Mechanistic Neural Networks for Scientific Machine Learning
Authors: Adeel Pervez, Francesco Locatello, Stratis Gavves
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To empirically validate the claim and showcase the power, versatility, and generality of Mechanistic Neural Networks, we perform a large array of experiments comparing and consistently outperforming the specialized golden standards: SINDy for equation discovery (Brunton et al., 2016) (Section 5.1), Neural ODE variants (Chen et al., 2018; Norcliffe et al., 2020) for modelling linear and nonlinear dynamics (Sections 5.3, 5.5, 5.4), and Neural operators (Li et al., 2020c; Brandstetter et al., 2022) for PDE modelling (Section 5.2). |
| Researcher Affiliation | Academia | 1Informatics Institute, University of Amsterdam, Amsterdam, The Netherlands 2Institute of Science and Technology, Klosterneuburg, Austria. |
| Pseudocode | No | The paper describes the methods in prose but does not include structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | Source code is available at https://github.com/alpz/mech-nn. |
| Open Datasets | Yes | We use planetary ephemerides data from the JPL Horizons database for solar system dynamics (Giorgini, 2015). The data is positions and velocities for the 25 largest bodies in the solar system from 1980 to 2015 with a step size of 12 hours. ... We test MNN on the nested spheres dataset (Dupont et al., 2019)... We reproduce an experiment with a real-world aircraft benchmark dataset (Noël and Schoukens, 2017; Norcliffe et al., 2020). ... We use the 2d Darcy Flow dataset used by (Li et al., 2020c) scaled to 85x85. |
| Dataset Splits | Yes | We use the first 70% of the data for training and the rest for evaluation. |
| Hardware Specification | No | The paper mentions "GPU parallel processing" and "GPU parallelizable for large ODE systems" but does not specify any particular hardware models (e.g., NVIDIA A100, Intel Xeon, etc.) used for experiments. |
| Software Dependencies | No | The paper mentions comparing against "RK4 from scipy and torchdiffeq" but does not provide specific version numbers for these software packages or any other dependencies. |
| Experiment Setup | Yes | We use a second order ODE with coefficients computed with a single layer and the right hand side is set to 0. We use a step size of 0.1 and length 30. (Section B.2). For this experiment (Section 5.5) we use an MNN with a second order ODE, step size of 0.1 and 200 steps during training. The coefficients and constant terms are computed with MLPs with 1024 hidden units. (Section B.3). We use a step size of 0.01 and run for 50 epochs. (Section B.4). |