Non-Linear Operator Approximations for Initial Value Problems
Authors: Gaurav Gupta, Xiongye Xiao, Radu Balan, Paul Bogdan
ICLR 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We perform experiments on non-linear systems such as Korteweg-de Vries (Kd V) and Kuramoto Sivashinsky (KS) equations to show that the proposed approach achieves the best performance and at the same time is data-efficient. We also show that urgent real-world problems like epidemic forecasting (for example, COVID19) can be formulated as a 2D time-varying operator problem. The proposed Pad e exponential operators yield better prediction results (53% (52%) better MAE than best neural operator (non-neural operator deep learning model)) compared to state-of-the-art forecasting models. |
| Researcher Affiliation | Academia | Gaurav Gupta 1, Xiongye Xiao 1, Radu Balan 2, Paul Bogdan 1 1 Ming Hsieh Department of Electrical and Computer Engineering University of Southern California Los Angeles, CA 90089, USA 2 Department of Mathematics and the Norbert Wiener Center for Harmonic Analysis and Applications University of Maryland College Park, MD 20742, USA |
| Pseudocode | No | The paper includes Figure 1 titled 'Pad e Exponential Model', which is a diagram of a recurrent neural architecture, but it does not provide formal pseudocode or an algorithm block. |
| Open Source Code | No | The paper does not provide an explicit statement about releasing its source code or a link to a code repository for the implemented methodology. |
| Open Datasets | Yes | The COVID-19 data set 3 from April 12th 2020 to August 28th 2021 is provided by Johns Hopkins University (Dong et al., 2020). We take the data of 50 US States, and for each state, we have the total counts of daily reported confirmed (C), recovered (R), and deaths (D). We normalize the data of each state by their total population. Therefore, we have a daily collection of 2-dimensional data of size 50 ˆ 3. https://github.com/CSSEGISandData/COVID-19 |
| Dataset Splits | Yes | In total, we take N training samples, and unless stated otherwise, N 1000 and we test on 200 samples for the synthetic datasets. ... Due to data scarcity (484 samples in total), we do a 10-fold resampling of the dataset to obtain train/test samples and the averaged results are presented for all models. |
| Hardware Specification | Yes | All experiments are done on an Nvidia A100 40GB GPUs. |
| Software Dependencies | No | The paper mentions software components like 'Adam optimizer' and 'chebfun package' but does not specify exact version numbers for these or any other key software dependencies. |
| Experiment Setup | Yes | All neural operator models are trained using Adam optimizer with a learning rate of 0.001 and decay of 0.95 after every 100 steps. The loss function is taken as the relative L2 error. For synthetic datasets we train for a total of 500 epochs and for real-world COVID-19 dataset we train for a total of 750 epochs. |