Implicit Neural Spatial Representations for Time-dependent PDEs
Authors: Honglin Chen, Rundi Wu, Eitan Grinspun, Changxi Zheng, Peter Yichen Chen
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. |
| Researcher Affiliation | Academia | 1Department of Computer Science, Columbia University, New York, USA 2Department of Computer Science, University of Toronto, Toronto, Canada 3Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, USA. |
| Pseudocode | Yes | Algorithm 1 Time integration |
| Open Source Code | Yes | Videos and codes are available on the project page.1 1Project webpage: http://www.cs.columbia.edu/cg/INSR-PDE/ |
| Open Datasets | No | The paper's experiments involve solving PDEs with analytical ground truths or high-resolution reference solutions (e.g., 1D advection, 2D Taylor-Green vortex, elasticity problems). It does not refer to or provide access information for traditional, pre-existing publicly available datasets used for training in a machine learning sense. |
| Dataset Splits | No | The paper describes a PDE solver, not a model trained with explicit train/validation/test dataset splits. It evaluates the solver's accuracy by comparing its results to ground truth or reference solutions, which is a different evaluation paradigm. |
| Hardware Specification | Yes | We implemented our method using the PyTorch library and performed experiments on an NVIDIA GeForce RTX 3090 GPU. |
| Software Dependencies | No | The paper mentions 'PyTorch library', 'Adam' (optimizer), 'Bartels', and 'Taichi' but does not provide specific version numbers for these software components. |
| Experiment Setup | Yes | We set an initial learning rate lr0 and reduce it by a factor of 0.1 if the loss value does not decrease for iterp iterations. We stop the optimization process when the learning rate is lower than lrmin or until it reaches a maximum of itermax iterations. Specific values of these hyper-parameters are described for each example below. We further report all the parameters and experiment setup in Table 6. |