Optimizing maritime operations, particularly fuel consumption for vessels, is crucial, considering its significant share in global trade. As fuel consumption is closely related to the shaft power of a vessel, predicting shaft power accurately is a crucial problem that requires careful consideration to minimize costs and emissions. Traditional approaches, which incorporate empirical formulas, often struggle to model dynamic conditions, such as sea conditions or fouling on vessels. In this paper, we present a hybrid, physics-guided neural network-based approach that utilizes empirical formulas within the network to combine the advantages of both neural networks and traditional techniques. We evaluate the presented method using data obtained from four similar-sized cargo vessels and compare the results with those of a baseline neural network and a traditional approach that employs empirical formulas. The experimental results demonstrate that the physics-guided neural network approach achieves lower mean absolute error, root mean square error, and mean absolute percentage error for all tested vessels compared to both the empirical formula-based method and the base neural network.

Dynamical models in the form of systems of ordinary differential equations have become a standard tool in systems biology. Many parameters of such models are usually unknown and have to be inferred from experimental data. Gradient-based optimization has proven to be effective for parameter estimation. However, computing gradients becomes increasingly costly for larger models, which are required for capturing the complex interactions of multiple biochemical pathways. Adjoint sensitivity analysis has been pivotal for working with such large models, but methods tailored for steady-state data are currently not available. We propose a new adjoint method for computing gradients, which is applicable if the experimental data include steady-state measurements. The method is based on a reformulation of the backward integration problem to a system of linear algebraic equations. The evaluation of the proposed method using real-world problems shows a speedup of total simulation time by a factor of up to 4.4. Our results demonstrate that the proposed approach can achieve a substantial improvement in computation time, in particular for large-scale models, where computational efficiency is critical.

Ordinary differential equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be limiting. AMICI is a modular toolbox implemented in C++/Python/MATLAB that provides efficient simulation and sensitivity analysis routines tailored for scalable, gradient-based parameter estimation and uncertainty quantification. AMICI is published under the permissive BSD-3-Clause license with source code publicly available on https://github.com/AMICI-dev/AMICI. Citeable releases are archived on Zenodo.