What A lot of research has been devoted to finding quantum algorithms to be run on quantum computers in the future. What has only be realised very recently is that some of the building blocks of these algorithms can also lead to faster classical algorithms to be run on available classical hardware. One area where these quantum-inspired have very recently provided dramatic speedup is in solving partial differential equations. This project aims to develop the full potential of quantum inspired algorithms, and ambitions to dramatically speedup the solution and simulation of partial differential equations in a wide variety of settings. Why Solving partial differential equations to high precision is essential for many applications in science, engineering and finance, including: chip design, radar cross section, computational fluid dynamics, seismic imaging, quantum chemistry, derivatives pricing in finance, and many more. Globally, a large fraction of high performance computing resources are allocated to solving PDEs. Hence, algorithmic progress will have substantial industrial and scientific impact, while mitigating the CO2 footprint of these massive simulations. How The essential toolset, upon which the project is built, is tensor networks. Tensor networks were originally developed for simulating strongly correlated quantum materials. They are especially well suited for describing high dimensional objects that contain strong, but ordered, correlations across the dimensions. Solutions to partial differential equations exhibit exactly these sorts of correlations due to their differential origin. Hence, we will leverage a large body of work into a new field, and expect constructive cross-fertilisation.