We consider the isogeometric analysis for fractional PDEs involving the fractional Laplacian
in two dimensions. An isogeometric collocation method is developed to discretize the …

We propose a new generative modeling technique for learning multidimensional cumulative
distribution functions (CDFs) in the form of copulas. Specifically, we consider certain classes …

We propose a framework for training neural networks that are coupled with partial differential
equations (PDEs) in a parallel computing environment. Unlike most distributed computing …

In many application areas it is common to come across time series data which challenge the
assumptions of well-known methods, such as by being non-stationary, non-Gaussian, or …

Lévy processes are useful tools for analysis and modeling of jump‐diffusion processes.
Such processes are commonly used in the financial and physical sciences. One approach to …

This dissertation presents my work on solving inverse problems in computational science
and engineering using a combination of partial differential equations (PDEs) and deep …

This paper presents a framework of imitating the price behavior of the underlying stock for
reinforcement learning option price. We use accessible features of the equities pricing data …