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.