# Efficient FRW Transitions via Stochastic Finite Differences for Handling Non-Stratified Dielectrics

arXiv: https://arxiv.org/abs/2507.09730 · HTML: https://mlsanity.com/paper/2507.09730/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2025.

## Built on by (most cited first, 2 of 2)

- [DeepRWCap: Neural-Guided Random-Walk Capacitance Solver for IC Design](https://mlsanity.com/paper/2511.06831/) (2025)
- [CapBench: A Multi-PDK Dataset for Machine-Learning-Based Post-Layout Capacitance Extraction](https://mlsanity.com/paper/2604.11202/) (2026)

## Abstract (arXiv)

The accuracy of floating-random-walk (FRW) based capacitance extraction stands only when the recursive FRW transitions are sampled unbiasedly according to surrounding dielectrics. Advanced technology profiles, featuring complicated non-stratified dielectrics, challenge the accuracy of existing FRW transition schemes that approximate dielectrics with stratified or eight-octant patterns. In this work, we propose an algorithm named MicroWalk, enabling accurate FRW transitions for arbitrary dielectrics while keeping high efficiency. It is provably unbiased and equivalent to using transition probabilities solved by finite difference method, but at orders of magnitude lower cost (802× faster). An enhanced 3-D capacitance solver is developed with a hybrid strategy for complicated dielectrics, combining MicroWalk with the special treatment for the first transition cube and the analytical algorithm for stratified cubes. Experiments on real-world structures show that our solver achieves a significant accuracy advantage over existing FRW solvers, while preserving high efficiency.