Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data
Authors: Shaowu Pan, Steven L. Brunton, J. Nathan Kutz
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the utility of NIF for parametric surrogate modeling, enabling the interpretable representation and compression of complex spatio-temporal dynamics, efficient many-spatial-query tasks, and improved generalization performance for sparse reconstruction. [...] 1. NIF generalizes 40% better in terms of root-mean-square error (RMSE) than a generic mesh-agnostic MLP [...] 2. NIF outperforms both (linear) SVD and (nonlinear) CAE in terms of nonlinear dimensionality reduction [...] 3. Compared with the original implicit neural representation [...] NIF enables efficient spatial sampling with 30% less CPU time and around 26% less memory consumption [...] 4. NIF outperforms the state-of-the-art method (POD-QDEIM [...] with 34% smaller testing error |
| Researcher Affiliation | Academia | Shaowu Pan EMAIL Department of Applied Mathematics University of Washington Seattle, WA 98195-4322, USA Steven L. Brunton EMAIL Department of Mechanical Engineering University of Washington Seattle, WA 98195-4322, USA J. Nathan Kutz EMAIL Department of Applied Mathematics University of Washington Seattle, WA 98195-4322, USA |
| Pseudocode | No | The paper describes methods and formulations using mathematical equations and descriptive text, such as in Section 2 "Neural Implicit Flow" and Section 2.1 "Data-fit parametric surrogate modeling for PDEs". However, it does not include any explicitly labeled "Pseudocode" or "Algorithm" blocks with structured steps. |
| Open Source Code | Yes | The code and data for the following applications is available at https://github.com/ pswpswpsw/paper-nif. The Python package for NIF is available at https://github.com/ pswpswpsw/nif. |
| Open Datasets | Yes | We use the forced isotropic turbulence dataset from JHU Turbulence dataset (Li et al., 2008) with Taylor-scale Reynolds number Reλ around 433. [...] We obtain the weekly averaged sea surface temperature data since 1990 to present from NOAA website 10. [...] https://downloads.psl.noaa.gov/Datasets/noaa.oisst.v2/sst.wkmean.1990-present.nc |
| Dataset Splits | Yes | The training data consists of 20 points in the parameter µ space (i.e., 20 simulations with distinct µ). The testing data consists of 59 simulations with a finer sampling of µ. [...] We sample the flowfield uniformly in time and split such single trajectories into 84 training and 28 testing snapshots in a way that the testing snapshots fall in between the training snapshots. [...] We take snapshots from 1990 to 2006 as training data and that of the next 15 years, until 2021, as testing data. |
| Hardware Specification | Yes | For all the results shown in this paper, we have used Nvidia Tesla P100 (16 GB), Nvidia Ge Force RTX 2080 GPU (12 GB), and Nvidia A6000 GPU (48 GB). |
| Software Dependencies | No | The paper mentions several software tools and frameworks such as "Tensorflow (Abadi et al., 2016)", "Adam optimizer (Kingma and Ba, 2014)", "L4 optimizer (Rolinek and Martius, 2018)", and the "scikit-image package (Van der Walt et al., 2014)". However, it does not specify any version numbers for these software components, which is necessary for reproducible setup. |
| Experiment Setup | Yes | For NIF, we take 4 layers with units for Parameter Net as 2-30-30-2-6553 and 5 layers with units 1-56-56-56-1 with Res Net-like skip connection for Shape Net. [...] The model parameters are initialized with a truncated normal with standard deviation of 0.1 [...] We adopt the Adam optimizer (Kingma and Ba, 2014) with a learning rate of 1e-3, batch size of 1024 and 40000 epochs. [...] The learning rate is 2e-5 for NIF and 1e-3 for CAE with a batch size of 3150 for NIF and 4 for CAE. The total learning epoch is 10,000 for CAE and 800 for NIF. |