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VENI, VINDy, VICI: Un marco generativo de orden reducido con cuantificación de la incertidumbre

Paolo Conti¹, Jonas Kneifl², Andrea Manzoni¹

¹MOX - Department of Mathematics, Politecnico di Milano, Milan, Italy.

Neural networks : the official journal of the International Neural Network Society

|January 18, 2026

Resumen

Presentamos un nuevo marco para modelos generativos que garantiza la coherencia física en las predicciones científicas. Este enfoque integra métodos basados en datos con modelado probabilístico para modelos de orden reducido precisos y conscientes de la incertidumbre.

Área de la Ciencia:

Ciencia Computacional
Aprendizaje Automático Informado por la Física
Modelado Basado en Datos

Sus antecedentes:

Los modelos generativos ofrecen una exploración eficiente de escenarios, pero a menudo carecen de coherencia física.
La ciencia computacional se basa en la coherencia física para obtener predicciones fiables.
Los modelos existentes luchan por equilibrar los conocimientos basados en datos con las leyes físicas.

Objetivo del estudio:

Desarrollar un marco generativo físico novedoso para crear modelos de orden reducido físicamente consistentes.
Integrar la identificación de sistemas basada en datos con el modelado probabilístico para la cuantificación de la incertidumbre.
Mejorar la toma de decisiones en fenómenos físicos complejos garantizando la fiabilidad del modelo.

Principales métodos:

VENI (Codificación Variacional de Entradas Ruidosas): Utiliza autoencoders variacionales para identificar coordenadas reducidas a partir de datos ruidosos y de alta dimensión.
VINDy (Identificación Variacional de Dinámicas No Lineales): Extiende la identificación de sistemas dispersos con modelado probabilístico para descubrir la dinámica del sistema.
VICI (Inferencia Variacional con Intervalos de Credibilidad): Permite la generación eficiente de soluciones de tiempo completo y proporciona cuantificación de la incertidumbre.

Principales resultados:

El marco propuesto construye con éxito modelos de orden reducido físicamente consistentes.
Demostró una cuantificación eficaz de la incertidumbre para parámetros y condiciones iniciales no vistos.
Validó el rendimiento en diversos sistemas, incluida la dinámica no lineal caótica y de alta dimensión.

Conclusiones:

El marco VENI, VINDy, VICI ofrece una solución robusta para la modelización generativa físicamente consistente.
Este enfoque mejora la fiabilidad y aplicabilidad de los modelos generativos en la ciencia y la ingeniería.
Abre el camino para una exploración computacional más confiable y eficiente de sistemas físicos complejos.

Palabras clave:

Métodos basados en datos IA generativa Dinámica no lineal Modelado de orden reducido Identificación de sistemas dispersos Autoencoders variacionales

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