4 papers
THINNs: Thermodynamically Informed Neural Networks
Javier Castro, Benjamin Gess
Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equ…
The Calderón's problem via DeepONets
Javier Castro, Claudio Muñoz, Nicolás Valenzuela
We consider the Dirichlet-to-Neumann operator and the direct and inverse Calderón's mappings appearing in the Inverse Problem of recovering a smooth bounded and positive isotropic…
The Kolmogorov Infinite Dimensional Equation in a Hilbert space Via Deep Learning Methods
Javier Castro
We consider the nonlinear Kolmogorov equation posed in a Hilbert space , not necessarily of finite dimension. This model was recently studied by Cox et al. [24] in the framework…
Deep Learning Schemes For Parabolic Nonlocal Integro-Differential Equations
Javier Castro
In this paper we consider the numerical approximation of nonlocal integro differential parabolic equations via neural networks. These equations appear in many recent applications,…