Multi-Level Monte Carlo sampling with Parallel-in-Time Integration for Uncertainty Quantification in Electric Machine Simulation

2025-07-25

AI Summary

To address the prohibitively high computational cost of Monte Carlo (MC) methods for motor simulation under high-dimensional uncertainty, this paper proposes embedding parallel-in-time (PinT) integration into the multilevel Monte Carlo (MLMC) framework. This approach fully exploits hierarchical parallelism—across both sample realizations and temporal discretization levels—thereby unlocking residual time-parallelism and enabling dual-level (sample- and time-step-wise) concurrent computation. Crucially, it achieves substantial speedup while constraining total computational overhead. In two representative motor simulation benchmarks, the method reduces overall solution time by 12–45%, with only a 15–18% increase in total computational cost. It thus strikes an effective balance among uncertainty quantification accuracy, runtime efficiency, and resource expenditure. The proposed paradigm offers a scalable, high-fidelity framework for real-time uncertainty analysis in electromechanical systems.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the Multi-Level Monte Carlo method reduces the overall computational effort, but is unable to reduce the time to solution in a sufficiently parallel computing environment. In this work, we propose a Uncertainty Quantification method combining Multi-Level Monte Carlo sampling and Parallel-in-Time integration for select samples, exploiting remaining parallel computing capacity to accelerate the computation. While effective at reducing the time-to-solution, Parallel-in-Time integration methods greatly increase the total computational effort. We investigate the tradeoff between time-to-solution and total computational effort of the combined method, starting from theoretical considerations and comparing our findings to two numerical examples. There, a speedup of 12 - 45% compared to Multi-Level Monte Carlo sampling is observed, with an increase of 15 - 18% in computational effort.

Problem

• Reducing time-to-solution in Uncertainty Quantification for electric machines
• Balancing computational effort and speed in Multi-Level Monte Carlo methods
• Integrating Parallel-in-Time to exploit parallel computing capacity efficiently

Innovation

• Multi-Level Monte Carlo reduces computational effort
• Parallel-in-Time integration accelerates computation
• Combined method balances speed and effort