Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamics
Authors: Cristopher Salvi, Maud Lemercier, Andris Gerasimovics
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments on various semilinear SPDEs, including the stochastic Navier-Stokes equations, demonstrate how the Neural SPDE model is capable of learning complex spatiotemporal dynamics in a resolution-invariant way, with better accuracy and lighter training data requirements compared to alternative models, and up to 3 orders of magnitude faster than traditional solvers. |
| Researcher Affiliation | Academia | Cristopher Salvi Imperial College London & The Alan Turing Institute c.salvi@imperial.ac.uk Maud Lemercier University of Warwick maud.lemercier@warwick.ac.uk Andris Gerasimoviˇcs University of Bath ag2616@bath.ac.uk |
| Pseudocode | No | No pseudocode or algorithm block was found in the provided text. |
| Open Source Code | Yes | The code for the experiments is provided in the supplementary material. |
| Open Datasets | No | We run experiments on three semilinear SPDEs: the stochastic Ginzburg-Landau equation in 4.1, the stochastic Korteweg-De Vries equation in 4.2, and the stochastic Navier-Stokes equations in 4.3. (The paper describes how they generate their own data by solving these SPDEs, e.g., 'the response paths are generated by solving the SPDE along each sample path of the noise ξ'. It does not provide access information for a public or open dataset.) |
| Dataset Splits | No | We consider two data-regimes: a low data regime where the total number of training observations is N = 1 000, and a large data regime where N = 10 000. In both cases, the response paths are generated by solving the SPDE... Relative L2 error on the test set. (The paper mentions training and test sets but does not explicitly describe a validation set or its split details.) |
| Hardware Specification | Yes | Experiments are run on a Tesla P100 NVIDIA GPU. |
| Software Dependencies | No | We found that the ODE approach is approximately 10 times slower than the Fixed Point approach. We believe this is largely an implementation issue of the torchdiffeq library, while the FFT is a highly optimised transform in Pytorch. (Software names like 'torchdiffeq' and 'Pytorch' are mentioned, but specific version numbers are not provided.) |
| Experiment Setup | No | The hyper-parameters for all the models are selected by grid-search (see Appendix B.2 for further experimental details). (While it indicates hyperparameters are discussed in Appendix B.2, the specific values or detailed training configurations are not explicitly present in the provided text snippet.) |