n Adaptive Similarity Learning Method for Inverse Model Calibration
Please login to view abstract download link
Model calibration plays a pivotal role in refining computer models to faithfully represent the underlying physical processes[1]. However, due to inherent theoretical imperfections and stochastic influences, biases between the model and reality are often inevitable[2], especially in small samples scenarios. While it may seem tempting to blindly minimize discrepancies, such an approach risks pushing the calibrated parameters further away from the true physical values[3]. To address this challenge, this paper introduces a novel correlation-based calibration method, which prioritizes achieving "maximum similarity" between the computer model and the physical process rather than merely pursuing "closest proximity". A key contribution of this method lies in its ability to distinguish between parameter uncertainty and simulation bias. The proposed method, which incorporates distance correlation-based parameter calibration, effectively retains the intrinsic discrepancies between the two domains, while simultaneously decoupling parameter uncertainty from model uncertainty.Where the Brownian distance correlation preserves the inherent discrepancy between the computer model and the physical process, and achieves the decoupling of parameter uncertainty and model uncertainty. Meanwhile, we utilize the Nested Stochastic Kriging model with response uncertainty parameters decoupled from other surrogate model parameters, which can significantly improve the accuracy of uncertainty quantification and modeling efficiency. Furthermore, we develop an innovative sequential sample infusion strategy tailored for small-sample contexts, which independently updates design variables and calibration parameters to enhance estimation accuracy. This method achieves high-precision calibration with low computational cost and provides comprehensive uncertainty quantification. The proposed method is verified by several numerical examples and one engineering example. The results show that our proposed method can obtain an accurate inversion of the model parameters, which also improves the prediction accuracy of the model.
