Learning physically consistent differential equation models from data using group sparsity
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
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.
Details
Original language | English |
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Article number | 042310 |
Journal | Physical Review E |
Volume | 103 |
Issue number | 4 |
Publication status | Published - Apr 2021 |
Peer-reviewed | Yes |
External IDs
PubMed | 34005966 |
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ORCID | /0000-0003-4414-4340/work/142252157 |