Mechanical MNIST Datasetshttps://hdl.handle.net/2144/393712021-05-19T02:58:41Z2021-05-19T02:58:41ZMechanical MNIST - FashionLejeune, Emmahttps://hdl.handle.net/2144/414502020-10-09T14:06:35Z2020-01-01T00:00:00ZMechanical MNIST - Fashion
Lejeune, Emma
Each dataset in the Mechanical MNIST collection contains the results of 70,000 (60,000 training examples + 10,000 test examples) finite element simulation of a heterogeneous material subject to large deformation. Mechanical MNIST - Fashion is generated by first converting the fashion MNIST bitmap images (https://github.com/zalandoresearch/fashion-mnist) to 2D heterogeneous blocks of material. Consistent with the MNIST bitmap ($28 \times 28$ pixels), the material domain is a $28 \times 28$ unit square. In “Mechanical MNIST - Fashion,” the material is Neo-Hookean with a varying modulus. In the Uniaxial Extension (UE) case, the bottom of the domain is fixed (Dirichlet boundary condition), the left and right edges of the domain are free, and the top of the domain is fixed horizontally and moved vertically to a given fixed displacement (d). In the Equibiaxial Extension (EE) case, the top of the domain is free horizontally and moved vertically to a given fixed displacement (d), the right of the domain is free vertically and moved horizontally to a given fixed displacement (d), the bottom of the domain is free horizontally and moved vertically to a given fixed displacement (-d), and the left of the domain is free vertically and moved horizontally to a given fixed displacement (-d). The results of the simulations include: (1) change in strain energy at a perturbation level step (d=0.001), and at the final applied displacement (d=14 for UE, d=7 for EE) (2) total reaction force at a perturbation level step (d=0.001 for UE, d=.0005 for EE), and at the final applied displacement (d=14 for UE, d=7 for EE), and (3) full field displacement at a perturbation level step (d=0.001), and at the final applied displacement (d=14 for UE, d=7 for EE). The x-reaction (first column) and y-reaction (second column) forces are given. For the UE case, this corresponds to the top boundary. For the EE case, this correspond to the left and top boundaries. All simulations are conducted with the FEniCS computing platform (https://fenicsproject.org). The code to reproduce these simulations and import these text files is hosted on GitHub (https://github.com/elejeune11/Mechanical-MNIST-fashion).
The paper "Mechanical MNIST: A benchmark dataset for mechanical metamodels" can be found at https://doi.org/10.1016/j.eml.2020.100659. All code necessary to reproduce these finite element simulations is available on GitHub (https://github.com/elejeune11/Mechanical-MNIST-fashion). For questions, please contact Emma Lejeune (elejeune@bu.edu).
2020-01-01T00:00:00ZMechanical MNIST - Multi-FidelityLejeune, Emmahttps://hdl.handle.net/2144/413572020-10-09T12:58:00Z2020-07-01T00:00:00ZMechanical MNIST - Multi-Fidelity
Lejeune, Emma
Each dataset in the Mechanical MNIST collection contains the results of 70,000 (60,000 training examples + 10,000 test examples) finite element simulation of a heterogeneous material subject to large deformation. Mechanical MNIST is generated by first converting the MNIST bitmap images (http://www.pymvpa.org/datadb/mnist.html) to 2D heterogeneous blocks of material. Consistent with the MNIST bitmap ($28 \times 28$ pixels), the material domain is a $28 \times 28$ unit square. The material is Neo-Hookean with a varying modulus dictated by the input bitmap. The simulation results included here are the change in strain energy at a fixed level of applied displacement. The cases considered are as follows:
*UE: uniaxial extension, full fidelity dataset (fully refined mesh, quadratic triangular elements, applied displacement is $1/2$ of a side length);
*EE: equibiaxial extension, full fidelity dataset;
*3D: uniaxial extension and out of plane twist, full fidelity three dimensional dataset (fully refined mesh, quadratic tetrahedral elements, applied displacement is $1/7$ of a side length, twist is $\pi/8$ radians, block thickness is $1/7$ of a side length);
*UE-CM-28: uniaxial extension, $28 \times 28 \times 2$ linear triangular elements;
*UE-CM-14: uniaxial extension, $14 \times 14 \times 2$ linear triangular elements;
*UE-CM-7: uniaxial extension, $7 \times 7 \times 2$ linear triangular elements;
*UE-CM-7-quad: uniaxial extension, $7 \times 7 \times 2$ quadratic triangular elements;
*UE-CM-4: uniaxial extension, $4 \times 4 \times 2$ linear triangular elements;
*UE-CM-4-quad: uniaxial extension, $4 \times 4 \times 2$ quadratic triangular elements;
*UE-perturb: uniaxial extension, applied displacement is a perturbation (.001 units);
*UE-CM-28-perturb: uniaxial extension, $28 \times 28 \times 2$ linear triangular elements, applied displacement is a perturbation (.001 units).
All simulations are conducted with the FEniCS computing platform (https://fenicsproject.org). The code to reproduce these simulations is hosted on GitHub (https://github.com/elejeune11/Mechanical-MNIST-Transfer-Learning).
The paper "Exploring the potential of transfer learning for metamodels of heterogeneous material deformation" is forthcoming. All code necessary to reproduce the metamodels demonstrated in the manuscript is available on GitHub (https://github.com/elejeune11/Mechanical-MNIST-Transfer-Learning). For questions, please contact Emma Lejeune (elejeune@bu.edu).
2020-07-01T00:00:00ZMechanical MNIST: A benchmark dataset for mechanical metamodelsLejeune, Emmahttps://hdl.handle.net/2144/398132020-03-26T06:24:38Z2020-04-01T00:00:00ZMechanical MNIST: A benchmark dataset for mechanical metamodels
Lejeune, Emma
Metamodels, or models of models, map defined model inputs to defined model outputs. Typically, metamodels are constructed by generating a dataset through sampling a direct model and training a machine learning algorithm to predict a limited number of model outputs from varying model inputs. When metamodels are constructed to be computationally cheap, they are an invaluable tool for applications ranging from topology optimization, to uncertainty quantification, to multi-scale simulation. By nature, a given metamodel will be tailored to a specific dataset. However, the most pragmatic metamodel type and structure will often be general to larger classes of problems. At present, the most pragmatic metamodel selection for dealing with mechanical data has not been thoroughly explored. Drawing inspiration from the benchmark datasets available to the computer vision research community, we introduce a benchmark data set (Mechanical MNIST) for constructing metamodels of heterogeneous material undergoing large deformation. We then show examples of how our benchmark dataset can be used, and establish baseline metamodel performance. Because our dataset is readily available, it will enable the direct quantitative comparison between different metamodeling approaches in a pragmatic manner. We anticipate that it will enable the broader community of researchers to develop improved metamodeling techniques for mechanical data that will surpass the baseline performance that we show here.
2020-04-01T00:00:00ZMechanical MNIST - ShearLejeune, Emmahttps://hdl.handle.net/2144/394292020-04-27T13:55:24Z2020-02-01T00:00:00ZMechanical MNIST - Shear
Lejeune, Emma
Each dataset in the Mechanical MNIST collection contains the results of 70,000 (60,000 training examples + 10,000 test examples) finite element simulation of a heterogeneous material subject to large deformation. Mechanical MNIST is generated by first converting the MNIST bitmap images (http://www.pymvpa.org/datadb/mnist.html) to 2D heterogeneous blocks of material. Consistent with the MNIST bitmap ($28 \times 28$ pixels), the material domain is a $28 \times 28$ unit square. In "Mechanical MNIST - Shear," the material is Neo-Hookean with a varying modulus. The bottom of the domain is fixed (Dirichlet boundary condition), the left and right edges of the domain are free, and the top of the domain is fixed vertically and moved horizontally to a set of given fixed displacements (d = [0.0, 0.001, 0.01, 0.1, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5]). The results of the simulations include: (1) change in strain energy at each step, (2) total reaction force at the top boundary at each step, and (3) full field displacement at each step. All simulations are conducted with the FEniCS computing platform (https://fenicsproject.org). The code to reproduce these simulations is hosted on GitHub (https://github.com/elejeune11/Mechanical-MNIST/tree/master/generate_dataset).
The paper "Mechanical MNIST: A benchmark dataset for mechanical metamodels" can be found at https://doi.org/10.1016/j.eml.2020.100659. All code necessary to reproduce the metamodels demonstrated in the manuscript is available on GitHub (https://github.com/elejeune11/Mechanical-MNIST). For questions, please contact Emma Lejeune (elejeune@bu.edu).
2020-02-01T00:00:00ZMechanical MNIST - Equibiaxial ExtensionLejeune, Emmahttps://hdl.handle.net/2144/394282020-04-27T13:47:05Z2020-02-01T00:00:00ZMechanical MNIST - Equibiaxial Extension
Lejeune, Emma
Each dataset in the Mechanical MNIST collection contains the results of 70,000 (60,000 training examples + 10,000 test examples) finite element simulation of a heterogeneous material subject to large deformation. Mechanical MNIST is generated by first converting the MNIST bitmap images (http://www.pymvpa.org/datadb/mnist.html) to 2D heterogeneous blocks of material. Consistent with the MNIST bitmap ($28 \times 28$ pixels), the material domain is a $28 \times 28$ unit square. In "Mechanical MNIST - Equibiaxial Extension," the material is Neo-Hookean with a varying modulus. The top of the domain is free horizontally and moved vertically to a set of given fixed displacements (d = [0.0, 0.0005, 0.005, 0.05, 0.25, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]), the right of the domain is free vertically and moved horizontally to a set of given fixed displacements (d = [0.0, 0.0005, 0.005, 0.05, 0.25, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]), the bottom of the domain is free horizontally and moved vertically to a set of given fixed displacements (d = [-0.0, -0.0005, -0.005, -0.05, -0.25, -0.5, -1.0, -2.0, -3.0, -4.0, -5.0, -6.0, -7.0 ]), and the left of the domain is free vertically and moved horizontally to a set of given fixed displacements (d = [-0.0, -0.0005, -0.005, -0.05, -0.25, -0.5, -1.0, -2.0, -3.0, -4.0, -5.0, -6.0, -7.0 ]). The results of the simulations include: (1) change in strain energy at each step, (2) total reaction force at the top and right boundaries at each step, and (3) full field displacement at each step. All simulations are conducted with the FEniCS computing platform (https://fenicsproject.org). The code to reproduce these simulations is hosted on GitHub (https://github.com/elejeune11/Mechanical-MNIST/tree/master/generate_dataset).
The paper "Mechanical MNIST: A benchmark dataset for mechanical metamodels" can be found at https://doi.org/10.1016/j.eml.2020.100659. All code necessary to reproduce the metamodels demonstrated in the manuscript is available on GitHub (https://github.com/elejeune11/Mechanical-MNIST). For questions, please contact Emma Lejeune (elejeune@bu.edu).
2020-02-01T00:00:00ZMechanical MNIST - Confined CompressionLejeune, Emmahttps://hdl.handle.net/2144/394272020-04-27T13:47:46Z2020-02-01T00:00:00ZMechanical MNIST - Confined Compression
Lejeune, Emma
Each dataset in the Mechanical MNIST collection contains the results of 70,000 (60,000 training examples + 10,000 test examples) finite element simulation of a heterogeneous material subject to large deformation. Mechanical MNIST is generated by first converting the MNIST bitmap images (http://www.pymvpa.org/datadb/mnist.html) to 2D heterogeneous blocks of material. Consistent with the MNIST bitmap ($28 \times 28$ pixels), the material domain is a $28 \times 28$ unit square. In "Mechanical MNIST - Equibiaxial Extension," the material is Neo-Hookean with a varying modulus. The top of the domain is free horizontally and moved vertically to a set of given fixed displacements (d = [-0.0, -0.001, -0.01, -0.1, -0.5, -1.0, -1.5, -2.0, -2.5, -3.0, -3.5] ), the right and left sides of the domain are free vertically and fixed horizontally, and the bottom of the domain is free horizontally and fixed vertically. The results of the simulations include: (1) change in strain energy at each step, (2) total reaction force at the top and right boundaries at each step, and (3) full field displacement at each step. All simulations are conducted with the FEniCS computing platform (https://fenicsproject.org). The code to reproduce these simulations is hosted on GitHub (https://github.com/elejeune11/Mechanical-MNIST/tree/master/generate_dataset).
The paper "Mechanical MNIST: A benchmark dataset for mechanical metamodels" can be found at https://doi.org/10.1016/j.eml.2020.100659. All code necessary to reproduce the metamodels demonstrated in the manuscript is available on GitHub (https://github.com/elejeune11/Mechanical-MNIST). For questions, please contact Emma Lejeune (elejeune@bu.edu).
2020-02-01T00:00:00ZMechanical MNIST - Uniaxial ExtensionLejeune, Emmahttps://hdl.handle.net/2144/386932020-04-27T13:46:01Z2019-12-01T00:00:00ZMechanical MNIST - Uniaxial Extension
Lejeune, Emma
Each dataset in the Mechanical MNIST collection contains the results of 70,000 (60,000 training examples + 10,000 test examples) finite element simulation of a heterogeneous material subject to large deformation. Mechanical MNIST is generated by first converting the MNIST bitmap images (http://www.pymvpa.org/datadb/mnist.html) to 2D heterogeneous blocks of material. Consistent with the MNIST bitmap ($28 \times 28$ pixels), the material domain is a $28 \times 28$ unit square. In “Mechanical MNIST - Uniaxial Extension,” the material is Neo-Hookean with a varying modulus. The bottom of the domain is fixed (Dirichlet boundary condition), the left and right edges of the domain are free, and the top of the domain is fixed horizontally and moved vertically to a set of given fixed displacements (d = [0.0, 0.001, 0.01, 0.1, 0.5, 1.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0 ]). The results of the simulations include: (1) change in strain energy at each step, (2) total reaction force at the top boundary at each step, and (3) full field displacement at each step. All simulations are conducted with the FEniCS computing platform (https://fenicsproject.org). The code to reproduce these simulations is hosted on GitHub (https://github.com/elejeune11/Mechanical-MNIST/tree/master/generate_dataset).
The paper "Mechanical MNIST: A benchmark dataset for mechanical metamodels" can be found at https://doi.org/10.1016/j.eml.2020.100659. All code necessary to reproduce the metamodels demonstrated in the manuscript is available on GitHub (https://github.com/elejeune11/Mechanical-MNIST). For questions, please contact Emma Lejeune (elejeune@bu.edu).
2019-12-01T00:00:00Z