Multi-rate Sampling for Hierarchical Monte Carlo Analysis
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Solution Overview
Problem
Monte Carlo simulations for complex systems, such as circuit designs, face challenges in computational time and accuracy when using reduced circuit descriptions, leading to inaccurate statistical analysis due to incomplete representation of statistical variables.
Innovation Solution
A multi-rate sampling method for Monte Carlo analysis, where statistical variables are sampled at different rates based on the actual number of subcircuits, generating multiple variants to determine the worst-case performance and associating it with a master Monte Carlo sample, allowing for statistically accurate results with reduced computational resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If full Monte Carlo simulations are performed with complete system models, then statistical accuracy is improved, but computational time increases prohibitively
Solution Approach 1:
The patent segments the system model into hierarchical levels (e.g., device level, circuit level, system level) and performs Monte Carlo simulations at each level separately. This segmentation allows the simulation to focus computational resources on critical subcomponents while using simplified models for less critical parts, thereby reducing overall computational time while maintaining statistical accuracy for key performance parameters.
Solution Approach 2:
The patent applies partial Monte Carlo sampling by performing simulations on only the most critical subcomponents with full detail, while using reduced-order models or analytical methods for less critical portions of the system. This partial action approach achieves sufficient statistical accuracy for the overall system without the prohibitive computational cost of full-system simulations.
2Device complexity
If reduced circuit descriptions are used to accelerate simulations, then computational complexity is reduced, but statistical accuracy deteriorates due to incomplete representation of statistical variables
Solution Approach 1:
The patent applies local quality by using detailed circuit descriptions only for critical subcomponents where statistical accuracy is essential, while using simplified reduced-order models for non-critical portions. This localized approach to model fidelity maintains statistical accuracy where needed while reducing overall computational complexity.
Solution Approach 2:
The patent creates simplified copies (reduced-order models) of non-critical circuit components that capture the essential statistical behavior without the full complexity of the original circuits. These copies are then used in the hierarchical simulation to reduce computational complexity while maintaining sufficient statistical accuracy through the aggregation of results from detailed simulations of critical components.
Data Source
AI summary
System analysis by receiving a model of a complex system design. The model includes at least one layer. The analysis includes performing a plurality of simulations of the performance of the layer. The number of simulations is determined according to a number of system components associated with the layer. The analysis further includes determining a worst-case result for a set of simulations from the plurality of simulations and assigning the worst-case result to an overall system simulation.