TOWARDS PRECISION-CONTROLLED PARTONIC STRUCTURES FROM FIRST PRINCIPLES

The internal structure of hadrons is governed by nonperturbative Quantum Chromodynamics (QCD) and is being probed with increasing precision by modern high-energy experiments. This dissertation presents first-principles calculations of partonic observables using lattice QCD together with effective field theory methods, with controlled systematic uncertainties, advancing from collinear structure to transverse-momentum-dependent distributions (TMDs) that encode the three-dimensional partonic structure of hadrons. Within the large momentum effective theory (LaMET) framework, this work presents state-of-the-art calculations of pion distribution amplitudes and systematic studies of nucleon parton distributions, with control of renormalization, excited-state contamination, Fourier-transform systematics, and power corrections. A Coulomb-gauge formulation of quasi-distributions is implemented to simplify ultraviolet structure by avoiding Wilson-line related linear divergences. Systematic effects associated with Gribov copies are quantified and found to be negligible at current statistical precision, supporting the effectiveness of this approach. Building on these developments, this dissertation reports first-principles lattice determinations of key TMD quantities, including nucleon TMD parton distributions, the Collins-Soper kernel, the intrinsic soft function, and pion TMD observables. These results provide nonperturbative inputs directly relevant to global QCD analyses and to the precision hadron-structure program at current and future facilities, including the Electron-Ion Collider. In parallel, this dissertation explores machine-learning acceleration of lattice gauge simulations through neural field transformations embedded in Hybrid Monte Carlo. In two-dimensional U(1) tests, the method significantly reduces autocorrelation and improves performance toward finer lattice spacing. Such gains support precision-controlled partonic calculations by enabling finer lattices and larger hadron boosts, thereby reducing LaMET power corrections and improving control of discretization effects. The dissertation also outlines emerging directions using AI agents and foundation models to advance lattice data-analysis workflows under physics-based constraints.