Improving neural network based equations solvers - Livestream

Neural Networks (NNs) have ushered in new methods of constructing solution approximations to complex mathematical equations. However, especially in the context of Differential Equations (DEs), such approximations are often reliant on external methods/solutions to reliably estimate the errors associated with them. This occurs because cost functions are seldom explicitly dependent on the difference between the true solution and the NN based approximation. Thus, NN DE solvers retain an element of ambiguity vis a vis the fitness of their approximations that cannot seemingly be resolved without prior knowledge of an external solution - severely limiting their practicality and trustworthiness. We show how simple mathematical transformations upon the cost functions at hand can help address this issue, by creating explicit relationships between them and the error associated with the NN based approximations. We further show how such relationships allow for the construction of efficient error correction schemes.

Speaker: Akshunna Shaurya Dogra, UC Berkeley