PIED: Physics-Informed Experimental Design for Inverse Problems
Authors: Apivich Hemachandra, Gregory Kang Ruey Lau, See-Kiong Ng, Bryan Kian Hsiang Low
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Through experiments based on noisy simulated data and even real world experimental data, we empirically show that given limited observation budget, PIED significantly outperforms existing ED methods in solving IPs, including for challenging settings where the PDE parameters are unknown functions rather than just finite-dimensional. |
| Researcher Affiliation | Academia | Apivich Hemachandra , Gregory Kang Ruey Lau , Department of Computer Science, National University of Singapore, Singapore 117417 CNRS@CREATE, 1 Create Way, #08-01 Create Tower, Singapore 138602 EMAIL See-Kiong Ng & Bryan Kian Hsiang Low Department of Computer Science, National University of Singapore, Singapore 117417 EMAIL, EMAIL |
| Pseudocode | Yes | We present the pseudocode for FIST in Alg. 1 of the Appendix. We present the pseudocode for Mo TE in Alg. 2 in the Appendix. We summarize PIED via a pseudocode presented in Alg. 3. |
| Open Source Code | Yes | 1The code for the project can be found at https://github.com/apivich-h/pied. The code for the project can be found at https://github.com/apivich-h/pied. |
| Open Datasets | Yes | Specifically, we consider the ED problem applied to the groundwater flow dataset collated by Shadab et al. (2023), and the scratch assay cell population growth data collected by Jin et al. (2016), where the design parameters indicate the location to make the observations at constrained, fixed time intervals. |
| Dataset Splits | No | The paper describes generating problem instances for evaluation and using existing datasets but does not explicitly provide training/test/validation splits for its own experiments. It states: 'In each instance of the IP, we draw a random ground-truth PDE parameter, and generate the observations according to the model and the random ground-truth PDE parameter.' |
| Hardware Specification | Yes | The damped oscillator, wave equation, Eikonal equation and groundwater experiments were conducted on a machine with AMD EPYC 7713 64-Core Processor and NVIDIA A100-SXM4-40GB GPU, while the remaining experiments were done on AMD EPYC 7763 64-Core Processor CPU and NVIDIA L40 GPU. |
| Software Dependencies | No | All of the code were implemented based on the JAX library (Bradbury et al., 2018), which allows for NN training and auto-differentiation of many mathematical modules within. Criteria which are optimized by Bayesian optimization are done so using BOTORCH (Balandat et al., 2020), while criteria optimized using gradient-based methods are done so using JAXOPT (Blondel et al., 2021). While specific libraries are mentioned, no version numbers are provided for JAX, BOTORCH, or JAXOPT. |
| Experiment Setup | Yes | The architectures of the PINNs and other NNs used are listed in Table 4. Note that we only use multi-layer perceptrons in our experiments. The training process hyperparameters for the forward and inverse PINNs are listed in Table 5. Table 5: Training hyperparameters Problem Training steps # PDE Col. Pts. # IC/BC Col. Pts. Optimizer Damped oscillator 30k 300 1 Adam (lr = 0.01) 1D wave 200k 15k 2k L-BFGS 2D Navier-Stokes 100k 2k 300 Adam (lr = 0.001) 2D Eikonal 50k 10k 1 Adam (lr = 0.001) Groundwater flow 50k 500 1 L-BFGS Cell population 50k 1k 100 Adam (lr = 0.001) |