Coffee brewing trajectories from recipe-level records: a conservation-constrained framework for filter coffee

Abstract

Abstract Filter coffee recipes specify brewing operations and selected beverage outcomes but do not resolve the extraction trajectory within the coffee bed. Here, we develop a reduced-order, conservation-constrained framework that reconstructs conditional water and dissolved-solids trajectories from limited recipe inputs. Effective process quantities are estimated from controlled brews with measured coarse, medium, and fine particle-size distributions and fixed before prediction of the held-out medium-coarse and medium-fine conditions. Across the two held-out condition means, mean absolute errors are 6.7 s for drawdown time, 0.58 g for beverage mass, and 0.020 percentage points for total dissolved solids, and all six endpoint predictions fall within one experimental standard deviation. Extraction yield is treated as a derived quantity, whereas retained water, solids partitioning, and time-dependent inventories are model-implied quantities. The framework is also applied to 53 public filter-coffee recipe records. Reported finish time is the only observed outcome directly compared with model-calculated drawdown time, while beverage composition and internal inventories remain conditional calculations. Although the present study does not directly validate internal states or establish general prediction across brewing systems, the results demonstrate that conventional filter-coffee recipe inputs provide a quantitative basis for interpolating measured beverage outcomes within the tested particle-size range and reconstructing the associated process trajectories.