Designing new ML tools for discovery in the physical sciences, and statistical analysis of LHC data.1. Created new ML density model architecture for high-dimensional physical datasets. By studying the impacts of data representation, architecture and initialisation, I designed an inductive bias tailored towards the key structural features of physical datasets. Implemented model and pipeline in Python using TensorFlow+Keras.Enables tasks: approximate inference, generative modelling and likelihood-based classification.Solved difficult non-convex optimisation task, eliminating traditional stability problems.2. Created interpretable AI algorithm for an “automated scientific advisor” in particle physics, to enable better analysis optimisation.Novel solution to nuanced regression task: find regions of feature-space that minimise expected p-values, based on understanding of the statistical theory of LHC measurements.3. With co-author FB, we demonstrated + corrected a serious problem with a leading method for estimating p-values in EFT searches.Derived the correct asymptotic distribution of profile-likelihood-ratio test-statistic using probability theory, geometry and linear algebra. Designed novel numerical algorithm using Jax to solve analytically intractable problem. 4. Implemented ML architectures including MLPs, GANs, CNNs and VAEs in exploratory research and teaching. Gained theoretical and applied experience with these foundational ML techniques. 5. Performed large statistical analysis: search for new-physics effects in measurements of electroweak Z+jets events for the ATLAS Collaboration. Performed numerical simulations to study expected sensitivity, bias, coverage and global significance.