Publications and highlights associated with Javier Castro.
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 equation. Focusing on non-equilibrium fluctuating systems, we propose a physically informed choice of penalization that…
Published · Vietnam Journal of Mathematics 52, 775–806 (2024). 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 conductivity of a material filling a smooth…
We consider the nonlinear Kolmogorov equation posed in a Hilbert space $H$, not necessarily of finite dimension. This model was recently studied by Cox et al. [24] in the framework of weak convergence rates of stochastic wave models. Here, we…
Published · Partial Differential Equations and Applications 3 (2022). In this paper we consider the numerical approximation of nonlocal integro differential parabolic equations via neural networks. These equations appear in many recent applications, including finance, biology and others, and have been…
