneous medium from the far-field patterns of scattered waves. The inverse scattering problem is generally ill-posed and nonlinear, and the iterative…
In image processing, solving inverse problems is the task of finding plausible reconstructions of an image that was corrupted by some (usually known) degradation operator. Commonly, this process is done using a generative image model that…
This paper introduces a methodology designed to augment the inverse design optimization process in scenarios constrained by limited compute, through the strategic synergy of multi-fidelity evaluations, machine learning models, and…
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…
This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures. A fundamental step in any typical iterative inversion method, is the numerical solution of the underlying direct…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…
Discovering new physical products and processes often demands enormous experimentation and expensive simulation. To design a new product with certain target characteristics, an extensive search is performed in the design space by trying out…
Determining a process-structure-property relationship is the holy grail of materials science, where both computational prediction in the forward direction and materials design in the inverse direction are essential. Problems in materials…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
A method is presented for the registration and correlation of intrinsic property maps of materials, including data from nanoindentation hardness, Electron Back-Scattered Diffraction (EBSD), Electron Micro-Probe Analysis (EPMA). This highly…
Contemporary material characterisation techniques that leverage deformation fields and the weak form of the equilibrium equations face challenges in the numerical solution procedure of the inverse characterisation problem. As material…
Stochastic parameterizations are increasingly being used to represent the uncertainty associated with model errors in ensemble forecasting and data assimilation. One of the challenges associated with the use of these parameterizations is…
3D-printed materials are used in many different industries (automotive, aviation, medicine, etc.). Most of these 3D-printed materials are based on ceramics or polymers whose mechanical properties vary with frequency. For numerical modeling,…
This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…
In this paper, we extend the previous method for solving inverse problems for steady-state equations using the Generalized Collage Theorem by searching for an approximation that not only minimizes the collage error but also maximizes the…
The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…
Inverse material design is a cornerstone challenge in materials science, with significant applications across many industries. Traditional approaches that invert the structure-property (SP) linkage to identify microstructures with targeted…
The following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from global EM scattering measurements, at various incidences and wave frequencies.…