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DE Seminar: Animikh Biswas (UMBC)

Local Faculty DE Series


Mathematics/Psychology : 401

Date & Time

May 16, 2022, 11:00 am12:00 pm


Title: Data Assimilation, Parameter Identification and Physics Informed Deep Neural Network in hydrodynamics.

Abstract: Recently, there has been a proliferation of literature on computational methods for solving a variety of
forward and inverse problems using deep neural network (so called Physics Informed Neural Network
(PINN)). In essence, a Deep Feed Forward Neural Network (DFNN) is a function approximator that is
comprised of many layers (or repeated composition) of functions where each layer is an affine map
composed with a sigmoid activation function. In many PDE applications, this sigmoid function is often
taken to be smooth, e.g., the tanh function. Due to its importance in applications, there has been a
recent surge of interest in parameter determination and estimation problem from finitely many
observed data. A number of ad hoc algorithms have been proposed, some employing PINNS, for
parameter determination and estimation from observed data. We provide explicit examples to show that
the parameter-to-data map need not be injective and thus the parameters are not identifiable and
consequently, these ad hoc methods are destines to fail. We develop a rigorous framework for parameter identification and estimation employing the determining map. For the case of the Navier-
Stokes equations, an interesting connection to an analytical question concerning the attractor emerges.