AutoIP: A United Framework to Integrate Physics into Gaussian Processes
Authors: Da Long, Zheng Wang, Aditi Krishnapriyan, Robert Kirby, Shandian Zhe, Michael Mahoney
ICML 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Auto IP shows improvement upon vanilla GPs in both simulation and several real-world applications, even using rough, incomplete equations. In this section, we evaluate Auto IP on two illustrative and two more realistic problems. |
| Researcher Affiliation | Collaboration | 1University of Utah 2University of California, Berkeley 3Lawrence Berkeley National Laboratory 4International Computer Science Institute. Correspondence to: Shandian Zhe <zhe@cs.utah.edu>. |
| Pseudocode | No | No structured pseudocode or algorithm blocks were found. The algorithm is described in narrative text and mathematical equations within Section 3. |
| Open Source Code | No | No explicit statement about releasing the source code for the described methodology or a direct link to a code repository was found. |
| Open Datasets | Yes | We used the CMU motion capture database.2 http://mocap.cs.cmu.edu/ and We used the solution data released in https://github.com/maziarraissi/PINNs. and The dataset includes measurements of seven metals (Zn, Ni, Cr, etc.) at 300 locations in a region of 14.5 km2. The concentration is normally modeled by a diffusion equation, u t = α u, where is the Laplace operator, u = 2u x2 2 . However, the dataset does not include the time information when these concentrations were measured. We followed prior work (Alvarez et al., 2009) to assume a latent time point ts and estimate the solution at ts, namely h(x1, x2) = u(x1, x2, ts). Thereby, the equation can be rearranged as, h = g(x1, x2) where g(x1, x2) = 1 α u(x1,x2,t) t |t=ts is viewed as a latent source term. Note that LFM views u(x1, x2, 0) as the latent source, yet uses a convolution operation to derive an induced kernel for h in terms of locations, where ts is considered as a kernel parameter jointly learned from data. We tested four tasks, namely predicting: (1) Zn with the location and Cd, Ni concentration; (2) Zn with the location and Co, Ni, Cr concentration; (3) Ni with the location and Cr concentration; and (4) Cr with the location and Co concentration. For each task, we randomly sampled 50 example for training and another 200 examples for testing. The experiments were repeated for five times, and we computed the average RMSE, average NMLL and their standard deviation. For our method, we used the training inputs as the collocation points. The results are reported in Table 3. Auto IP consistently outperforms the competing approaches, again confirming the advantage of our method. |
| Dataset Splits | No | No explicit mention of a separate validation dataset split was found. The paper details training and testing set sizes and sampling methods. |
| Hardware Specification | No | No specific hardware details (e.g., GPU/CPU models, memory) used for running experiments were mentioned in the paper. |
| Software Dependencies | Yes | We implemented both Auto IP and standard GPR with Pytorch (Paszke et al., 2019) |
| Experiment Setup | Yes | We performed stochastic optimization with ADAM (Kingma and Ba, 2014). We used learning rate 10^-2 and ran both methods with 10K epochs. We used the SE-ARD kernel for both Auto IP and GPR, with the same initialization. For Auto IP, we let κg and κu share the same kernel parameters. and We ran GPR and our method for 200K epochs with the learning rate 10^-3 (a larger learning rate will hurt the performance). |