Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEs
Authors: S Chandra Mouli, Danielle C. Maddix, Shima Alizadeh, Gaurav Gupta, Andrew Stuart, Michael W. Mahoney, Bernie Wang
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our empirical results show that OPERATOR-PROBCONSERV enhances OOD model performance for a variety of challenging PDE problems and satisfies physical constraints such as conservation laws. |
| Researcher Affiliation | Collaboration | 1Department of Computer Science, Purdue University, West Lafayette, IN, USA (Work done during an internship at AWS AI Labs.) 2AWS AI Labs, Santa Clara, CA, USA 3Department of Computing and Mathematical Sciences, Caltech, Pasadena, CA, USA 4Amazon Search, Pasadena, CA, USA 5Amazon Supply Chain Optimization Technologies, New York, NY, USA. |
| Pseudocode | No | No pseudocode or algorithm blocks were found in the paper. |
| Open Source Code | Yes | The code is available at https://github.com/amazon-science/operator-probconserv. |
| Open Datasets | No | The paper describes how the training data was generated and its characteristics (e.g., 'Our training dataset consists of N = 400 input/output pairs'), and provides parameter ranges in Table 1, but does not provide concrete access information (link, DOI, citation for dataset repository) to the actual datasets used for training. |
| Dataset Splits | No | The paper mentions using 'in-domain validation MSE' for hyperparameter selection but does not explicitly provide specific percentages, sample counts, or citations for train/validation/test splits. |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory) used for running the experiments were provided in the paper. |
| Software Dependencies | No | The paper mentions the use of 'Adam optimizer' and specific frameworks like 'Fourier Neural Operator (FNO)' and 'PROBCONSERV', but it does not specify version numbers for any software dependencies (e.g., PyTorch, Python, CUDA versions). |
| Experiment Setup | Yes | We use the standard optimization procedure for training FNO models (Li et al., 2020a). In particular, we use the Adam optimizer with a weight decay. We optimize the objective, and learn over batches of a given batch size B (fixed to B = 20 in our experiments). We use a learning rate scheduler that halves the learning rate after every 50 epochs." Also refer to Table 2 which lists hyperparameters like 'Number of Fourier layers 4', 'Channel width {32, 64}', 'Number of Fourier modes 12', 'Batch size 20', 'Learning rate {10-4, 10-3, 10-2}' for FNO, and 'Number of heads M 10', 'Diversity regularization λdiverse {10-2, 10-1, 1, 101, 102}' for DIVERSENO. |