Optimal deep learning of holomorphic operators between Banach spaces
Authors: Ben Adcock, Nick Dexter, Sebastian Moraga Scheuermann
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we present numerical results demonstrating the practical performance on challenging problems including the parametric diffusion, Navier-Stokes-Brinkman and Boussinesq PDEs. |
| Researcher Affiliation | Academia | Ben Adcock Department of Mathematics Simon Fraser University Canada Nick Dexter Department of Scientific Computing Florida State University USA Sebastian Moraga Department of Mathematics Simon Fraser University Canada |
| Pseudocode | No | The paper does not contain structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | We provide all the necessary software to reproduce our experiments along with instructions for running the code to generate the results. |
| Open Datasets | No | We generate the measurements Yi using mixed variational formulations of the parametric elliptic, Navier-Stokes-Brinkman and Boussinesq PDEs discretized using FEni CS with input data Xi. The noise Ei Y encompasses the discretization errors from numerical solution. |
| Dataset Splits | No | The paper does not provide specific dataset split information (exact percentages, sample counts, citations to predefined splits, or detailed splitting methodology) needed to reproduce the data partitioning. It mentions early stopping but no explicit validation set. |
| Hardware Specification | Yes | We train the DNN models in single precision on the Digital Research Alliance of Canada s Cedar compute cluster (see https://docs.alliancecan.ca/wiki/Cedar), using Intel Xenon Processor E5-2683 v4 CPUs with either 125GB or 250GB per node. |
| Software Dependencies | Yes | We use the open-source finite element library FEni CS, specifically version 2019.1.0 [9], and Google s Tensor Flow version 2.12.0. |
| Experiment Setup | Yes | To solve (2.5) we use Adam [47] with early stopping and an exponentially decaying learning rate. We train our DNN architectures for 60,000 epochs and results are averaged over a number of trials. ... We train our models for 60,000 epochs or until converging to a tolerance level of ϵtol = 5 10 7 in single precision. ... Based on the strategies in [1], we fix the number of nodes per layer N and depth L such that the ratio β := L/N is β = 0.5. In addition, we initialize the weights and biases using the He Uniform initializer from keras setting the seed to the trial number. |