Wasserstein Metric for Multidimensional Simulation Validation
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Solution Overview
Problem
Conventional validation metrics, such as the area validation metric, are inadequate for comparing multidimensional simulation and reference data sets, particularly in cases of highly correlated outputs, and fail to account for correlations between signals, limiting their applicability to complex systems like time series data.
Innovation Solution
The method employs the 1 Wasserstein metric to determine a distance between probability distributions of simulation and reference data, establishing a cost matrix and computing an optimal transport plan to expand validation capabilities to multidimensional signals, incorporating statistical variances and correlations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If the conventional area validation metric is used to compare simulation and reference data, then the validation process is simple to implement, but the metric fails to accurately capture correlations between multidimensional signals and outputs
Solution Approach 1:
The patent changes the mathematical parameter used for validation from the area validation metric to the Wasserstein distance. This parameter change enables the metric to handle multidimensional signals and capture correlations between outputs, while maintaining computational feasibility through established optimization techniques for computing the Wasserstein distance between empirical distributions.
2Adaptability or versatility
If the area validation metric is extended to multidimensional signals, then validation capability is expanded, but the volume enclosed by two measurements becomes infinitely large
Solution Approach 1:
The patent replaces the geometric volume-based approach with a probability distribution-based approach. Instead of calculating volumes enclosed by measurements in multidimensional space, the Wasserstein distance computes the minimum cost to transport probability mass between empirical distributions, providing a finite and meaningful metric for multidimensional signal validation.
3Productivity
If individual metric results are simply added to one another, then computation is straightforward, but correlations between signals are not taken into consideration
Solution Approach 1:
The patent merges the validation of multiple signals into a single unified metric computation. The Wasserstein distance between empirical distributions simultaneously accounts for correlations between all signals, eliminating the need to compute and sum individual metric results separately, thus capturing correlation information that would be lost in simple addition.
Data Source
AI summary
A computer-implemented method for validating simulation data of a simulation model of a technical system. The method includes the following steps: providing simulation data including a number of simulation signals and providing reference data including a number of reference signals, the simulation signals and the reference signals being multidimensional signals, at least two-dimensional signals, and determining a metric between a first probability distribution including the simulation data and a second probability distribution including the reference data by using the 1 Wasserstein metric.