DNN-based Topology Optimisation: Spatial Invariance and Neural Tangent Kernel
Authors: Benjamin Dupuis, Arthur Jacot
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We empirically confirm our theoretical observations and study how the filter size is affected by the architecture of the network. Our solution can easily be applied to any other coordinates-based generation method. ... We confirm and illustrate these theoretical observations with numerical experiments. |
| Researcher Affiliation | Academia | Benjamin Dupuis Chair of Statistical Field Theory Ecole Polytechnique F ed erale de Lausanne Lausanne, Switzerland benjamin.dupuis@epfl.ch; Arthur Jacot Chair of Statistical Field Theory Ecole Polytechnique F ed erale de Lausanne Lausanne, Switzerland arthur.jacot@epfl.ch |
| Pseudocode | No | The paper describes methods and propositions but does not include structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | Our implementation of the algorithm will be made public at https://github.com/benji Dupuis/Deep Topo. |
| Open Datasets | No | The paper describes a topology optimization problem on a grid and does not mention using or providing access to any specific publicly available dataset. It refers to established methods for SIMP ([1] and [18]) but not for the data itself. |
| Dataset Splits | No | The paper describes an optimization problem setup and does not mention explicit training, validation, or test dataset splits in the context of machine learning datasets. |
| Hardware Specification | No | The paper does not provide specific hardware details such as GPU/CPU models or memory specifications used for running experiments. It only mentions that 'Most of our experiments were conducted with a torus embedding or a gaussian embedding.' |
| Software Dependencies | No | The paper mentions that its SIMP implementation is based on [1] and [18], and that it uses sparse Cholesky factorisation [9, 8] or BICGSTAB method [33]. However, it does not specify versions for any programming languages, libraries, or software packages (e.g., Python, PyTorch, TensorFlow, specific solvers with version numbers). |
| Experiment Setup | Yes | Here are the hyperparameters used in the experiments. For the Gaussian embedding, we used n0 = 1000 and a length scale ℓ= 4. This embedding was followed by one hidden linear layer of size 1000 with standardized Re Lu (x 7 2 max(0, x)) and a bias parameter β = 0.5. For the torus embedding we set the torus radius to r = 2 ... and the discretisation angle to δ = π 2 max(nx,ny). It was followed by 2 linear layers of size 1000 with β = 0.1. ... We used a cosine activation of the form x 7 cos(ωx), ... When not stated otherwise we used ω = 5. ... we obtain similar results with other optimizers such as RPROP [24] (learning rate 10 3) and ADAM [16] (learning rate 10 3). |