Low-Rank Registration Based Manifolds for Convection-Dominated PDEs
Authors: Rambod Mojgani, Maciej Balajewicz399-407
AAAI 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the efficacy and interpretability of our proposed approach on several challenging manufactured computer vision-inspired tasks and physical systems. ... The implementations, data and the results are available at https://github.com/rmojgani/Physics Aware AE. ... Experiments |
| Researcher Affiliation | Collaboration | Rambod Mojgani,1,2 Maciej Balajewicz 1,3 1 University of Illinois at Urbana-Champaign, 2 Rice University, 3 Siemens Technology |
| Pseudocode | Yes | Algorithm 1 The map from the constant grid to the parameter/time-varying grid, G (.) ... Algorithm 2 The map from the parameter/time-varying grid to the constant grid to , G 1 (.) ... Algorithm 3 Training of the proposed low-rank registration based manifold |
| Open Source Code | Yes | The implementations, data and the results are available at https://github.com/rmojgani/Physics Aware AE. |
| Open Datasets | Yes | The implementations, data and the results are available at https://github.com/rmojgani/Physics Aware AE. |
| Dataset Splits | No | The paper defines training and extrapolation ranges for time-series data but does not explicitly mention or specify a separate validation dataset split. |
| Hardware Specification | No | The paper does not specify the hardware used for running its experiments. |
| Software Dependencies | No | The paper mentions 'Sequential Least Squares Programming in scipy for the Python implementation' and 'fmincon for the MATLAB implementation', and 'Keras', but does not provide specific version numbers for any of these software components. |
| Experiment Setup | Yes | In this problem, Ux is down-sampled to size of 7, i.e. the total of 49 control points. Moreover, vmin = 0, Γ1 = 100Dxx and Γ2 = (100/π) Dθθ... A rank-2 time-varying grid (r = 2) is learned via (5) setting kr = 4, and γ1 = γ2 = 0.05... An implicit second order time discretization is used with t = 8 10 3 and space is uniformly discretized where x = 1 10 2. In the proposed architecture, the rank-1 time-varying grid (r = 1), representing the low-rank auto-encoder, is learned as in (5) with kr = 4. In this problem, vmin = 10 3, Γ1 = γ1Dxx and Γ2 = γ2Dtt, where γ1 = γ2 = 1... |