Gaussian Random Processes for Time-Series Model-Error Validation
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Solution Overview
Problem
Existing methods for validating simulation models, particularly in the context of time-series signals, fail to account for model form errors effectively, especially when comparing simulation results with reference data from different distributions.
Innovation Solution
A method involving Gaussian random processes is employed to determine simulation probability distributions by integrating model form errors using the 2-Wasserstein distance, updating means and variances of Gaussian random processes to align with reference distributions, thereby incorporating model form errors into the simulation data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional validation methods (area validation metric) are used, then scalar simulation data can be validated, but time-series simulation data cannot be validated due to inability to account for model form errors
Solution Approach 1:
The patent transforms the validation approach by changing from scalar parameter comparison to time-series parameter comparison using Gaussian random processes. It introduces new parameters including mean functions μ(t), covariance functions K(t,s), and the 2-Wasserstein distance metric to quantify differences between simulation and reference time-series data, enabling validation of temporal variations that conventional methods cannot handle.
Solution Approach 2:
The patent introduces Gaussian random processes as an intermediary framework to bridge simulation data and reference data. By representing both datasets as Gaussian random processes with mean functions and covariance functions, the method creates a common mathematical language that allows rigorous comparison and validation of time-series data while accounting for model form errors through the 2-Wasserstein distance.
2Productivity
If simulation models are used at unvalidated points, then simulation can be performed, but model form errors cannot be accounted for
Solution Approach 1:
The patent performs preliminary validation by computing the 2-Wasserstein distance between Gaussian random processes representing simulation and reference data at validated points. This preliminary characterization of model form errors through distributional distance metrics enables the system to account for uncertainties when extending simulations to unvalidated points, maintaining reliability while expanding productivity.
3Measurement precision
If distribution-based validation is used, then natural variability in reference data is captured, but model form error propagation to unvalidated points is not possible
Solution Approach 1:
The patent establishes a feedback mechanism where the 2-Wasserstein distance computed from distribution-based validation at reference points feeds into the characterization of model form errors. This feedback information is then used to adjust and propagate error estimates to unvalidated points, enabling the system to maintain measurement precision while achieving adaptability for error propagation through the Gaussian random process framework.
Data Source
AI summary
A method for determining simulation data. The method includes: providing a simulation probability distribution including a number x of simulation time series, and providing a reference probability distribution including a number y of reference time series; determining a first Gaussian random process for the simulation probability distribution, and determining a second Gaussian random process for the reference probability distribution, a Gaussian random process being assigned a mean and a covariance matrix; calculating a model error with the aid of the 2-Wasserstein distance between the first Gaussian random process and the second Gaussian random process over the Euclidian distance of the means of the first and second Gaussian random processes and the trace of the covariance matrices of the first and second Gaussian random processes; and determining a family of simulation probability distributions by integrating the model form error into an updated Gaussian random process.