# PCGD: Physics-Guided Conditional Graph Diffusion for TCAD Device Simulation

arXiv: https://arxiv.org/abs/2606.29272 · HTML: https://mlsanity.com/paper/2606.29272/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 28 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints](https://mlsanity.com/paper/2506.08604/) (2025)
- [Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks](https://mlsanity.com/paper/2504.02843/) (2025)
- [Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanics](https://mlsanity.com/paper/2506.06045/) (2025)
- [M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation](https://mlsanity.com/paper/2412.04134/) (2024)
- [Arbitrarily-Conditioned Multi-Functional Diffusion for Multi-Physics Emulation](https://mlsanity.com/paper/2410.13794/) (2024)
- [GenCP: Towards Generative Modeling Paradigm of Coupled Physics](https://mlsanity.com/paper/2601.19541/) (2026)

## Abstract (arXiv)

Technology computer-aided design (TCAD) semiconductor device simulation is fundamentally constrained by the high computational cost of iteratively solving coupled drift-diffusion equations. Existing ML surrogates either reduce internal physics to macroscopic scalar regressions, or rely on single-step mappings that lack the iterative refinement required to resolve stiff, coupled fields. To address this, we introduce PCGD, a Physics-Guided Conditional Graph Diffusion framework operating natively on unstructured TCAD meshes to predict coupled electrostatic and carrier density fields. PCGD employs a Condition-Aware MeshGraphNet denoiser that explicitly injects boundary conditions and device structure context via global cross-attention. By augmenting data-driven denoising with a physics-guided hybrid objective that integrates exponent-free quasi-Fermi gradient matching with noise-aware PDE residuals, PCGD progressively enforce physical constraints in the iterative diffusion trajectory. This strategy successfully bypasses the numerical instabilities typical of stiff drift-diffusion equations. Evaluated on a challenging mixed PN/MOS benchmark, PCGD significantly outperforms deterministic one-step regression (1.207% error) and local diffusion (1.585% error) baselines by achieving a sub-percent mean relative field error of 0.835%, while concurrently reducing maximum PDE residual errors by nearly three orders of magnitude compared to pure diffusion. It also transfers robustly to unseen SOI topologies (0.815% error) via LoRA adaptation, using 5.30× less data and 14.34× fewer parameters than full fine-tuning. Ultimately, PCGD bridges the computational efficiency of generative surrogates with the rigorous physical fidelity of traditional TCAD, unlocking highly scalable, field-level analysis for robust device engineering.