Investigating Model Form Error Estimation for Sparse Data

Computational simulations of dynamical systems involve the use of mathematical models and algorithms to mimic and analyze complex real-world phenomena. By leveraging computational power, simulations enable researchers to explore and understand systems that are otherwise challenging to study experimentally. They offer a cost-effective and efficient means to predict and analyze the behavior of physical, biological, and social systems. However, model form error arises in computational simulations from simplifications, assumptions, and limitations inherent in the mathematical model formulation. Several methods for addressing model form error have been proposed in the literature, but their robustness in the face of challenges inherent to real-world systems has not been thoroughly investigated. In this work, a data assimilation-based approach for model form error estimation is investigated in the presence of sparse observation data. Including physics-based domain knowledge to improve estimation performance is also explored. The Lotka-Volterra equations are employed as a simple computational simulation for demonstration.