Research

Research

• Graph neural networks

• Model-based deep learning

• Numerics-informed neural networks

• Reduced order models

• Parareal time integrators based AI

• Inverse problems

Publications

Celaya, Kirk, Fuentes, Riviere. ''Solutions to elliptic and parabolic problems via finite difference based unsupervised small linear convolutional neural networs'', Computers and Mathematics with Applications, 174, 31-42, 2024, doi 

Cangelosi, Heinkenschloss. "Sensitivity of ODE solutions with respect to component functions in the dynamics", arXiv:2411.09655, 2024.

Cox, Segarra, Elvira. "Learning state and proposal dynamics in state-space models using differentiable particle filters and neural networks", arXiv:2411.15638, 2024.

Li, Verma, Efimov, Kumar, Segarra. "GLANCE: graph-based learnable digital twin for communication networks", arXiv:2408.09040, 2024.

Celaya, Wang, Fuentes, Riviere. "Learning discontinuous Galerkin solutions to elliptic problems via small linear convolutional neural networks", arXiv:2502.08783, 2025.

Ding, Ren, Zhang. "Coupling deep learning with full waveform inversion", submitted, 2025.

Celaya, Fuentes, Riviere. "An adaptive collocation point strategy for physics informed neural networks via the QR discrete empirical interpolation method", arXiv:2501.07700, 2025.