Data-Driven Corrections of Partial Lotka-Volterra Models.

Area of Science:

• Computational modeling
• Applied mathematics
• Scientific computing

Background:

• Many scientific and engineering applications utilize reduced-order models focusing on a subset of system dynamics.
• These partial models often omit numerous species or interactions, leading to inherent model error.
• Accurate prediction with these simplified models, especially under extrapolation, remains a challenge.

Purpose of the Study:

• To develop and evaluate a novel embedded, sparse, and data-driven discrepancy operator.
• To augment partial interaction models and systematically correct for errors introduced by model reduction.
• To enhance the reliability and predictive capability of reduced-order models under extrapolative conditions.

Main Methods:

• An embedded discrepancy operator is incorporated into the differential equations of existing partial models.
• The operator is constructed using sparse, data-driven techniques, requiring only a small fraction of the omitted terms.
• The operator is constrained by physical information and calibrated across multiple scenarios for robustness.

Main Results:

• Preliminary results demonstrate that sparse operators can effectively capture model errors arising from severe reductions (e.g., hundreds of terms).
• The embedded nature of the operator allows for interpretable analysis of its corrective action.
• The approach shows promise in maintaining physical consistency and robustness across diverse scenarios.

Conclusions:

• A sparse, data-driven discrepancy operator offers a viable method for augmenting reduced-order models.
• This technique can mitigate model errors caused by significant simplifications, improving predictive accuracy.
• The operator's interpretability, physical consistency, and robustness support reliable predictions, particularly in extrapolative regimes.