Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities
Authors: Samuel Lanthaler, Roberto Molinaro, Patrik Hadorn, Siddhartha Mishra
ICLR 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | This paper investigates, both theoretically and empirically, the operator learning of PDEs with discontinuous solutions. ... Our theoretical findings are confirmed by empirical results for advection equation, inviscid Burgers equation and compressible Euler equations of aerodynamics. |
| Researcher Affiliation | Academia | Samuel Lanthaler Computing and Mathematical Science California Institute of Technology Pasadena, CA, USA slanth@caltech.edu Roberto Molinaro, Patrik Hadorn & Siddhartha Mishra Seminar for Applied Mathematics ETH Zurich Zurich, Switzerland {roberto.molinaro,siddhartha.mishra}@ethz.ch |
| Pseudocode | No | The paper does not contain any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain an explicit statement about the availability of open-source code or a link to a code repository. |
| Open Datasets | No | The paper describes generating its own training data based on specific parameters and measures (e.g., 'sampled from a Gaussian Random field', 'drawn from the measure'), but does not provide access to these generated datasets or refer to an existing public dataset with concrete access information (link, DOI, or specific citation to the dataset itself). |
| Dataset Splits | Yes | For all the benchmarks, a training set with 1024 samples, and a validation and test set each with 128 samples, are used. |
| Hardware Specification | No | The paper does not specify any particular hardware used for running the experiments (e.g., GPU models, CPU types, or memory). |
| Software Dependencies | No | The paper mentions 'ADAM optimizer' and 'ALSVINN code Lye (2020)' for data generation, but does not provide specific version numbers for any software, libraries, or frameworks used for training the models (e.g., Python, PyTorch, TensorFlow, CUDA versions). |
| Experiment Setup | Yes | The training is performed with the ADAM optimizer, with learning rate 5 10 4 for 10000 epochs and minimizing the L1-loss function. We use the learning rate schedulers defined in table 2. We train the models in mini-batches of size 10. A weight decay of 10 6 is used for Res Net (all numerical experiments), DON and s DON (linear advection equation, Burgers equation, and shock-tube problem). On the other hand, no weight decay is employed for remaining experiments and models. 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 saved for testing. Therefore, no early stopping is used. The models hyperparameters are selected by running grid searches over a range of hyperparameter values and selecting the configuration realizing the lowest relative L1-error on the validation set. |