In-depth characterisation of quantum devices is crucial not just for the optimal operation of high fidelity gates but more importantly, to identify true system parameters for creating an accurate model of the QPU and its control stack. Such an accurate digital twin of the system is critical for generating an error budget - a quantitative breakdown of the contribution of different error generating factors to the bottomline benchmarks of a QPU's performance. We use modern Machine Learning tools to combine a differentiable physics accurate digital twin with data from a broad set of characterisation experiments to build a model with a high predictive power that accurately predicts the outcome of experiments even outside the training dataset. This predictive model is then used to extrapolate the error contributions from different system and environmental factors. We test these tools on superconducting QPUs and discuss various demonstrative results.