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arxiv: 2606.19853 · v1 · pith:DN4NQR7Nnew · submitted 2026-06-18 · 💻 cs.LG · physics.comp-ph

Physics-Informed Neural Network with Squeeze-Excitation-like Attention

Yun-Fei Song , Long-Gang Pang , Fu-Peng Li , Jun-Jie Zhang This is my paper

Pith reviewed 2026-06-26 18:00 UTC · model grok-4.3

classification 💻 cs.LG physics.comp-ph
keywords physics-informed neural networkssqueeze-excitation attentionstable initializationbenchmark problemshigh-frequency problemsneural network architecture
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The pith

A squeeze-excitation attention module added to physics-informed neural networks yields stable initialization and competitive accuracy on 17 of 20 benchmarks.

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

The paper presents SEA-PINN, which embeds a squeeze-excitation-like attention mechanism into physics-informed neural networks to recalibrate neuron importance across layers. This produces nearly negligible variance and lower initial loss on 17 out of 20 benchmark problems, creating a more deterministic starting point for optimization. The architecture reaches accuracy comparable to models designed for high-frequency cases even without Fourier feature embeddings or periodic activations. When combined with TSA-PINN, it improves performance by 42.49 percent, positioning the module as a lightweight addition that strengthens convergence reliability.

Core claim

SEA-PINN incorporates a Squeeze-Excitation-like attention mechanism into physics-informed neural networks to dynamically recalibrate the importance of neurons across layers. On 17 out of 20 benchmark problems, SEA-PINN exhibits nearly negligible variance and significantly reduced initial loss, establishing a quasi-deterministic and favorable starting point for optimization. Without employing Fourier feature embeddings or periodic activation functions, SEA-PINN attains competitive accuracy compared with TSA-PINN, and integrating SEA-PINN into TSA-PINN boosts performance by 42.49 percent.

What carries the argument

The squeeze-excitation-like attention mechanism that dynamically recalibrates neuron importance across layers in the PINN architecture.

If this is right

  • SEA-PINN functions as a lightweight plug-in module that enhances nonlinear representation power in physics-informed networks.
  • The architecture promotes more robust and efficient convergence during optimization.
  • SEA-PINN strengthens the overall reliability of physics-informed learning across the tested benchmarks.
  • Integration of the module into specialized models such as TSA-PINN produces measurable performance gains.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The stable initialization property could reduce the computational cost of repeated random restarts when applying PINNs to new problems.
  • The attention recalibration might interact differently with other common PINN enhancements such as adaptive weighting or domain decomposition.
  • Extending the benchmarks to include time-dependent or multi-scale problems would test whether the observed stability holds beyond the current set.

Load-bearing premise

The 20 benchmark problems and evaluation protocol represent the distribution of physics problems that practitioners solve, and the attention mechanism does not systematically bias the physics residual terms outside these cases.

What would settle it

Training SEA-PINN on a new high-frequency PDE problem outside the given 20 benchmarks and measuring high variance in initial loss or accuracy below that of TSA-PINN would falsify the stability and competitiveness claims.

Figures

Figures reproduced from arXiv: 2606.19853 by Fu-Peng Li, Jun-Jie Zhang, Long-Gang Pang, Yun-Fei Song.

Figure 1
Figure 1. Figure 1: FIG. 1: Early-training performance comparison of PINNs methods. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Difference from Ground Truth and training convergence. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Comparison of loss components for NS2D_BackStep (Case 11) [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Jacobian-based sensitivity of FNN-PINN and SEA-PINN at initialization. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Heat2D_ Multiscale(ID=7):Heatmaps of FNN-PINN and SEA-PINN at [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Architecture of SEA-PINN within PINNs: The complete set of outputs from the [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

We introduce SEA-PINN, a novel architecture that incorporates a Squeeze-Excitation-like attention mechanism into physics-informed neural networks to dynamically recalibrate the importance of neurons across layers. A key feature of SEA-PINN is its highly stable initialization. On 17 out of 20 benchmark problems, SEA-PINN exhibit nearly negligible variance and significantly reduced initial loss, establishing a quasi-deterministic and favorable starting point for optimization. Notably, without employing Fourier feature embeddings or periodic activation functions, SEA-PINN attained competitive accuracy (83\% vs. 90\% improvement relative to FNN-PINN on the high-frequency case 7) as compared with TSA-PINN-a model specifically engineered for high-frequency problems via learnable frequencies in sinusoidal activations. Furthermore, integrating SEA-PINN into TSA-PINN boosted performance by 42.49\%. These results underscore SEA-PINN as a lightweight plug-in module that enhances nonlinear representation power, promotes more robust and efficient convergence, and strengthens the overall reliability of physics-informed learning.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces SEA-PINN, a PINN variant that inserts a Squeeze-Excitation-like attention block to dynamically recalibrate channel-wise neuron importance across layers. The central empirical claims are that the architecture yields quasi-deterministic initialization (negligible variance and markedly lower initial loss on 17 of 20 benchmark PDEs), achieves competitive accuracy on high-frequency problems without Fourier features or periodic activations (83 % improvement relative to FNN-PINN on case 7, versus 90 % for TSA-PINN), and delivers an additional 42.49 % gain when the same attention module is grafted onto TSA-PINN.

Significance. If the reported stability and accuracy gains are reproducible under standard experimental controls, the work would supply a lightweight, architecture-agnostic module that improves training reliability for PINNs without requiring specialized activations or feature mappings. Such a module could be adopted as a default component in PINN pipelines, particularly for problems where initialization variance currently forces extensive hyper-parameter search.

major comments (2)
  1. [Results paragraph] Results paragraph (and any accompanying tables/figures): the headline claims of “nearly negligible variance” and “significantly reduced initial loss” on 17/20 problems are presented without network widths, depth, loss-term weights, optimizer settings, number of independent runs, or statistical tests. These omissions make it impossible to assess whether the reported stability is an artifact of the chosen experimental protocol rather than a property of the attention mechanism.
  2. [Abstract / Results paragraph] Abstract and results paragraph: the assertion that SEA-PINN is a “reliable plug-in” for arbitrary physics problems rests on a fixed suite of 20 benchmarks. No analysis is supplied showing that the collocation-point distributions or PDE types are representative of the broader distribution of problems encountered in practice, nor is there a test demonstrating that the channel-wise recalibration does not systematically alter gradient flow through the physics residual on problems outside this suite.
minor comments (1)
  1. [Abstract] The sentence “SEA-PINN exhibit nearly negligible variance” contains a subject-verb agreement error.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [Results paragraph] Results paragraph (and any accompanying tables/figures): the headline claims of “nearly negligible variance” and “significantly reduced initial loss” on 17/20 problems are presented without network widths, depth, loss-term weights, optimizer settings, number of independent runs, or statistical tests. These omissions make it impossible to assess whether the reported stability is an artifact of the chosen experimental protocol rather than a property of the attention mechanism.

    Authors: We agree that these details were insufficiently specified. In the revised manuscript we will add an experimental setup section reporting network widths and depths, loss-term weights, optimizer settings, the number of independent runs performed (five), and standard deviations with basic statistical comparisons. This will allow readers to evaluate whether the observed stability arises from the attention mechanism. revision: yes

  2. Referee: [Abstract / Results paragraph] Abstract and results paragraph: the assertion that SEA-PINN is a “reliable plug-in” for arbitrary physics problems rests on a fixed suite of 20 benchmarks. No analysis is supplied showing that the collocation-point distributions or PDE types are representative of the broader distribution of problems encountered in practice, nor is there a test demonstrating that the channel-wise recalibration does not systematically alter gradient flow through the physics residual on problems outside this suite.

    Authors: We accept that the original wording overstated generality. We will revise the abstract and results text to qualify the claims as applying to the evaluated benchmark suite. We will also add a short gradient-flow analysis for the attention module and a limitations paragraph discussing the scope of the 20 benchmarks. A full representativeness study across all possible PDEs lies outside the present scope. revision: partial

Circularity Check

0 steps flagged

No circularity; empirical architecture proposal with external benchmarks

full rationale

The paper proposes SEA-PINN as an architectural modification (Squeeze-Excitation-like attention inserted into PINNs) and evaluates it empirically on a fixed suite of 20 benchmark PDE problems. No derivation chain, uniqueness theorem, ansatz, or prediction is presented that reduces by construction to quantities defined or fitted inside the paper itself. Claims rest on reported loss curves, variance statistics, and accuracy deltas versus external baselines (FNN-PINN, TSA-PINN), none of which are shown to be self-referential or forced by the authors' own prior definitions. The evaluation protocol is external to any internal fitting loop, satisfying the self-contained criterion.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, mathematical axioms, or new physical entities; the architecture itself is the proposed addition.

pith-pipeline@v0.9.1-grok · 5712 in / 1106 out tokens · 37390 ms · 2026-06-26T18:00:24.878073+00:00 · methodology

discussion (0)

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Reference graph

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    In the top two plots, SEA-PINN’s average prediction (orange line) stays closer to the true function (dashed black line) in the extrapolation regions ( x<0 and x>1 ). Furthermore, its uncertainty band (orange shading) is significantly smaller than the FNN-PINN’s (blue shading), indicating that SEA-PINN’s predictions are not only more accurate but also more...

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    a(k) N   =   ζ1 sin f (k) 1 z(k) 1 +ζ 2 cos f (k) 1 z(k) 1 ζ1 sin f (k) 2 z(k) 2 +ζ 2 cos f (k) 2 z(k) 2

    Trainable Sine Activation (TSA) where the final output of thek-th layer is: a(k) =   a(k) 1 a(k) 2 ... a(k) N   =   ζ1 sin f (k) 1 z(k) 1 +ζ 2 cos f (k) 1 z(k) 1 ζ1 sin f (k) 2 z(k) 2 +ζ 2 cos f (k) 2 z(k) 2 ... ζ1 sin f (k) N z(k) N +ζ 2 cos f (k) N z(k) N   (S1) where: •z (k) i is the output of thei-th neuron in thek-th layer...

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    Slope Recovery Mechanism The slope recovery termS(a)dynamically adjusts the slope of the activation function, maintaining active and effective gradient propagation throughout the network. S(a) = 1 1 L−1 PL−1 k=1 exp 1 Nk PNk i=1 f (k) i (S2) where: •Lis the total number of layers, •N k is the number of neurons in thek-th layer. This slope recovery term is...

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    Compute the standard TSA-PINN activation outputa(l): a(l) i =ζ 1 sin(f (l) i z(l) i ) +ζ 2 cos(f (l) i z(l) i )(S4) wherez (l) i =w (l) i ·ˆ a(l−1) +b (l) i

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    Element-wise multiply the weight vector with the activation output to obtain the final layer output: ˆ a(l) =λ (l) ⊙a (l) (S6) By combining TSA-PINN with our weighting module, the TSA_SEA-PINN model explores whether the adaptive weighting mechanism can serve as a general enhancement module, further improving the performance of existing advanced PINN archi...

    2000