Learning Space-Time Continuous Latent Neural PDEs from Partially Observed States
Authors: Valerii Iakovlev, Markus Heinonen, Harri Lähdesmäki
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Our model demonstrates state-of-the-art performance on complex synthetic and real-world datasets, overcoming limitations of previous approaches and effectively handling partially-observed data. The proposed model outperforms recent methods, showing its potential to advance data-driven PDE modeling and enabling robust, grid-independent modeling of complex partially-observed dynamic processes. |
| Researcher Affiliation | Academia | Valerii Iakovlev Markus Heinonen Harri Lähdesmäki Department of Computer Science, Aalto University, Finland {valerii.iakovlev, markus.o.heinonen, harri.lahdesmaki}@aalto.fi |
| Pseudocode | No | The paper describes the generative model and inference procedure in textual form with mathematical equations, but does not include a pseudocode block or algorithm. |
| Open Source Code | Yes | Source code and datasets can be found in our github repository. |
| Open Datasets | Yes | The datasets used for training, validation, and testing contain 60, 20, and 20 trajectories, respectively. |
| Dataset Splits | Yes | All datasets contain 60/20/20 training/validation/testing trajectories. ... Validation. We use validation set to track the performance of our model during training and save the parameters that produce the best validation performance. |
| Hardware Specification | Yes | Training is done on a single NVIDIA Tesla V100 GPU, with a single run taking 3-4 hours. |
| Software Dependencies | No | The latent spatiotemporal dynamics are simulated using differentiable ODE solvers from the torchdiffeq package (Chen, 2018) (we use dopri5 with rtol=1e-3, atol=1e-4, no adjoint). |
| Experiment Setup | Yes | We train our model for 20k iterations with constant learning rate of 3e-4 and linear warmup. The latent spatiotemporal dynamics are simulated using differentiable ODE solvers from the torchdiffeq package (Chen, 2018) (we use dopri5 with rtol=1e-3, atol=1e-4, no adjoint). Training is done on a single NVIDIA Tesla V100 GPU, with a single run taking 3-4 hours. We use the mean absolute error (MAE) on the test set as the performance measure. Error bars are standard errors over 4 random seeds. For forecasting we use the expected value of the posterior predictive distribution. See Appendix C for all details about the training, validation, and testing setup. |