Hybrid model- and data-driven neural operators for acoustic inverse problems
Description:
Neural networks, the backbone of artificial intelligence, has recently been increasingly used for scientific problems. Particularly, it is has been applied to solving inverse problems in medicine and geophysics. Another recent advancement is the neural operator. These neural networks are able to map functions to functions and are mainly used in scientific computing as fast surrogate models for solving complex PDEs.
In inverse problems involving partial differential equations (PDEs), these neural operators can be very important as they are much quicker in solving the PDEs and hence can help in solving the inverse problem faster. One issue, however, is that the neural operators are mainly data-driven. Hence, there are no guarantees that the PDE is solved accurately. This is in contrast when solving the PDE via (slower) model-driven numerical methods. The lack of guarantees is a big issue of the neural operators as inaccurate PDE solutions can have significant negative impact on the obtained solution.
This project tries to tackle this problem for inverse problems in (photo)acoustics. Particularly, we want to combine the model-driven approach with the data-driven neural operators. The goal is to develop a general method that provides improved and faster reconstructions to the inverse problem by using neural operators but that has some additional guarantees by incorporating model-driven components, hence creating a hybrid model.
Output:
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