# Physics-Constrained Adaptive Neural Networks Enable Real-Time Semiconductor Manufacturing Optimization with Minimal Training Data

arXiv: https://arxiv.org/abs/2511.12788 · HTML: https://mlsanity.com/paper/2511.12788/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 22 references that are in the map.
- First posted on arXiv 16 Nov 2025.

## Builds on (most cited first, 3 of 3)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Inverse Lithography Physics-informed Deep Neural Level Set for Mask Optimization](https://mlsanity.com/paper/2308.12299/) (2023)
- [Leveraging Transfer Learning to Overcome Data Limitations in Czochralski Crystal Growth](https://mlsanity.com/paper/2506.18774/) (2025)

## Abstract (arXiv)

The semiconductor industry faces a computational crisis in extreme ultraviolet (EUV) lithography optimization, where traditional methods consume billions of CPU hours while failing to achieve sub-nanometer precision. We present a physics-constrained adaptive learning framework that automatically calibrates electromagnetic approximations through learnable parameters boldsymbolθ = θd, θa, θb, θp, θc while simultaneously minimizing Edge Placement Error (EPE) between simulated aerial images and target photomasks. The framework integrates differentiable modules for Fresnel diffraction, material absorption, optical point spread function blur, phase-shift effects, and contrast modulation with direct geometric pattern matching objectives, enabling cross-geometry generalization with minimal training data. Through physics-constrained learning on 15 representative patterns spanning current production to future research nodes, we demonstrate consistent sub-nanometer EPE performance (0.664-2.536 nm range) using only 50 training samples per pattern. Adaptive physics learning achieves an average improvement of 69.9% over CNN baselines without physics constraints, with a significant inference speedup over rigorous electromagnetic solvers after training completion. This approach requires 90% fewer training samples through cross-geometry generalization compared to pattern-specific CNN training approaches. This work establishes physics-constrained adaptive learning as a foundational methodology for real-time semiconductor manufacturing optimization, addressing the critical gap between academic physics-informed neural networks and industrial deployment requirements through joint physics calibration and manufacturing precision objectives.