# DE Seminar: Animikh Biswas (UMBC)

## Local Faculty DE Series

Monday, May 16, 2022

11:00 AM – 12:00 PM

11:00 AM – 12:00 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.

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