What’s Next?
Quite a lot! Here are some research directions I am looking forward to pursuing next:
Applying forward simulation techniques I’ve developed to novel scientific contexts
Efficient forward simulations for solving inverse problems
Incorporating data science of observations to better guide numerical simulations to the right initial hypotheses
Combining Machine Learning surrogate modeling with multiscale simulation frameworks with reliable error control
Adaptive subgrid methods that more efficiently use computational resources by adapting our accuracy to each term in the PDE system we model