One of the limitations of applying machine learning methods in real-world scenarios is the existence of a domain shift between the source (i.e., training) and target (i.e., test) datasets, which typically entails a significant performance drop. This is further complicated by the lack of annotated data in the target domain, making it impossible to quantitatively assess the model performance. As such, there is a pressing need for methods able to estimate a model’s performance on unlabeled target data. Most of the existing approaches addressing this train a linear performance predictor, taking as input either an activation-based or a performance-based metric. As we will show, however, the accuracy of such predictors strongly depends on the domain shift. Recent research highlights the significance of network weights in understanding model generalizability. The early work of [46] proposes a method to predict out-of-distribution error by comparing the weights of the original model and fine-tuned model on the target data. However, this process is computationally demanding, especially for large models and input sizes. To address this, we propose an efficient approach for assessing a model’s performance on target datasets by leveraging the gradients and Hessian of a model as indicators of weight differences. Our approach builds on the idea that lower norms of gradient and Hessian matrices signify a flatter training landscape and better adaptability to new data. Our extensive experiments on standard object recognition benchmarks, using diverse network architectures, demonstrate the benefits of our method, outperforming both activation-based and performance-based baselines by a large margin. It also outperforms [46]’s weight-based approach in efficiency by avoiding parameter updates and effectively estimates out-of-domain performance. Our code is available in the following repository: https://github.com/khramtsova/hessian_performance_estimator/.