Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domains
Authors: Razmik Khosrovian, Takaharu Yaguchi, Hiroaki Yoshimura, Takashi Matsubara
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluated Po Di NNs and related methods to demonstrate their modeling performance using seven simulation datasets, as shown in Fig. 2. Due to page limitations, we briefly overview their characteristics. The full explanations can be found in Appendix F. |
| Researcher Affiliation | Academia | 1Osaka University 2Kobe University 3Waseda University 4Hokkaido University |
| Pseudocode | No | The paper describes mathematical formulations, definitions, and equations, but it does not contain a clearly labeled 'Pseudocode' or 'Algorithm' section, nor does it present any structured, code-like algorithmic steps. |
| Open Source Code | Yes | For full reproducibility, it is recommended to run the source code attached as supplementary material. |
| Open Datasets | No | We evaluated Po Di NNs and related methods to demonstrate their modeling performance using seven simulation datasets, as shown in Fig. 2. Due to page limitations, we briefly overview their characteristics. The full explanations can be found in Appendix F. |
| Dataset Splits | Yes | Each training subset consisted of 1,000 trajectories of 1,000 steps, and each test subset consisted of 10 trajectories of 10,000 steps. |
| Hardware Specification | Yes | All experiments were conducted on a single NVIDIA A100 GPU. |
| Software Dependencies | Yes | We implemented all experimental code from scratch using Python v3.11.9, along with numpy v1.26.4, scipy v1.12.1, pytorch v2.3.1, and desolver v4.1.1 (Paszke et al., 2017). |
| Experiment Setup | Yes | Following previous studies (Greydanus et al., 2019; Matsubara et al., 2020), we used fully-connected neural networks with two hidden layers to implement any vector fields and energy functions for all models. Each hidden layer had 200 units, followed by a hyperbolic tangent activation function. Weight matrices were initialized using Py Torch s default algorithm. In Po Di NNs, each element of the bivector B related to energy-dissipating components was initialized from a uniform distribution U( 0.1, 0.1), while the remaining elements are set to zero... Unless stated otherwise, the time step size was set to t = 0.1... The Dormand Prince method (dopri5) with absolute tolerance atol = 10 7 and relative tolerance rtol = 10 9 was used to integrate the ground truth ODEs and neural network models (Dormand & Prince, 1986). The Adam optimization algorithm (Kingma & Ba, 2015) was applied with parameters (β1, β2) = (0.9, 0.999) and a batch size of 100 for updates. The learning rate was initialized at 10 3 and decayed to zero using cosine annealing (Loshchilov & Hutter, 2017). The number of training iterations was set to 100,000. |