Modern applications in computational science, such as in biomedicine and climate science, are governed by multi-scale and partially unknown physically processes, and hence are numerically challenging to solve. The plummeting cost of sensors, computational power, and data storage in the last decade offers new opportunities for data-driven modelling of such physical systems. However, while both physical modelling and purely data-driven methods are active independent research areas, surprisingly little attention has been paid to the intersection of the two. In order to enable a shift towards simulation models that are either parametrised or controlled by data-driven algorithms, there is a pressing need
for new mathematical tools, new numerical abstractions and new algorithms. The ambition of DataSim is therefore to develop efficient algorithms to enable data-driven simulation described by partial differential equations. Specifically, we will propose simulation models that consist of coupled partial differential equations and machine learning models, and develop a high-level software framework for specifying, evaluating and training such models. Based on this approach, we
will investigate new algorithms for model identification and adaptive control methods for partially unknown and dynamically changing physical systems. The capabilities of the new algorithms will be demonstrated by identifying cell growth models for breast cancer tumours and by optimising treatment therapies.
The outcomes of DataSim could have a transformative scientific impact for complex physical simulations and control problems in computational science, and societal impact through the development of
improved breast cancer models and treatment strategies.
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