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8 results for “Inverse Problems”
Synthetic data for the solution of geophysical inverse problems
<p>The synthetic LAB used to define an inverse problem is discretized in different number of parameters. Each "LAB" file is one specific discretization and contains the coordinatates X and Y and the value of the LAB at each position</p> <p>The reference velocity fields obtained from solving the Stokes equation with the synthetic LABs are found in "velo" files. They contain, X, Y, and Z and the field Vx, Vy and Vz.</p> <p>Another synthetic data set represents the african lithosphere. The first two columns of its LAB file contain the longitude and latitude of each point and the third column is the value of the LAB. The reference velocity field obtained from solving Stokes is found in the corresponding "velo" file.</p>
Reconstructing the Image Scanning Microscopy Dataset: an Inverse Problem
<p>It contains the simulation scripts and the data acquired and analyzed to produce the manuscript "Reconstructing the Image Scanning Microscopy Dataset: an Inverse Problem" (DOI: <a href="https://doi.org/10.1088/1361-6420/accdc5"> 10.1088/1361-6420/accdc5</a>).</p>
Database for Research Projects to Solve the Inverse Heat Conduction Problem
<p>To achieve the optimal performance of an object to be heat treated, it is necessary to know the exact value of the Heat Transfer Coefficient (HTC) describing the amount of heat exchange between the work piece and the cooling medium. The prediction of the HTC is a typical Inverse Heat Transfer Problem (IHCP), which cannot be solved by direct numerical methods. There are numerous techniques used to solve the IHCP based on heuristic search algorithms having very high computational demand. As another approach, it would be possible to use machine-learning methods for the same purpose, which are capable of giving prompt estimations about the main characteristics of the HTC function. As known, a key requirement for all successful machine-learning projects is the availability of high quality training data. In this case, the amount of real-world measurements is far from satisfactory because of the high cost of these tests. As an alternative, it is possible to generate the necessary databases using simulations. This paper presents a novel model for random HTC function generation based on control points and advanced smoothing techniques. As an additional step, a GPU accelerated finite-element method was used to simulate the cooling process resulting in the required temporary data records. These datasets make it possible for researchers to develop and test their IHCP solver algorithms.</p>
Optimal Experimental Design for Large-Scale Inverse Problems via Multi-PDE-constrained Optimization - supplementary files
<p>The file data.xlsx contains information about four experiments defined in: A. Petrocchi, M.K. Scharrer, F. Pichler, S. Volkwein, Optimal Experimental Design for Large-Scale Inverse Problems via Multi-PDE-constrained Optimization, 2024, Submitted. Preprint available at https://arxiv.org/abs/2404.15797.</p> <p>Some information is included in the file data.pdf.</p>
Data from: Waterjet and laser etching: the nonlinear inverse problem
In waterjet and laser milling, material is removed from a solid surface in a succession of layers to create a new shape, in a depth-controlled manner. The inverse problem consists of defining the control parameters, in particular, the two-dimensional beam path, to arrive at a prescribed freeform surface. Waterjet milling (WJM) and pulsed laser ablation (PLA) are studied in this paper, since a generic nonlinear material removal model is appropriate for both of these processes. The inverse problem is usually solved for this kind of process by simply controlling dwell time in proportion to the required depth of milling at a sequence of pixels on the surface. However, this approach is only valid when shallow surfaces are etched, since it does not take into account either the footprint of the beam or its overlapping on successive passes. A discrete adjoint algorithm is proposed in this paper to improve the solution. Nonlinear effects and non-straight passes are included in the optimization, while the calculation of the Jacobian matrix does not require large computation times. Several tests are performed to validate the proposed method and the results show that tracking error is reduced typically by a factor of two in comparison to the pixel-by-pixel approach and the classical raster path strategy with straight passes. The tracking error can be as low as 2–5% and 1–2% for WJM and PLA, respectively, depending on the complexity of the target surface.
Replication data for "Spatial Resolution in Inverse Problems: The EZIE satellite mission"
<p>Pandas dataframe contain synthetic measurements of an EZIE satellite.</p>
Data from: Waterjet and laser etching: the nonlinear inverse problem
Open the record for dataset details and reuse information.
Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems"
<p>Data for: "A Neural-Network-Based Convex Regularizer for Inverse Problems". The corresponding scripts can be accessed on GitHub (https://github.com/axgoujon/convex_ridge_regularizers).</p> <p>The data is organized as follows:</p> <p>- ct_data_sets.tar.gz: contains preprocessed validation (aka calibration) and test sets with:</p> <ul> <li>ground truth images,</li> <li>FBP reconstructions,</li> <li>measurements, for the various settings explored (3 noise levels).</li> </ul> <p>- mri_data_sets.tar.gz: contains preprocessed validation (aka calibration) and test sets with:</p> <ul> <li>subsampling cartesian masks,</li> <li>sensitivity masks,</li> <li>ground truth image,</li> <li>measurements, for the various settings explored: single- and multi-coil MRI, various acceleration rates (2, 4, and 8), synthetic noise, and different image types (fat suppression or not).</li> </ul> <p>For completeness, the code used to generate the preprocessed data from the raw data can be found on the GitHub repository.</p>
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