Stochastic Simulation Sensitivity via Weight Function

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Solution Overview

Problem

Monte Carlo simulations for stochastic systems with numerous parameters face challenges in calculating sensitivity of expected values due to resource constraints, as they require running multiple simulations for each parameter change, which is computationally intensive and time-consuming.

Innovation Solution

A simulation system that calculates sensitivity by using a weight function to determine differential coefficients based on random number vectors and parameter changes, allowing for the calculation of sensitivity from a single set of Monte Carlo simulations, reducing the need for multiple simulations and resource usage.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If multiple Monte Carlo simulations are run for each parameter change to calculate sensitivity, then measurement precision of sensitivity is improved, but use of energy and loss of time increase significantly

Engineering Contradiction:

Improvesensitivity calculation accuracyVSAvoidcomputing resources

Core Design Contradiction:

Measurement precisionVSUse of energy by stationary object

Solution Approach 1:

The patent combines multiple sensitivity calculations into a single Monte Carlo simulation run. By using analytical differentiation of the stochastic model with respect to parameters, the system extracts sensitivity information for all parameters simultaneously from one simulation, rather than running separate simulations for each parameter. This merging approach maintains measurement precision while dramatically reducing computing resource consumption.

Inventive Principle:

Principle #5Merging (Combining)

Solution Approach 2:

The patent replaces the mechanical approach of running multiple numerical simulations with an analytical mathematical approach. By deriving analytical expressions for sensitivity through differentiation of the stochastic model, the system eliminates the need for repeated numerical simulations, substituting computational brute force with mathematical elegance to achieve the same sensitivity measurements.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Measurement precision

If multiple Monte Carlo simulations are run for each parameter change to calculate sensitivity, then measurement precision of sensitivity is improved, but loss of time increases significantly

Engineering Contradiction:

Improvesensitivity calculation accuracyVSAvoidsimulation time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent merges multiple sensitivity calculations into a single Monte Carlo simulation run. By using analytical differentiation of the stochastic model with respect to parameters, the system extracts sensitivity information for all parameters simultaneously from one simulation, rather than running separate simulations for each parameter. This merging approach maintains measurement precision while dramatically reducing computing resource consumption.

Inventive Principle:

Principle #5Merging (Combining)

Solution Approach 2:

The patent performs preliminary analytical differentiation of the stochastic model to derive sensitivity expressions before running the actual Monte Carlo simulation. This preliminary mathematical preparation allows the system to extract sensitivity information directly from the simulation results without needing to repeat the simulation for each parameter, thereby saving time.

Inventive Principle:

Principle #10Preliminary action

3Productivity

If a single set of Monte Carlo simulations is used to calculate sensitivity for all parameters, then use of energy and loss of time are reduced, but device complexity increases due to weight function calculations

Engineering Contradiction:

Improvesimulation efficiencyVSAvoidcalculation method complexity

Core Design Contradiction:

ProductivityVSDevice complexity

Solution Approach 1:

The patent introduces a weight function as an intermediary mathematical tool that bridges the stochastic model and the sensitivity calculations. This weight function, derived from the analytical differentiation process, allows the system to extract sensitivity information from a single Monte Carlo simulation run. While the weight function adds mathematical complexity, it enables the overall system to achieve higher productivity by eliminating repeated simulations.

Inventive Principle:

Principle #24Intermediary (Mediator)

Data Source

PatentUS11003810B2Simulation system and simulation method

Publication Date: 2021.05.11 HITACHI LTD

AI summary

A simulation system obtains multiple random number vectors and a parameter vector and calculates realized values of the behavior of a stochastic system corresponding to each obtained random number vector. Based on each obtained random number vector, on the obtained parameter vector, and on a weight function, the system calculates the weight of each obtained random number vector regarding each of the parameters in the obtained parameter vector, and calculates an evaluation value of the behavior of the stochastic system corresponding to each obtained random number vector. Based on the calculated behavior evaluation value corresponding to each obtained random number vector and on the weight of each obtained random number vector regarding the parameter selected from the obtained parameter vector, the system calculates the sensitivity of an expected value for the behavior evaluation value of the stochastic system with regard to the selected parameter.