Unifying physical systems’ inductive biases in neural ODE using dynamics constraints
Authors: Yi Heng Lim, Muhammad Firmansyah Kasim
TMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In order to see if the methods described above work, we tested them on various physical systems. Task 1 Ideal mass-spring system. ... Task 4 Damped single rod-pendulum with redundant states. ... We trained all models in all tasks with Adam optimiser (Kingma & Ba, 2014) and the same learning rate of 10^-4. ... To test, we started from a randomly generated state at time 0, and rolled out the subsequent states from time 0 to 100, and logged the RMSE of the energy deviations. |
| Researcher Affiliation | Industry | Yi Heng Lim EMAIL Machine Discovery Ltd. Oxford, United Kingdom Muhammad Firmansyah Kasim EMAIL Machine Discovery Ltd. Oxford, United Kingdom |
| Pseudocode | No | The paper describes methods using mathematical equations and prose but does not include any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | Yes | Our code for this paper is available at https://anonymous.4open.science/r/constr-F2D4/. |
| Open Datasets | No | For Task 1 and Task 2, ... We generated the data by randomly initialising the state from a normal distribution, and added white noise with σ = 0.1 to the state trajectory. For training, we generated 250 trajectories... For Task 3, ... generated the data by randomly initialising the state from a normal distribution and obtained the trajectory. ... For Task 4, ... we modified the code from Open AI pendulum gym (Brockman et al., 2016) to include a damping factor of 0.05 to the pendulum motion. The paper primarily uses generated data or data generated from a modified environment, not publicly available datasets with direct access information. |
| Dataset Splits | Yes | For training, we generated 250 trajectories, with 30 samples in each trajectory equally spaced within t = [0, 2π]. ... For Task 3, ... 2000 trajectories, with 300 samples in each trajectory equally spaced within t = [0, 2π]. ... To test, we started from a randomly generated state at time 0, and rolled out the subsequent states from time 0 to 100, and logged the RMSE of the energy deviations. Note that the initial state at testing is different from the training data. |
| Hardware Specification | Yes | We ran all experiments for 1000 epochs on a single NVIDIA Tesla T4 GPU. |
| Software Dependencies | No | The paper mentions using 'Adam optimiser' and the 'FrEIA package' but does not specify version numbers for these or any other software components. |
| Experiment Setup | Yes | We trained all models in all tasks with Adam optimiser (Kingma & Ba, 2014) and the same learning rate of 10^-4. We constructed multi-layer perceptrons (MLPs) for all models, with 3 layers of 200 hidden units in each case. INN with 8 blocks was used where needed, with each block having 2 layers of 100 hidden units. We chose softplus as the activation function for all models... For our method, we set the coefficient of the constraint as large as possible... In Task 1, 2, 3 and 4 respectively, we set the coefficient to be 10^5, 10^4, 10^3 and 10^2. We used a batch size of 32 for Task 1, Task 2 and Task 4, and a larger batch size of 1280 for Task 3... We ran all experiments for 1000 epochs. |