Lachlan Astfalck: FlowGP: Physically Coherent ML for Probabilistic Field Reconstruction
FlowGP is a new machine-learning framework for physically coherent spatial and spatio-temporal inference of environmental fields. Classical kriging and optimal interpolation (OI) remain central to environmental learning because they are transparent, data-efficient and uncertainty-aware, but their Gaussian-linear structure makes it difficult to respect governing physics or assimilate observations linked to the target field through nonlinear transformations. FlowGP retains these strengths whilst also incorporating constrained, non-Gaussian or nonlinear data into a latent GP space, yielding predictions that respect constraints such as conservation relationships or dynamical coherence. We present FlowGP as a practical bridge between statistical interpolation and modern generative ML. The method requires no bespoke neural network architecture and can be implemented on top of existing GP/kriging/OI workflows, making it attractive for scientific users who need robust uncertainty quantification rather than black-box forecasts. More broadly, the framework opens a route to kriging-like inference for modern observing systems: fusing heterogeneous sensors, embedding physical constraints, and handling non-Gaussian measurements without abandoning the interpretability and calibration that make Gaussian-linear methods trusted.