Learning continuous-time PDEs from sparse data with graph neural networks
Authors: Valerii Iakovlev, Markus Heinonen, Harri Lähdesmäki
ICLR 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate our model s performance in learning the dynamics of known physical systems. We compare to state-of-the-art competing methods, and begin by performing ablation studies to measure how our model s performance depends on measurement grid sizes, interval between observations, irregular sampling, amount of data and amount of noise. |
| Researcher Affiliation | Academia | Valerii Iakovlev, Markus Heinonen & Harri Lähdesmäki Department of Computer Science Aalto University Helsinki, Finland {valerii.iakovlev, markus.o.heinonen, harri.lahdesmaki}@aalto.fi |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | Scripts and data for reproducing the experiments can be found in this github repository. |
| Open Datasets | No | The paper states that training data was obtained by solving initial-boundary value problems and downsampling these solutions. It does not provide concrete access information (e.g., a link, DOI, or formal citation with authors/year) for a publicly available dataset. |
| Dataset Splits | No | The paper specifies the training and testing data sizes but does not explicitly mention a validation data split or its details. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory) used for running its experiments. |
| Software Dependencies | No | The paper mentions “torchdiffeq Python package” and “Rprop optimizer” but does not provide specific version numbers for these software components or the Python language. |
| Experiment Setup | Yes | The model used for all following experiments contains a single graph layer. The mean was selected as the aggregation function. Functions φ(1)(ui, ) and γ(1)(ui, uj ui, xj xi) were represented by multilayer perceptrons with 3 hidden layers and hyperbolic tangent activation functions. Input/output sizes for φ(1) and γ(1) were set to 4/40 and 41/1 respectively. The number of hidden neurons was set to 60. This gives approximately 20k trainable parameters. [...] adaptive-order implicit Adams solver was used with rtol and atol set to 1.0 10 7. Rprop (Riedmiller & Braun, 1992) optimizer was used with learning rate set to 1.0 10 6 and batch size set to 24. |