FasterRW: An Efficient Prior-Assisted Random Walk Solver for Thermal Analysis
Abstract
Thermal simulation is becoming increasingly critical in modern IC design and manufacturing. Feynman--Kac random walk methods can estimate localized temperatures without solving the global field, but in practical settings without Dirichlet boundaries they require very long paths to control the truncation residual. This paper presents FasterRW, a continuation-value framework for accelerating Feynman--Kac thermal random walks. We prove a stopping-time residual identity showing that the expected tail after truncation equals the current attenuation weight multiplied by the temperature at the stopping location. This identity enables a prior-corrected single-point estimator: a cheap, noisy prior replaces the unknown continuation value, making the truncation bias scale with prior error rather than absolute temperature and yielding an error-controlled threshold-selection rule. For multi-point queries, FasterRW further converts cross-query pass-through tails into pseudo-samples and refines the resulting observations in prior-error coordinates through kriging. Compared with prior state-of-the-art methods, FasterRW achieves up to 28× acceleration while maintaining accuracy. Our code is open-sourced at https://github.com/ShiningSord/FastRW.
Related
- The Efficient Frontier from a LASSO Solver
- DeHNSSo-v2: A compressible, curvilinear, and efficient extension of the Delft Harmonic Navier-Stokes Solver
- An adaptive current–voltage step size solver for accurate and efficient modeling of solar photovoltaic modules
- RAPTOR: RAndom-projection Physics-informed Transient sOlveR
- PrecPack: An Efficient Open-Source Exact Solver for Bin Packing with Generalized Precedence Constraints
BibTeX
@misc{wang2026fasterrw,
title = {{FasterRW: An Efficient Prior-Assisted Random Walk Solver for Thermal Analysis}},
author = {Zixiao Wang and Tianshu Hou and Chenghan Wang and Zhen Zhuang and Leilei Jin and Tsung-Yi Ho and Farzan Farnia and Bei Yu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08490},
eprint = {2611.08490},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08490},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - FasterRW: An Efficient Prior-Assisted Random Walk Solver for Thermal Analysis
AU - Zixiao Wang
AU - Tianshu Hou
AU - Chenghan Wang
AU - Zhen Zhuang
AU - Leilei Jin
AU - Tsung-Yi Ho
AU - Farzan Farnia
AU - Bei Yu
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.08490
UR - https://arxiv.org/abs/2611.08490
AB - Thermal simulation is becoming increasingly critical in modern IC design and manufacturing. Feynman--Kac random walk methods can estimate localized temperatures without solving the global field, but in practical settings without Dirichlet boundaries they require very long paths to control the truncation residual. This paper presents FasterRW, a continuation-value framework for accelerating Feynman--Kac thermal random walks. We prove a stopping-time residual identity showing that the expected tail after truncation equals the current attenuation weight multiplied by the temperature at the stopping location. This identity enables a prior-corrected single-point estimator: a cheap, noisy prior replaces the unknown continuation value, making the truncation bias scale with prior error rather than absolute temperature and yielding an error-controlled threshold-selection rule. For multi-point queries, FasterRW further converts cross-query pass-through tails into pseudo-samples and refines the resulting observations in prior-error coordinates through kriging. Compared with prior state-of-the-art methods, FasterRW achieves up to 28× acceleration while maintaining accuracy. Our code is open-sourced at https://github.com/ShiningSord/FastRW.
ER -