Observable-Reduction-Guided Sparse Regression for Partially Observed Active-Quiescent Systems

What the math gives to ML

The paper provides a constructive observable-reduction mechanism: when compartmental dynamics are only partially observed, the measured variable generally obeys a higher-order closed equation with nonlinear coefficient relations, rather than the original first-order compartment equation. Its transferable asset is an observation-aware dynamics library that eliminates hidden states before sparse regression, preventing models that fit trajectories but fail coefficient or transfer checks. In neural networks, this can be implemented as a constrained neural state-space or world model whose output dynamics are parameterized in the reduced observable coordinates appropriate to the sensor map. The key falsifiable prediction is that aggregate observations require second-order temporal features and that the learned coefficients must satisfy algebraic relations inherited from the hidden-compartment model.