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cs.LG2025
Convergence, design and training of continuous-time dropout as a random batch method
Antonio Álvarez-López, Martín Hernández
We study continuous-time dropout in controlled differential equations. We introduce a random-batch approximation of additive vector fields. On each time interval of length , a r…
math.NA2025
Random domain decomposition for parabolic PDEs on graphs
Martín Hernández
The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require consider…
math.NA2025
Random Batch Methods for Discretized PDEs on Graphs
Martin Hernandez, Martín Hernández, Enrique Zuazua
Diffusion and transport processes on networks arise in applications such as pipeline systems, traffic and information flow, and energy and thermal networks. In these settings the d…