Expert-Constrained Data Completion for Partially Observed Dynamical Systems with Uncertainty Quantification

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Abstract
Industrial dynamical systems contain states measured only at sparse checkpoints, whileengineers often know which mechanisms govern their evolution. We propose an expertconstrained completion model that learns initial conditions and corrections to an imperfectaffine dynamical system from sparse observations. Two neural networks use operating context to estimate the initial state and dynamical coefficients. Nested binary supports specifyadmissible state and control couplings and their possible context modulation. Hard masksenforce expert knowledge, soft penalties allow additional corrections, and evanescent regularization stabilizes training. A local Laplace approximation uses Gauss-Newton curvatureand Kronecker factorization to estimate trajectory uncertainty, followed by calibration onvalidation measurements.A synthetic benchmark evaluates fixed latent trajectories under five observation schedules and several expert-support regimes. The correct hard-constrained model attains a testtrajectory RMSE of 0.0452 ± 0.0129 across five training seeds under the reference sparseschedule. Measurement timing changes completion accuracy at fixed observation budget,and omitted true couplings bias the hard model. Retrospective conditioning on measurements from the same run improves initial-state inference in three of five channels under thelearned dynamics.