Physics-informed Neural Networks for Space Applications

Background

Physics Informed Neural Networks (PINNs) are a novel deep learning paradigm with the ability to solve both forward and inverse problems for non-linear Partial Differential Equations (PDEs) [1]. By embedding underlying physical constraints into the feed-forward neural network architecture, PINNs are able to be trained as a surrogate model with minimal or no labelled data for PDE solution inference [2]. In current literature, the implementation of PINNs is considered both in complementarity to, and as a potential alternative to existing numerical techniques across a diverse range of research fields within science and engineering [3, 4, 5].

Although the conducted research on PINNs highlights the models feasibility of replacing these existing data-intensive numerical techniques, the efficiency of these models is impaired by the necessity to distinguish an optimal balance between inevitable computational cost and the magnitude of the calculated losses. In order for PINNs to become better established as an alternative approach towards complex problems, advances must be made in enhancing the operating efficiency of such algorithms.

Project Overview

This project aims to (literally) amend the boundaries on the current perception of PINNs and deliver an effective machine learning tool that will enable - through parameterisation of the underlying physical constraints - the ability to adopt a class of solutions towards complex space applications. This would significantly improve the operating efficiency of such models by avoiding the computationally expensive re-training of the model for unique physical information. More specifically, the intended goals and objectives of this project consist of the following:

• Development of a PINN architecture that introduces parameterised constraints and defines parameter values as a network input. By the feed-forward process, one can then predict a full class of solutions characterised by the inputs.
• Perform inversion techniques on the generated model to evaluate the feasibility of learning a specific parameter value from chosen solution states/evolutions.
• Implement this tool towards complex problems with space applications. A primary topic of interest is to implement PINNs with parametric physical constraints for modelling the sloshing dynamics of spacecraft fuel within partially filled containers [6]. As a result of external excitation, the equilibrium state of a contained liquid is disrupted. In cases where the external excitation either emulates the natural frequencies, or is of a large enough amplitude, the effects of sloshing behaviour can be severe, inducing violent oscillations and energy dissipation [7]. Such behaviour can have a direct impact of the stability of the craft due to these nutations [8]. Therefore, accurately and efficiently quantifying fluid flow and behaviour evolution on the liquid free-surface within such vessels is paramount for minimising disruptive behaviour on missions. Furthermore, by the previously discussed inversion techniques, we also consider the ability to infer predictions of the fuel load, based upon the evolution of the sloshing behaviour.
• Decide upon other multi-disciplinary areas of research to implement this new tool within to highlight the diversity of its application. Current areas being considered include, but are not exclusive to, Biomimetics and Quantum Physics. Particular topics of interest include problems related to microfluidics, quasi-normal mode analysis of black holes and magnetohydrodynamics.

References

[1] Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686-707 (2019).

[2] Cuomo, S. et al. Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next. J. Sci. Comput. 92, 88 (2022).

[3] Mao, Z., Jagtap, A. D. & Karniadakis, G. E. Physics-informed neural networks for high-speed flows. Comput. Methods Appl. Mech. Eng. 360, 112789 (2020).

[4] Buoso, S., Joyce, T. & Kozerke, S. Personalising left-ventricular biophysical models of the heart using parametric physics-informed neural networks. Med. Image. Anal. 71 102066,(2021).

[5] Cai, S. et al. Physics-Informed Neural Networks for Heat Transfer Problems. J. Heat. Transfer. 143, 060801 (2021).

[6] Ibrahim, R. Liquid Sloshing Dynamics: Theory and Applications. Cambridge University Press. (2005).

[7] Luo, X., Kareem, A., Yu, L., & Yoo, S. A Machine Learning-based Characterization Framework for Parametric Representation of Nonlinear Sloshing. arXiv e-prints, (2022).

[8] Rafiee, A., Pistani, F. & Thiagarajan, K. Study of liquid sloshing: numerical and experimental approach. Comput. Mech. 47, 65–75 (2011).