Paper: Continual Graph Learning for Thermal Analysis of Composite Materials under Interface Variations (ICLR-2024)

Reviewer comment (Novelty):
Problem not described very clearly, and related work not comprehensive enough. Graph Neural Networks is not covered thoroughly, in a way that walks the reader through the main developments in the field. I would have hoped that some of the seminal works (e.g. Kipf and Welling [1]) would have warranted a mention.

Author response:
Thanks for the suggestion. We will add more references in the background section about the GNNs.

Reviewer comment (Theory):
Process not described in adequate detail. It is mentioned that the boundary conditions are 'frozen' while solving the sub-domain problem, and then corrected during the aggregation step. This should be explained through equations and a presentation of how the correction takes place, both for the FEM case, and for GNNs.

Author response:
FEM is only used for local thermal analysis so there is no correction phase. For GNN, 
the edge/node encoder and aggregator we choose help explain how the correction is done. To predict the thermal on each node, the edge encoder and aggregator collects all the neighbouring thermal contributions, and the node encoder utilizes the collected data in conjunction with the node's local thermal information to generate the corrected thermal prediction. As discussed in section 3.2.1, this steps are similar to the precedure of solving PDEs, where we collected the necessary boundary and initial conductions to get the final solutions.

Reviewer comment (Experiments):
Datasets - Did the authors try this on any public datasets that would allow for experimentation? What about comparison with baseline methods?

Author response:
We did not test our algorithm on a real chip yet since it requires the thermal camera to capture the temperature. But we created a more complex experiment involving a dummy chiplet that incorporates multiple functional blocks, including AES, SRAM, and EMIB. The conductivity and power of these blocks are extracted from the real physical design data. The chiplet size is 250(L)×230(W)×2.5(H)μm. It is subdivided into 15x13x5 subblocks.  Same as the previous experiments, we randomly generating training samples, incorporating arbitrary power maps and conductivities, to train GNN and then test its performance on this chiplet. The MAPE is ~0.05. We then manually add interface defects at the conjonction of AES and substrate, and apply our continual learning strategy. The updated prediction successfully shows the hotspot at the location of defects with ~0.07 MAPE.  

We use FEM as the baseline since it provides the most accurate evalution. And to the best of our knowledge, our method is the first ML algorithm tackling the interface varitions problem, therefore there is lack of other methods for comparison.

Reviewer comment (Experiments):
The dataset size is extremely small (320 for training and 20 for testing). I am not sure if such a small dataset size makes sense, especially given that the datasets are generated by simulation (with the simple heat equation) instead of from real-world experiment data.

Author response:
Despite the small amount of training samples, each sample is a small graph which consists of 25 nodes. The GNN is optimized on a per-node basis so there are 8000 nodes in total for GNN training. We are sorry for the confusion. We will add more detail in the next version.

Reviewer comment (Theory):
I am not sure the finetuning stage with random defect nodes should be called "continual learning". Continual learning, to the best of my knowledge, means the setting where the data can only be accessed from an online data stream and therefore can only be sampled in an non-iid way. I do not see any reason to brand the process of "finetuning with additional noisy data" as continual learning.

Author response:
We fully agree.  Since our algorithm doesn't necessitate retraining the GNN using noisy data in a continual learning pattern, we believe that the term "adaptive learning" would be a more fitting description.

Reviewer comment (Experiments):
There are many baselines ML methods for efficiently solving PDEs - for instance, Fourier neural operator (FNO). Given that the heat equation is an simple one (of which the Green's function can be found as a simple heat kernel) compared to many other common benchmarks (Burger's eqn / Navier-Strokes eqn, as in FNO and many other papers in the field of PINN), a lack of comparison with some common baselines is detrimental to the quality of the paper.

Author response:
Our algorithm primarily addresses challenges related to thermal analysis, including the substantial computational costs associated with FEM and the limitations in handling interface variations. Subsequent research could focus on applying GNNs to address other PDEs.

Reviewer comment (Experiments):
The authors do not explain how these "defects" in the dataset are generated. Are they pure Gaussian noises, or something simulated through physical laws?

Author response:
We use FEM method to generate the golden data with "defects" inserted. Specifically, we manually establish a conductance of 0 between certain adjacent nodes, preventing heat exchange between them. FEM can accommodate this zero conductance condition and generate the corresponding thermal map. We are sorry for the confusion and will add more detail in the next version.

Reviewer comment (Theory):
The paper states that the "detect nodes" in the graph structure are introduced after checking where the prediction highly differs from the ground truth data. Do the authors imply that the location of the defects are highly predictable? If they are, why? The authors do not explain the reason behind their design.

Author response:
These locations are not predictable. They are detected by comparing the difference between GNN prediction and the actual measurement. 

Suppose we have a chip and a trained GNN. prior to the chip's manufacturing, we can conduct theoretical thermal analyses using GNN. This GNN prediction is based on the ideal scenario where no unforeseen defects manifest at any location. However upon the actual manufacturing of the chip, the real thermal measurements may deviate from the earlier predictions due to the presence of unforeseen defects. 
We need to compare the previous prediction with the actural meansurement to determine where the abnormal locations are and insert the defects node accordingly. 
This way, for the same chip, even when a different working load is applied in the future, the trained defect nodes can still be utilized to manage the adjusted predictions.

Reviewer comment (Presentation):
The presentation of this paper is not satisfactory: the figures presented in the paper are blurry; background knowledge like what each symbol in the heat equation means is not well explained; the algorithm is presented in a messy way, etc.

Author response:
Thanks for pointing out. We will further polish the paper.