A Novel Frequency-Spatial Domain Aware Network for Fast Thermal Prediction in 2.5D ICs

Changyin Sun; Dan Niu; Dekang Zhang; Jingweijia Tan; Yichao Dong; Zhou Jin

REVIEW 3 major objections 5 minor 16 references

A Novel Frequency-Spatial Domain Aware Network for Fast Thermal Prediction in 2.5D ICs

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read FSA-Heat claims that adding high-to-low frequency encoding to a 3D convolutional network predicts steady-state temperature fields in 2.5D chiplets with over 99% lower RMSE and 4.23x faster inference than the GCN+PNA baseline.

desk verdict Architecture is a sensible new combination and the ablations hold together, but the 99% RMSE claim rests on a near-random self-implemented baseline and missing artifacts. read the letter →

arxiv 2504.14237 v1 pith:DPP6MBGW submitted 2025-04-19 cs.LG

Dekang Zhang , Dan Niu , Zhou Jin , Yichao Dong , Jingweijia Tan , Changyin Sun This is my paper · ORCID

classification cs.LG

keywords Thermalanalysis2.5DICsfrequency-spatialdomainmulti-scaleinteractionpredictionchipletdeeplearning

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes FSA-Heat, a neural network that predicts steady-state temperature distributions across the four layers of 2.5D chiplet packages—heat source, thermal interface material, heat spreader, and heatsink—directly from geometric, heat-exchange, and heat-source parameters on a 64×64×4 grid. It aims to replace repeated runs of thermal solvers during design optimization, where speed matters as much as accuracy. The central claim is that extracting features in both the spatial and frequency domains lets the network capture global heat-dissipation structure that plain CNNs and graph networks miss, yielding over 99% RMSE reduction and a 4.23x inference speedup over the GCN+PNA baseline while generalizing to unseen thermal conductivities and heat-source counts. If the claim holds, thermal-aware floorplanning and hotspot checks for chiplet designs could run in milliseconds without a full simulation.

What carries the argument

The central object is a frequency-spatial thermal encoder block (FSTE) built around a 3D-DCT/IDCT branch with learnable anisotropic frequency weights $W_f = e^{-(E_u u^2 + E_w w^2 + E_p p^2)}$ plus a multiplicative gating signal, run in parallel with a residual 3D-convolution spatial branch. A second module, FCIFormer, replaces plain skip connections with cross-attention computed in the frequency domain between four encoder scales, and a frequency-spatial hybrid loss adds an L1 frequency-domain term to spatial MSE. Together these components give the network a global receptive field while preserving local boundary smoothness via even-symmetry continuation that mirrors the adiabatic Neumann boundary condition.

What would settle it

Generate the same chiplet layouts with a finite-element thermal simulator or measured silicon data and compare FSA-Heat's predictions to the solver's output at the hotspots; if the RMSE advantage over GCN+PNA does not stay near the reported 99% or the errors degrade under that distribution, the central claim is refuted.

Watch

Extended reading notes

Core claim

The authors claim that a frequency-spatial dual-domain architecture can serve as a fast surrogate for steady-state thermal analysis in 2.5D ICs. Their FSA-Heat network encodes the input thermal-conductance field through a 3D discrete cosine transform, multiplies the frequency coefficients by learnable high-to-low frequency weights, and transforms back, while a parallel 3D-convolution branch keeps local spatial detail; a cross-scale interaction module then fuses the multi-resolution encoder outputs in the frequency domain before a convolutional decoder emits the temperature field. Trained with a loss that combines spatial MSE with L1 penalties on the magnitude and phase of the 2D DFT, the model reports RMSE 0.0415 versus 5.1424 for GCN+PNA on the same 64×64×4 test grid, a PSNR of 68.078 versus 28.659, and 4.23x faster inference than the graph baseline.

Load-bearing premise

The central claim rests on HotSpot-generated synthetic data—Gaussian power densities, a 64×64×4 grid, and thermal conductivities varying by ±30%—faithfully representing real 2.5D chiplet packages.

Editorial extensions

If this is right

If the reported accuracy holds outside the training distribution, thermal-aware placement and floorplanning loops can call the network thousands of times per optimization run at millisecond latency instead of invoking a thermal solver each iteration.
The even-symmetry continuation of the 3D-DCT means the network respects the adiabatic edge condition by construction, so temperature predictions near package edges should not need special boundary handling.
Because the network also outputs the temperature dissipation gradient, it can directly support adaptive grid partitioning for higher-resolution thermal simulation.
A 64×64×4 grid prediction in 0.0549 seconds makes the method suited to interactive design-space exploration for chiplet packages.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The frequency branch's global receptive field suggests the same architecture could transfer to full 3D chiplet stacks or larger grids, but the paper only demonstrates 64×64×4 and excludes the DeepOHeat operator baseline, so cross-method comparison on 3D cases remains open.
The boundary-condition argument points to a testable variant: replacing the 3D-DCT with a sine transform for fixed-temperature Dirichlet boundaries would show whether the even-symmetry assumption is what carries the accuracy.
The claimed 99% RMSE reduction is measured against a single graph baseline on HotSpot-generated synthetic data; transfer to measured silicon temperatures or to other compact thermal solvers is not established by the paper.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: worth a read, but the headline comparison is not yet established. What is new is the specific combination of 3D-DCT frequency filtering with learned band weights, cross-scale cross-attention in the style of CrossViT, and a frequency-plus-spatial loss, all applied to 2.5D IC thermal prediction on a 64x64x4 grid. That package is new, and the paper applies it to the right kind of problem. The ablations in Table II are internally consistent: removing the frequency branch, the spatial branch, or the frequency loss each degrades accuracy in a plausible direction. The generalization tests on unseen thermal conductivities and heat source counts are the right check for a surrogate model.

Now the soft spots. The biggest is the comparison to GCN+PNA. The reported baseline RMSE of 5.14 and MAPE of 111% are close to random-guess numbers. Any reasonable learned model would show a massive relative improvement against that. The authors say they implemented the baseline according to the paper and matched accuracy on the original dataset, but they do not release code, weights, hyperparameters, or training budgets, so the fairness of that comparison cannot be checked. That makes the central quantitative claim unverifiable. A smaller issue: the paper claims 3D-DCT even symmetry satisfies the implicit Neumann adiabatic boundary condition, but the top heatsink boundary is convective, not adiabatic. That is a mismatch in the justification; it may not affect the learned predictions, but it should be addressed. Also, all numbers are single-run point estimates with no error bars or seed variance.

Who should read this: people building fast thermal surrogates for 2.5D/3D IC design-space exploration. If the authors fix the baseline comparison, release artifacts, and clarify the boundary comment, the architecture is worth publishing. As it stands, treat the standalone FSA-Heat accuracy as plausible but the comparative advantage as unproven. I would send this to peer review—it has enough substance to warrant referee time—but I would expect major revision.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes FSA-Heat, a neural network for fast steady-state thermal prediction in 2.5D chiplet ICs. The network combines a frequency-spatial thermal encoder (FSTE) with high-to-low frequency learnable weights, a frequency-domain cross-scale interaction module (FCIFormer), and a frequency-spatial hybrid loss (FSL). The model is trained and evaluated on 6,000 HotSpot-generated samples on a 64x64x4 grid. The authors report RMSE 0.0415, MAPE 0.861%, PSNR 68.078 dB, and an inference speed of 0.0549 s, claiming over 99% RMSE reduction and a 4.23x speedup over a re-implemented GCN+PNA baseline. They also claim robust generalization to unseen thermal conductivity values and heat-source counts, supported primarily by visual comparisons.

Significance. If the reported results hold under transparent evaluation, FSA-Heat would be a useful contribution: it addresses a real need for fast and accurate thermal surrogates in 2.5D chiplet design, and the proposed frequency-spatial architecture is a plausible and nontrivial design. The ablation study in Table II is internally coherent and suggests that each proposed component contributes to accuracy. However, the central comparative claim depends on a self-implemented, unreleased GCN+PNA baseline whose reported errors are near-random; the paper does not provide code, data, error bars, or seed-level variability. The generalization claims are also not quantified. These issues currently prevent verification of the headline results.

major comments (3)

[Section IV-B, Table I] The headline claim of 'over 99% RMSE reduction' is computed against a GCN+PNA implementation that is described only as 'implemented according to the detailed descriptions in [11]'. The baseline RMSE of 5.1424 and MAPE of 111.235% are so poor that they indicate the baseline is performing near chance; any reasonable learned model would show a massive RMSE reduction against it. The manuscript provides no hyperparameters, training budget, model selection procedure, or code for this baseline, and no independent verification that it matches the original GCN+PNA method. This makes the central comparative claim unverifiable. The authors should release code and trained weights, use the original authors' implementation if available, or perform a fair, tuned comparison with matched training budgets and multiple seeds, reporting the resulting baseline performance.
[Section IV-B, Figures 3 and 4] The generalization experiments for unseen thermal conductivities (50% and -50%) and unseen heat-source counts (10, 60, 80) are reported only through qualitative image comparisons. No numeric metrics such as RMSE, MAE, MAPE, or PSNR are given for these test sets, so the claim of 'robust generalization capabilities' is not quantitatively established. The authors should provide tables or plots with the same metrics used in Table I for these extrapolation sets, along with corresponding baseline results and error bars.
[Section IV-A and Table II] All reported metrics are single-run point estimates without standard deviations or confidence intervals. The ablation differences in Table II (e.g., RMSE 0.0415 vs. 0.0499 vs. 0.0519) are small and may be within run-to-run variance for deep networks. Without multiple seeds, the internal ablation conclusions and the claimed improvements over the spatial-only baseline are not statistically supported. The authors should report mean and standard deviation over at least three runs, or otherwise justify that the differences exceed noise.

minor comments (5)

[Section III-B1, Eq. (2)-(5)] The statement that 'the 3D-DCT and 3D-IDCT utilize even symmetry continuation to satisfy the implicit Neumann adiabatic boundary condition at the edges' needs a derivation or reference. DCT-II's implicit even extension enforces a zero derivative at the extension center, which is not generally identical to the Neumann condition at the physical grid boundary unless the grid point locations are explicitly matched. Since FSTE is a feature extractor, this does not invalidate the empirical results, but the physical justification should be corrected or qualified.
[Section IV-B] The text defines RMSE as 'root mean absolute error'; the correct expansion is 'root mean squared error' or 'root mean square error'.
[Figure 1] The figure contains placeholder symbols such as '?1', '?2', '?3', '?4', and '?', which obscure the description of the network. These should be replaced with concrete labels or a caption explains their meaning.
[Section IV-A] The paper does not report how the 6,000 samples are split into training, validation, and test sets, nor whether the test cases are generated from the same distribution as the training cases. Please specify the split and ensure that no test samples overlap with training samples.
[Figure 3 caption] The caption '?? increased by -50%' is confusing because a negative increase is a decrease. Rephrase as 'decreased by 50%'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: FSA-Heat is trained and tested against an external simulator (HotSpot) on held-out data; no predicted quantity reduces by construction to a fitted input or to a load-bearing self-citation.

full rationale

The paper's central derivation is a supervised surrogate model: HotSpot, an external simulator cited as [7], generates 6,000 four-layer samples with specified geometric, heat-exchange, and heat-source parameters, and FSA-Heat is trained with a combined spatial MSE and frequency-domain loss against those ground-truth temperature fields. Test metrics in Table I are computed on held-out generated cases, and the generalization tests in Section IV-B use unseen thermal conductivities and heat-source counts. The load-bearing architectural components — learnable frequency weights Wf, the FCIFormer cross-attention module, and the FSL loss — are trained parameters or fixed hyperparameters (e.g., alpha = 0.5), not quantities derived from the target outputs. The only self-citation ([3], cited as background on 2.5D/3D chiplet integration) is not load-bearing and does not support any uniqueness or forced-choice claim. The authors' reimplementation of GCN+PNA is not released, and the very poor reported baseline errors make the comparative claim a reproducibility and benchmarking-fairness concern, but that is a correctness risk rather than circularity: no equation in the paper reduces a predicted quantity to its own input by construction, and no fitted parameter is renamed as a prediction. Under the review rules, the derivation chain is self-contained against an external benchmark, so the circularity score is 0.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The central claim is an empirical ML performance claim. It introduces no new physical entities. It rests on the fidelity of the HotSpot simulator, the chosen boundary conditions and grid resolution, and unlisted architecture hyperparameters.

free parameters (4)

alpha (FSL harmonic weight) = 0.5
Chosen by hand to balance spatial and frequency losses in FSL = L_s + alpha*L_f (Section III-C).
beta (FSL phase loss weight) = not reported
Balance factor for the phase term in Eq. (7); its value is not specified anywhere.
Frequency-band exponents Eu, Ew, Ep = learned during training, values not reported
In Eq. (4), Wf = exp(-(Eu*u^2 + Ew*w^2 + Ep*p^2)) modulates DCT coefficients; described as learnable frequency weights but without initialization or final values.
Architecture hyperparameters (L_i, L_f, C, K) = unspecified
Number of FSTE blocks per scale, FCIFormer layers, channel width, and PPNet trunk depth are shown in Fig. 1 but numeric values are not stated, so the reported performance depends on unlisted choices.

assumptions (7)

standard math 3D-DCT and 3D-IDCT are invertible linear transforms and can be used as differentiable layers.
Invoked in Eqs. (2)-(5) and implemented in the HL-FSE block; this is a standard property of DCT.
domain assumption HotSpot's compact thermal model and its FEM/FDM discretization (GT = Qs) provide accurate ground truth temperatures for 2.5D chiplet packages.
All training and test labels come from HotSpot (Section IV-A); if HotSpot is inaccurate, the learned surrogate inherits that error.
domain assumption The Neumann boundary conditions used in dataset generation (convective heatsink top, adiabatic elsewhere) represent real 2.5D packages.
Stated in Section II; these conditions control the temperature fields HotSpot produces.
domain assumption A 64x64x4 grid resolves the relevant hotspots and thermal gradients.
Dataset uses a 64x64 grid per layer (Section IV-A); no grid convergence study is provided.
domain assumption PPNet can learn the mapping from geometry and heat exchange parameters to thermal conductance without explicit G-labels when co-trained with FSA-Heat.
Joint training is described in Section III-A; the paper provides no independent evidence that PPNet's learned preprocessing is physically meaningful.
domain assumption Even-symmetry continuation in 3D-DCT matches the physical boundary conditions of the problem.
Claimed in Section III-B1, but the top boundary is convective (Section II), not adiabatic, so the assumption is questionable for the z dimension.
domain assumption The trained network generalizes to out-of-distribution parameters (conductivity +/-50%, heat sources 10-80) based on 500 unseen test cases.
Generalization is tested in Section IV-B using extrapolated parameters, but only for a single synthetic dataset family.

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Cite this review

Pith. "Pith review of A Novel Frequency-Spatial Domain Aware Network for Fast Thermal Prediction in 2.5D ICs." pith.science (2026). https://pith.science/paper/DPP6MBGW

@misc{pith2026250414237,
  author       = {Pith},
  title        = {Pith review of: A Novel Frequency-Spatial Domain Aware Network for Fast Thermal Prediction in 2.5D ICs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DPP6MBGW}},
  note         = {Machine review of arXiv:2504.14237}
}

read the original abstract

In the post-Moore era, 2.5D chiplet-based ICs present significant challenges in thermal management due to increased power density and thermal hotspots. Neural network-based thermal prediction models can perform real-time predictions for many unseen new designs. However, existing CNN-based and GCN-based methods cannot effectively capture the global thermal features, especially for high-frequency components, hindering prediction accuracy enhancement. In this paper, we propose a novel frequency-spatial dual domain aware prediction network (FSA-Heat) for fast and high-accuracy thermal prediction in 2.5D ICs. It integrates high-to-low frequency and spatial domain encoder (FSTE) module with frequency domain cross-scale interaction module (FCIFormer) to achieve high-to-low frequency and global-to-local thermal dissipation feature extraction. Additionally, a frequency-spatial hybrid loss (FSL) is designed to effectively attenuate high-frequency thermal gradient noise and spatial misalignments. The experimental results show that the performance enhancements offered by our proposed method are substantial, outperforming the newly-proposed 2.5D method, GCN+PNA, by considerable margins (over 99% RMSE reduction, 4.23X inference time speedup). Moreover, extensive experiments demonstrate that FSA-Heat also exhibits robust generalization capabilities.

Figures

Figures reproduced from arXiv: 2504.14237 by the authors.

**Figure 1.** Proposed end-to-end chiplet thermal and its gradient prediction network (FSA-Heat) and detailed structures of each module. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** A visualization example of thermal and its gradient prediction com [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Thermal and its gradient prediction comparisons between ours and GCN+PNA under unseen thermal conductivity [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Thermal prediction comparisons between ours and GCN+PNA under unseen varying heat source numbers. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Ablation method error visualizations. Lastly, a truth thermal example map and the prediction error maps under different ablation methods are presented in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [11]

L. Chen, W. Jin, and S. X.-D. Tan, ”Fast thermal analysis for chiplet design based on graph convolution networks,” in 2022 27th Asia and South Pacific Design Automation Conference (ASP-DAC) , pp. 485-492, 2022

work page 2022

[2] [1]

Architecture, chip, and package codesign flow for interposer-based 2.5-D chiplet integration enabling heterogeneous IP reuse,

J. Kim, G. Murali, H. Park, E. Qin, H. Kwon, V . C. K. Chekuri, N. M. Rahman, N. Dasari, A. Singh, and M. Lee, “Architecture, chip, and package codesign flow for interposer-based 2.5-D chiplet integration enabling heterogeneous IP reuse,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems , vol. 28, no. 11, pp. 2424-2437, 2020

work page 2020

[3] [2]

Kumar, V

N. Kumar, V . Sankatali, Y . Chen, M. Brunion, S. Mishra, A. Gupta, P. Singh, F. Catthoor, J. Myers, J. Ryckaert, and D. Biswas, ”Thermal Analysis of High-Performance Server SoCs from FinFET to Nanosheet Technologies,” in 2024 IEEE International Reliability Physics Symposium (IRPS), pp. 8B.4-1-8B.4-8, 2024

work page 2024

[4] [3]

OSSP-PTA: An Online Stochastic Stepping Policy for PTA on Reinforcement Learning,

D. Niu, Y . Dong, Z. Jin, C. Zhang, Q. Li, and C. Sun, “OSSP-PTA: An Online Stochastic Stepping Policy for PTA on Reinforcement Learning,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 42, no. 11, pp. 4310-4323, 2023

work page 2023

[5] [4]

SAfEPaTh: A System-Level Approach for Efficient Power and Thermal Estimation of Convolutional Neural Network Accelerator

Y . Chen, S. Yang, D. Bhattacharjee, F. Catthoor, and A. Mallik, “SAfEPaTh: A System-Level Approach for Efficient Power and Thermal Estimation of Convolutional Neural Network Accelerator,” arXiv preprint arXiv:2407.17623, 2024

work page Pith review arXiv 2024

[6] [5]

Y . R. Zhuo, H. L. Chen, and Y . G. Chen, ”DOC: A Novel DOuble-Contour- Based Macro Placement Framework for Mixed-Size Designs,” in2023 Asia Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC), pp. 1392-1397, 2023

work page 2023

[7] [6]

Frequency- Domain Thermal Coupling Model of Multi-Chip Power Module,

M. Xu, K. Ma, Y . Qi, X. Cai, X. Li, A. Wang, and L. Zheng, “Frequency- Domain Thermal Coupling Model of Multi-Chip Power Module,” IEEE Transactions on Power Electronics, vol. 38, no. 5, pp. 6522-6532, 2023

work page 2023

[8] [7]

J.-H. Han, X. Guo, K. Skadron, and M. R. Stan, ”From 2.5 D to 3D chiplet systems: Investigation of thermal implications with HotSpot 7.0,” in 2022 21st IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (iTherm) , pp. 1-6, 2022

work page 2022