Enforcing Causality in Data-Driven Modeling of Complex Dynamical Systems

Abstract Modeling complex dynamical systems is crucial for addressing societal and industrial needs. Traditional approaches, including physics-based modeling and system identification, often require extensive expert knowledge or struggle to capture complex dynamical behavior due to the limitations of parameterized model structures. While recent advancements in machine learning, particularly neural networks, have mitigated some of these challenges, determining system order and enforcing prior system properties—such as temporal causality—remain significant obstacles in data-driven modeling. Motivated by these challenges, this work proposes a neural network-based modeling framework that enforces strict temporal causality by structuring the network’s weight matrices in a lower triangular form. The effectiveness of this approach is demonstrated through its application to modeling the in-cylinder pressure of multifuel compression-ignition engines using experimental data and an academic example. The results indicate that neural network models with enforced causality produce more accurate representations than standard neural networks.