This dissertation presents computationally efficient methods for predicting free-surface elevations in partially filled tanks and pools subjected to prescribed rigid-body motions, both regular and irregular, with piston-type actuators installed at their ends. The first
method is a shallow-water, frequency-domain formulation obtained by recasting the linearised mass and momentum conservation laws into a Helmholtz boundary-value problem.

Comprehensive validation is conducted against computational fluid dynamics (CFD) simulations that solve the unsteady Reynolds-averaged Navier-Stokes (URANS) equations and against experimental measurements. Comparative results show that, away from eigenfrequencies, the method reproduces free-surface elevations with deviations typically below 5% in passive scenarios (without actuators) and below 10% in active scenarios (with actuators), while requiring several orders of magnitude less computational cost. Owing to this efficiency, the method enables extensive parametric studies to identify actuator settings that minimise free-surface waves. The method’s predicted optimal actuator amplitudes are consistent with URANS results under shallow-water conditions and at off-resonant frequencies.

Second, to address the limitations of the physics-based model near resonance, a Kolmogorov-Arnold Network (KAN) is trained on experimental data and applied to predict nonlinear free-surface elevations. Building on this, a hybrid shallow-water-KAN framework is introduced, where the shallow-water model optimises the actuator amplitude and the KAN maps this choice to the corresponding nonlinear free-surface elevations. This combination enables near-real-time optimisation of actuator amplitudes to mitigate free-surface elevations in tanks and pools under complex excitation
conditions. The framework is modular and extensible, allowing the integration of alternative high-fidelity solvers or machine-learning models, and provides an efficient basis for AI-assisted wave control in shipboard pool environments.