Deeper-PINNs: Unlocking the power of deep physics-informed neural networks
Bibliographic record
Abstract
Physics-Informed Neural Networks (PINNs) have emerged as a promising framework for solving partial differential equations (PDEs) and have garnered significant attention across industrial and scientific domains. However, their effectiveness is often constrained by limited approximation capacity and performance degradation in deep network structures. In this work, we propose the Deeper Physics-Informed Neural Network (Deeper-PINN), a novel architecture designed to address these challenges. The Deeper-PINN incorporates element-wise multiplication operations into the PINN structure, which effectively mitigates the initialization pathologies of PINNs and enables the utilization of deeper network structures. Additionally, this operation projects features into high-dimensional, nonlinear spaces, thereby enhancing the approximation capacity of PINNs. The proposed architecture is evaluated on multiple benchmark problems, demonstrating that Deeper-PINNs can effectively leverage deep neural network structures while maintaining high parameter efficiency. The complete codes of the experiments can be found on https://github.com/flongjiang/Deeper-PINNs • A novel architecture, Deeper-PINNs is developed that mitigates the degradation problem of deep PINNs. • Element-wise multiplication is introduced to mitigate the initialization pathology, enabling PINNs to effectively utilize deep neural network structures. • The developed Deeper-PINNs can map the features into nonlinear high-dimensional space, which enables Deeper-PINNs with better expressiveness.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".