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Abstract:
We propose a statistical learning framework based on group-sparse regression that can be used to (i) enforce
conservation laws, (ii) ensure model equivalence, and (iii) guarantee symmetries when learning or inferring
differential-equation models from data. Directly learning interpretable mathematical models from data has
emerged as a valuable modeling approach. However, in areas such as biology, high noise levels, sensor-induced
correlations, and strong intersystem variability can render data-driven models nonsensical or physically inconsistent
without additional constraints on the model structure. Hence, it is important to leverage prior knowledge
from physical principles to learn biologically plausible and physically consistent models rather than models that
simply fit the data best. We present the group iterative hard thresholding algorithm and use stability selection to
infer physically consistent models with minimal parameter tuning. We show several applications from systems
biology that demonstrate the benefits of enforcing priors in data-driven modeling.
