Coastal flooding is among the most devastating natural disasters, with over 1.8 billion people living in vulnerable coastal regions. Although oceanic tides have been predicted for over a century, many compound tidal processes that drive real flood risk, including storm surges, tidal rivers, and tidal currents, remain difficult to forecast. Conventional approaches rely on numerical simulation constrained by the shallow-water equations, but their accuracy depends critically on bathymetry and boundary conditions. In many low- to middle-income regions, where 89% of vulnerable coastal populations live, such data are sparse or unavailable, limiting forecasting quality. This thesis develops several new frameworks for analysing and predicting tidal processes without requiring bathymetric information. The central contribution is RTide: a physics-informed machine learning approach based on the recognition that tidal processes can be represented as causal, time-invariant, weakly nonlinear responses to external forcing. By embedding Volterra Networks within an impulse-response framework, RTide learns nonlinear response functions directly from observational data while retaining an exact connection to the underlying physical representation. This removes the need to prescribe nonlinear interactions a priori and allows for predictions at arbitrary times from known or forecast forcing, including astronomical, meteorological, and hydrological inputs. For the first time, this enables the analysis and forecasting of arbitrary tidal processes without bathymetric information, with demonstrated applications to tidal rivers, storm surge, and tidal currents. RTide is operationally deployed within the Dutch storm surge forecast system and is being introduced into UK national forecasts, helping protect over £500 billion in assets and over 2 million people. By removing the need for bathymetric data, it lays the foundation for global storm surge forecasting, particularly in regions lacking conventional modeling infrastructure. Separately, using the methods developed in, this thesis presents the first observation of persistent fluid sloshing without an external driver lasting over a week.