Phase2vec: dynamical systems embedding with a physics-informed convolutional network
Authors: Matt Ricci, Noa Moriel, Zoe Piran, Mor Nitzan
ICLR 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Here, we propose, phase2vec, an embedding method that learns highquality, physically-meaningful representations of low-dimensional dynamical systems without supervision. Our embeddings are produced by a convolutional backbone that extracts geometric features from flow data and minimizes a physicallyinformed vector field reconstruction loss. The trained architecture can not only predict the equations of unseen data, but also produces embeddings that encode meaningful physical properties of input data (e.g. stability of fixed points, conservation of energy, and the incompressibility of flows) more faithfully than standard blackbox classifiers and state-of-the-art time series classification techniques. We additionally apply our embeddings to the analysis of meteorological data, showing we can detect climatically meaningful features. |
| Researcher Affiliation | Academia | Matthew Ricci School of Computer Science and Engineering The Hebrew University Jerusalem, Israel matthew.ricci@mail.huji.ac.il Noa Moriel School of Computer Science and Engineering The Hebrew University Jerusalem, Israel noa.moriel@mail.huji.ac.il Zoe Piran School of Computer Science and Engineering The Hebrew University Jerusalem, Israel zoe.piran@mail.huji.ac.il Mor Nitzan School of Computer Science and Engineering, Racah Institute of Physics, Faculty of Medicine The Hebrew University Jerusalem, Israel mor.nitzan@mail.huji.ac.il |
| Pseudocode | No | The paper does not contain any sections explicitly labeled "Pseudocode" or "Algorithm", nor does it present structured, code-like procedural steps. |
| Open Source Code | Yes | 1Code available here: https://github.com/nitzanlab/phase2vec |
| Open Datasets | Yes | Global wind vectors Data was downloaded from IRI/LDEO Climate Data Library (https://iridl.ldeo.columbia.edu/). World climate data We took climate data from World Clim V2 (http://www.worldclim.org). Corresponding K oppen labels were downloaded from Glo H2O, K oppen Geiger (http://www.gloh2o.org/koppen/). |
| Dataset Splits | Yes | Network hyperparameters were selected to minimize validation loss on two data sets: ... For each task we computed the relevant embeddings and then trained a logistic regressor on 80% of the data. The remaining 20% was held out for testing, using a stratified train-test split. An ℓ2 penalty was cross-validated using leave-one-out cross-validation on validation data split from the training set. |
| Hardware Specification | Yes | All experiments were carried out using pytorch v. 1.12 using an NVIDIA RTX 3060 GPU. |
| Software Dependencies | Yes | All experiments were carried out using pytorch v. 1.12 using an NVIDIA RTX 3060 GPU. |
| Experiment Setup | Yes | The convolutional part of the phase2vec embedding pipeline consisted of three convolutional blocks, each with kernel size 3 3, stride 2 2 and 128 channels. ... The model was trained with an ADAM optimizer using a learning rate of 1 10 4 over 200 iterations. ... MLP layers were alternated with batch norm layers as well as dropout layers whose rate we set to p = .1 during training. ... We set n = 64 ... We chose c = 3 (cubic degree) ... The same sparsity regularizer of β = 1 10 3 was used in both models. |