Simulation-based models, which are often formulated in terms of partial differential equations (PDEs), form the backbone of predictive modelling in the natural sciences and in engineering disciplines. Fundamentally, a scientific model is a simplification of reality that helps us the understand and predict the essential aspects of a system, either to forecast its future behaviour, or to optimize its design according to prescribed requirements. In deep learning research, a fundamentally different approach to predictive modelling has emerged, which employs large models, often with billions of parameters, that are optimized on similarly large datasets. Whilst interpreting these models can be very difficult due to their overparameterized nature, these models are achieving unparalleled predictive accuracy in an ever-increasing range of application domains.
We seek a PhD Candidate that will contribute to this project by carrying out research at the intersection of traditional PDE-based and deep learning methods. You will be positioned between the Amsterdam Machine Learning Lab (AMLab) and the Computational Science Lab (CSL) of the Informatics Institute. You will also be collaborating with Microsoft Research at the Science Park in Amsterdam.
What are you going to do?
One opportunity in this space is to leverage the flexibility of neural networks to learn fast approximate solutions to PDEs. A second frontier, with a huge potential, is learning PDE-based models from observational data. For lumped parameter models (systems of coupled ordinary differential equations) this has already been demonstrated. However, for spatio-temporal systems, which could be modelled by partial differential equations, only very few examples exist. You will work to advance the state of the art in these two domains:
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