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