Facultad de Ciencias, Tuxtla Gutiérrez, Chiapas, UNACH, marzo, 2026 Saúl Diaz Infante Velasco
Modeling transition
ODE → SDE
https://slides.com/sauldiazinfantevelasco/sefc-unach-2026
Two of the main approches:
Solving With PINNs
Strengths of Classical Methods
✔ Well-understood theory
✔ Convergence analysis
✔ Efficient for low-dimensional problems
Limitations
✖ Curse of dimensionality
✖ Requires time discretization
✖ Difficult for high-dimensional PDE connections
Deterministic PINNs Idea
For ODE:
Minimize residual:
\mathcal{L} =
\left \|
\dfrac{d}{dt} \widehat{x}(t)
-
f(\widehat(x)(t), t)
\right\|^2
Feature Finite Diff. PINNs
| Theory | Strong | Developing |
| Interpretability | High | Moderate |
| High dimension | Hard | Better |
| Data integration | Limited | Natural |
| Stability guarantees | Yes | Often unclear |
Gracias!
https://slides.com/sauldiazinfantevelasco/sefc-unach-2026
Seminario de estudiante Facultad de Ciencias UNACH, Marzo 2026
By Saul Diaz Infante Velasco
