Neural Inverse Operators for Solving PDE Inverse Problems
Authors: Roberto Molinaro, Yunan Yang, Björn Engquist, Siddhartha Mishra
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | A variety of experiments are presented to demonstrate that NIOs significantly outperform baselines and solve PDE inverse problems robustly, accurately and are several orders of magnitude faster than existing direct and PDE-constrained optimization methods. We test NIOs extensively on a suite of problems... |
| Researcher Affiliation | Academia | 1Seminar for Applied Mathematics (SAM), ETH, Z urich. 2Institute for Theoretical Studies (ITS), ETH Z urich. 3Department of Mathematics and the Oden Institute, The University of Texas at Austin, USA. 4ETH AI Center, ETH, Z urich. |
| Pseudocode | No | The paper describes the architecture and computations using mathematical formulas and prose but does not include any explicit pseudocode or algorithm blocks. |
| Open Source Code | Yes | The implementation of the experiments of the paper is realized within the Py Torch framework and available at https://github.com/mroberto166/nio.git |
| Open Datasets | Yes | For Seismic Imaging, "we choose two types of coefficients from (Deng et al., 2021), the so-called Style-A and Curve Vel A datasets." |
| Dataset Splits | Yes | At every epoch, the relative L1 error is computed on the validation set, and the set of trainable parameters resulting in the lowest error during the entire process is saved for testing. |
| Hardware Specification | Yes | The corresponding total time required to reconstruct the coefficient, amounts to less than 1 second (on CPU) for NIO and 8.5 hours for the traditional method. It is worth noting that the finite difference (FD) solver employed for solving the equation is implemented on GPU within the Py Torch framework. The method... while taking approximately 30 minutes of run-time on an 8-core M1-chip CPU. |
| Software Dependencies | No | The paper mentions using "Py Torch framework" but does not provide specific version numbers for PyTorch or any other software dependencies. |
| Experiment Setup | Yes | The training of the models, including the baselines, is performed with the ADAM optimizer, with a learning rate η for 1000 epochs (250 epochs in the Seismic imaging problem) and minimizing the L1-loss function. We also use a step learning rate scheduler and reduce the learning rate of each parameter group by a factor γ every epoch. We train the models in mini-batches of size 256, and a weight decay of magnitude w is used. Detailed hyperparameters are provided in Tables 3, 4, and 5. |