Environmental sensing and modeling occupy a critical intersection of applied mathematics, data science, and sustainability. Capturing the spatial and temporal dynamics of processes such as air pollution, soil contamination, and water quality requires transforming sparse and noisy measurements into continuous, interpretable fields. Despite notable advances in sensing technologies, environmental monitoring remains fundamentally limited by sensor coverage, economic constraints, and the nonlinear, heterogeneous nature of these systems.

This thesis introduces mathematical frameworks for data-driven environmental inference, addressing the challenge of reconstructing continuous environmental fields from incomplete observations. It comprises three integrated studies that span the sensing–inference continuum. The first study presents a novel vision-based approach to air quality estimation, demonstrating that physical quantities such as $CO_2$ and $PM_{2.5}$ can be indirectly inferred from visual cues in roadside imagery using deep convolutional neural networks. The second study develops the Ridiculously Simple Interpolation Method (RSIM), a mathematically principled yet computationally efficient technique that combines machine learning with physics-based digital twin simulations to reconstruct dense pollution maps from sparse sensor data. The third study generalizes the RSIM framework to soil and groundwater contamination, showing that the same formulation effectively captures spatial dependencies in subsurface transport despite discontinuities and heterogeneity in porous media.

Together, these contributions illustrate how mathematical reasoning and data-driven modeling can jointly overcome sensing limitations, offering a scalable path toward high-resolution, cross-domain environmental monitoring.