<p>Calibration is vital to estimate unknown parameters and update the model, while the multiple solution problem makes it difficult to obtain accurate and robust calibrated models. Besides, blindly pursuing the minimum discrepancy between the computer model and experimental data may lead to results deviating from the true values. In this paper, we propose a novel multi-objective calibration method to solve these two problems. First, an adaptive weighted multi-objective method is provided, which considers the preference level for the response function and the uncertainty of the calibration results for each response. The sample number and Gaussian model prediction variance for different objective functions are used to evaluate the weights. Second, a calibration method based on Brownian distance correlation is proposed, which focuses on the similarity between the computer model and the physical process. The Brownian distance correlation preserves the inherent discrepancy between the computer model and the physical process, and mitigates the confounding effect between parameter estimation and model discrepancy, thereby enhancing the physical interpretability of the calibrated parameters. The proposed method is verified by four numerical examples and one engineering example. The results show that the proposed method can obtain an accurate inversion of the model parameters, which also improves the prediction accuracy of the model.</p>