ImPhys Colloquium | Tariq A. Alkhalifah | Nov 8

Artificially intelligent waveform inversion using physics-guided neural network functions

Neural network models, in simple terms, are nothing but mathematical functions of the inputs. Unlike functions represented by Fourier, wavelet or any other basis functions, the parameters (coefficients) of the neural networks correspond to basis functions defined primarily by a stack of linear operations and activation functions. Thus, these parameters are evaluated through an optimization problem, and neural network models have proven to be good universal function approximators, granted the functions are continuous, like those describing wavefields, including our data. I will share examples of neural network functions that help us solve some of the outstanding challenges we face in waveform inversion. These include an NN misfit function, trained to measure the distance between the observed and synthetic data in a way that allows us to avoid cycle skipping. It also includes an NN wavefield functional solution to the wave equation that can also fit the data. The key feature of NN functions is their flexibility as they are optimized to implement specific tasks, and in our case these tasks are directed to support waveform inversion.