Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks
Authors: Sifan Wang, Bowen Li, Yuhan Chen, Paris Perdikaris
JMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We conduct comprehensive numerical experiments demonstrating that Pirate Nets achieve consistent improvements in accuracy, robustness, and scalability across various benchmarks. All code and data accompanying this manuscript will be made publicly available at https://github.com/Predictive Intelligence Lab/jaxpi/tree/pirate. In Section 5, comprehensive numerical experiments are performed to validate the proposed architecture. |
| Researcher Affiliation | Academia | Sifan Wang EMAIL Institution for Foundation of Data Science Yale University New Haven, CT 06520 Bowen Li EMAIL Department of Mathematics City University of Hong Kong Hong Kong SAR Yuhan Chen EMAIL Department of Electrical and Computer Engineering North Carolina State University Raleigh, NC 27695 Paris Perdikaris EMAIL Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia, PA 19104 |
| Pseudocode | No | The paper describes the model architecture using mathematical equations (19)-(24) and a block diagram (Figure 3) but does not contain a distinct block labeled 'Pseudocode' or 'Algorithm'. |
| Open Source Code | Yes | All code and data accompanying this manuscript will be made publicly available at https://github.com/Predictive Intelligence Lab/jaxpi/tree/pirate. |
| Open Datasets | Yes | All code and data accompanying this manuscript will be made publicly available at https://github.com/Predictive Intelligence Lab/jaxpi/tree/pirate. We solve the Allen-Cahn equation using conventional spectral methods. Specifically, assuming periodic boundary conditions, we start from the initial condition u0(x) = x2 cos(πx) and integrate the system up to the final time T = 1. Synthetic validation data is generated using the Chebfun package (Driscoll et al., 2014) with a spectral Fourier discretization with 512 modes and a fourth-order stiff time-stepping scheme (ETDRK4) (Cox and Matthews, 2002) with the time-step size of 10 5. We record the solution at intervals of t = 0.005, yielding a validation dataset with a resolution of 200 512. We compare our results against (Ghia et al., 1982). |
| Dataset Splits | No | The training data points {xi ic}Nic i=1, {ti bc, xi bc}Nbc i=1 and {ti r, xi r}Nr i=1 can be the vertices of a fixed mesh or points randomly sampled at each iteration of a gradient descent algorithm. Specifically, we employ random Fourier feature networks with 256 neurons in each hidden layer and hyperbolic tangent (Tanh) activation functions. The models are trained with a batch size of 1, 024 over 10^5 steps of gradient descent using the Adam optimizer (Kingma and Ba, 2014). We set the initial learning rate to 10^-3, and use an exponential decay rate of 0.9 every 2, 000 steps. For Grey-Scott equation: Specifically, we divide the temporal domain [0, 1] into 10 equal intervals, employ the Pirate Net architecture as a backbone and train a separate PINN model for each time window. For Poisson inverse problem: We sample data of u(x, y) with 2, 500 uniformly distributed 50 50 points and add Gaussian noise N(0, 0.1) to it. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, memory specifications) used for running the experiments. |
| Software Dependencies | No | We also thank the developers of the software that enabled our research, including JAX (Bradbury et al., 2018), Matplotlib (Hunter, 2007), and Num Py (Harris et al., 2020). The paper mentions software tools used, but does not provide specific version numbers for these dependencies. |
| Experiment Setup | Yes | Specifically, we employ random Fourier feature networks with 256 neurons in each hidden layer and hyperbolic tangent (Tanh) activation functions. The models are trained with a batch size of 1, 024 over 10^5 steps of gradient descent using the Adam optimizer (Kingma and Ba, 2014). We set the initial learning rate to 10^-3, and use an exponential decay rate of 0.9 every 2, 000 steps. For ease of replication, we detail all hyper-parameters used in our experiments in Tables 4, 5, 6, 7, and 8. |