101 citations · 308 across the 32 of their papers we have counts for
43 papers
Global Convergence of DGM and PINN Algorithms for Solving Nonlinear PDEs
Justin Sirignano, Konstantinos Spiliopoulos, Samuel Cohen
The Deep Galerkin Method (DGM) and Physics Informed Neural Networks (PINNs) have become widely-used methods for solving partial differential equations (PDEs) in the rapidly growing…
Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control
Samuel N. Cohen, Filippo de Feo, Jackson Hebner +1
We develop deep learning-based approximation methods for fully nonlinear second-order PDEs on separable Hilbert spaces, such as HJB equations for infinite-dimensional control, by p…
Global Convergence of Deep Galerkin and PINNs Methods for Solving Partial Differential Equations
Deqing Jiang, Justin Sirignano, Samuel N. Cohen
Numerically solving high-dimensional partial differential equations (PDEs) is a major challenge. Conventional methods, such as finite difference methods, are unable to solve high-d…
Exponential contractions and robustness for approximate Wonham filters
Samuel N. Cohen, Eliana Fausti
We consider the problem of estimating the state of a continuous-time Markov chain from noisy observations. We show that the corresponding optimal filter is strictly contracting pat…
Nowcasting using regression on signatures
Samuel N. Cohen, Giulia Mantoan, Lars Nesheim +3
We introduce a new method of nowcasting using regression on path signatures. Path signatures capture the geometric properties of sequential data. Because signatures embed observati…
Hedging option books using neural-SDE market models
Samuel N. Cohen, Christoph Reisinger, Sheng Wang
We study the capability of arbitrage-free neural-SDE market models to yield effective strategies for hedging options. In particular, we derive sensitivity-based and minimum-varianc…