Learning from Integral Losses in Physics Informed Neural Networks
Authors: Ehsan Saleh, Saba Ghaffari, Tim Bretl, Luke Olson, Matthew West
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our numerical results confirm the existence of the aforementioned bias in practice and also show that our proposed delayed target approach can lead to accurate solutions with comparable quality to ones estimated with a large sample size integral. Our implementation is open-source and available at https://github.com/ehsansaleh/btspinn. |
| Researcher Affiliation | Academia | 1Department of Computer Science 2Department of Aerospace Engineering 3Department of Mechanical Science and Engineering. University of Illinois Urbana-Champaign. |
| Pseudocode | Yes | Algorithm 1 The regularized delayed target method |
| Open Source Code | Yes | Our implementation is open-source and available at https://github.com/ehsansaleh/btspinn. |
| Open Datasets | No | The paper describes using synthetic problems (Poisson, Maxwell, Smoluchowski coagulation) that are set up and simulated, but it does not refer to them as pre-existing, publicly available datasets with links, DOIs, or citations to specific external data repositories. |
| Dataset Splits | No | The paper does not explicitly mention standard training/test/validation dataset splits with specific percentages, sample counts, or references to predefined splits for a fixed dataset. The problems involve continuous domains where points are sampled dynamically. |
| Hardware Specification | No | This work used GPU resources at the Delta supercomputer of the National Center for Supercomputing Applications through Allocation CIS220111 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services and Support (ACCESS) program (Boerner et al., 2023)... The mention of 'GPU resources' and a 'supercomputer' is too general, lacking specific GPU models (e.g., NVIDIA A100, Tesla V100) or CPU details required for detailed hardware specification. |
| Software Dependencies | No | The paper mentions software components like 'Adam' optimizer and 'SiLU or tanh activation functions' (Section D.7) and 'multi-layer perceptrons', but it does not provide specific version numbers for any programming languages, libraries (e.g., PyTorch, TensorFlow), or other software packages used in the implementation. |
| Experiment Setup | Yes | We employed 3-5 layer perceptrons as our deep neural network, using 64 hidden neural units in each layer, and either the Si LU or tanh activation functions. We trained our networks using the Adam (Kingma & Ba, 2014) variant of the stochastic gradient descent algorithm under a learning rate of 0.001. We afforded each method and configuration 1000 function evaluations for each epoch. Table 4 provides a summary of these hyper-parameters along with the volume and surface point. |