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AW-EL-PINNs: Una red neuronal informada por la física de aprendizaje multitarea para sistemas Euler-Lagrange en

Chuandong Li¹, Runtian Zeng¹

¹College of Electronic and Information Engineering, Southwest University, Chongqing, 400715, China.

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

|February 13, 2026

Resumen

Este resumen es generado por máquina.

Este estudio presenta las redes neuronales informadas por la física (PINN) combinadas con el teorema adaptativo ponderado de Euler-Lagrange (AW-EL-PINNs) para el control óptimo. Las AW-EL-PINNs mejoran la precisión y la estabilidad de la solución para sistemas Euler-Lagrange en comparación con los métodos tradicionales.

Palabras clave:

ponderación adaptativa de pérdidas teorema de Euler-Lagrange problemas de control óptimo redes neuronales informadas por la física problemas de valor de contorno de dos puntos

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Área de la Ciencia:

Matemáticas Computacionales
Aprendizaje Automático
Teoría del Control Óptimo

Sus antecedentes:

Los sistemas Euler-Lagrange son fundamentales en la mecánica clásica y el control óptimo.
La resolución de estos sistemas a menudo implica métodos numéricos complejos y ajuste manual de parámetros.
Las redes neuronales informadas por la física (PINN) existentes requieren un esfuerzo considerable para equilibrar las funciones de pérdida.

Objetivo del estudio:

Presentar un marco novedoso, las redes neuronales informadas por la física del teorema de Euler-Lagrange ponderado adaptativo (AW-EL-PINNs), para resolver sistemas de Euler-Lagrange en control óptimo.
Mejorar la eficiencia y la precisión de la resolución de problemas de control óptimo.
Reducir la necesidad de ajuste manual de los pesos de la función de pérdida en enfoques de aprendizaje profundo.

Principales métodos:

El marco propuesto AW-EL-PINNs integra el teorema de Euler-Lagrange con una arquitectura de aprendizaje profundo.
Los problemas de control óptimo se transforman sistemáticamente en problemas de valor de contorno de dos puntos (TPBVPs).
Un mecanismo adaptativo de ponderación de pérdidas equilibra dinámicamente los componentes de pérdida durante el entrenamiento, reduciendo la intervención manual.

Principales resultados:

Las AW-EL-PINNs demostraron una precisión de solución mejorada en cinco ejemplos numéricos.
El marco mantuvo la estabilidad durante todo el proceso de optimización.
El rendimiento fue superior a los métodos de referencia en términos de precisión y estabilidad.

Conclusiones:

Las AW-EL-PINNs ofrecen un método robusto y preciso para resolver sistemas de Euler-Lagrange en control óptimo.
El mecanismo adaptativo de ponderación de pérdidas mejora significativamente las PINN convencionales al reducir el ajuste manual.
Este marco es prometedor para aplicaciones en diversos sistemas físicos que requieren soluciones precisas de control óptimo.