Machine learning (ML) is becoming an increasingly powerful tool in particle physics, offering fast surrogates for expensive theoretical calculations and flexible methods for analysing complex, high-dimensional data. For precision applications, however, accurate predictions alone are not sufficient. They must be accompanied by reliable uncertainty estimates.
In this talk, I will discuss uncertainty-aware ML in controlled-theory settings, starting with neural-network surrogates for scattering amplitudes. With known target functions, amplitudes provide a clean benchmark for studying calibrated uncertainties, artificial noise, training-data gaps, and biases. I will then move on to a more complex inverse problem using a non-singlet PDF distribution as a controlled example, in which the target is inferred via a physics forward map rather than observed directly. I will compare neural-network ensembles, Gaussian processes, and neural tangent kernels as tools for uncertainty estimation and extrapolation.