Un Marco Teórico para la Evolución de Campos Cosmológicos con Operadores Neuronales Físicos y Aprendizaje Profundo Geométrico
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https://doi.org/10.65093/aci.v16.n4.2025.44Palabras clave:
cosmología, operadores neuronales, redes neuronales de grafos, materia oscuraResumen
los modelos cosmológicos estándar. Proponemos un marco teórico unificado que sintetiza seis paradigmas avanzados de aprendizaje automático para modelar la evolución de campos de materia oscura y la dinámica de la red cósmica. Este marco integra (1) Operadores Neuronales (NO) para aprender resolvedores de Ecuaciones Diferenciales Parciales (EDP) en el límite continuo, (2) Flujos Normalizadores (NF) para inferencia bayesiana basada en simulación con verosimilitudes exactas, (3) métodos topológicos y geométricos para caracterizar la estructura de la red cósmica, (4) teorías de campo efectivas (EFT) y coarse-graining para modelar la dinámica de la materia a múltiples escalas, (5) inferencia causal para desenredar efectos sistemáticos de la física subyacente, y (6) autoencoders geométricos para aprender representaciones latentes que preservan simetrías. Argumentamos que la hibridación de estos enfoques ofrece una ruta prometedora para construir emuladores cosmológicos de alta fidelidad, computacionalmente eficientes y físicamente consistentes, capaces de superar las limitaciones de los métodos actuales y explotar la riqueza de los datos de los próximos sondeos a gran escala.
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