Research
I study the ways to efficiently combine Partial Differential Equations (PDEs) with neural networks for systems modeling.
PDEs are the established mathematical models for many realworld problems.
However, only a handful of equations have an analytical solution while for the rest the solution is approximated numerically.
Traditional numerical solvers usually provide an accurate approximation but tend to be quite slow. Other limitation of traditional numerical algorithms is their inability to tune the solution according to observations from the real process.
Alternatively, neural networkbased solvers are datadriven in nature and have faster inference. These properties allow extension of neural solvers for applications where the equation itself is partially unknown but can be inferred from data. Finally, when the governing equations of the process are unknown, inductive biases from differential equations or traditional numerical solvers baked into neural network architecture significantly reduce data requirements and improve the results.
