This study investigates the generalization capabilities and robustness of purely deep learning (DL) models and hybrid models based on physical principles in fluid dynamics applications, specifically focusing on iteratively forecasting the temporal evolution of flow dynamics. Three autoregressive models were compared: a hybrid model (POD-DL) that combines proper orthogonal decomposition (POD) with a long short-term memory (LSTM) layer, a convolutional autoencoder combined with a convolutional LSTM (ConvLSTM) layer and a variational autoencoder (VAE) combined with a ConvLSTM layer. These models were tested on two high-dimensional, nonlinear datasets representing the velocity field of flow past a circular cylinder in both laminar and turbulent regimes. The study used latent dimension methods, enabling a bijective reduction of high-dimensional dynamics into a lower-order space to facilitate future predictions. While the VAE and ConvLSTM models accurately predicted laminar flow, the hybrid POD-DL model outperformed the others across both laminar and turbulent flow regimes. This success is attributed to the model's ability to incorporate modal decomposition, reducing the dimensionality of the data, by a non-parametric method, and simplifying the forecasting component. By leveraging POD, the model not only gained insight into the underlying physics, improving prediction accuracy with less training data, but also reduce the number of trainable parameters as POD is non-parametric. The findings emphasize the potential of hybrid models, particularly those integrating modal decomposition and deep learning, in predicting complex flow dynamics.

In this work, we thoroughly examine the main dynamics of a two-phase mixing layer formed by the interaction of two parallel planar jets. Using data-driven modal decomposition techniques applied to a direct numerical simulation database, the coherent structures governing the flow dynamics are identified. This study provides a novel and comprehensive characterization of the associated phenomena to the best of the authors' knowledge. The studied problem exhibits two main dynamics: interfacial wave propagation and flapping events associated with the emergence of small-scale interfacial structures linked to atomization. These two dynamics have been individually isolated and characterized. The coherent structures that govern the flow's dynamics are identified by means of higher order dynamic mode decomposition and spatiotemporal Koopman decomposition. Two characteristic modes of this problem dominate the dynamics of the system. The propagation of the interfacial wave is characterized by a wave packet, while flapping events result from the interaction of structures which move in the spanwise direction and others which are spanwise-stationary. Additionally, the analysis reveals the presence of other modes, arising from the nonlinear interaction between these two fundamental dynamics. The identification and characterization of these modes deepen our understanding of the underlying physics and also offer potential avenues for flow control.

Accurate modeling of the complex dynamics of fluid flows is a fundamental challenge in computational physics and engineering. This study integrates High-Order Singular Value Decomposition (HOSVD) with Long Short-Term Memory (LSTM) architectures to address the complexities of hybrid reduced-order modeling in fluid dynamics. The methodology is tested across numerical and experimental datasets, including two- and three-dimensional (2D and 3D) cylinder wake flows, spanning both laminar and turbulent regimes. The emphasis is also on exploring how the depth and complexity of LSTM architectures contribute to improving predictive performance. For simple laminar flows, architectures with a single dense layer effectively capture the periodic dynamics, demonstrating the network's ability to model non-linearities and complex dynamics. For the other cases, the addition of extra layers provides higher accuracy at minimal computational cost. Other results demonstrate that HOSVD shows improved accuracy, particularly in more complex cases, such as the 3D cylinder and experimental datasets, while differences remain modest for simpler flows. Efficient mode truncation by HOSVD-based models enables the capture of complex temporal patterns, leading to reliable predictions even in noisy datasets.

This thesis focuses on the development of reduced-order models that combine modal decomposition techniques with deep learning (DL) architectures to predict the dynamics of fluid systems at different Reynolds numbers. The use of artificial intelligence (AI)-based models to model physical systems represents a currently active field in the academic community with broad industrial applications. The motivation for studying these models is based on two main advantages: their highly nonlinear capacity to identify complex patterns within structured and unstructured datasets, and their low computational cost for inferring predictions after training. These characteristics are particularly attractive to the fluid mechanics community, which studies highly complex flows defined by multiple coherent structures at different spatio-temporal scales, difficult to capture and computationally expensive, with numerical simulation being unfeasible in some cases. However, these models require a rich and varied dataset for training, whose acquisition constitutes the main obstacle in fluid dynamics, where accurate data can only be obtained through computationally expensive numerical simulations or experiments with high monetary cost. Furthermore, each sample has a high spatial dimensionality, requiring complex DL architectures. To address these challenges, a hybrid methodology that combines modal decomposition with DL architectures was studied, where modal decomposition reduces the dimensionality of the samples, allowing the use of simpler architectures and reduced datasets, consuming fewer computational resources for training than purely DL-based models. Since AI-based models tend to generate predictions that rapidly diverge from the target dynamics, an adaptive methodology was developed that leverages the advantages of the hybrid model. This allows initial training on high-fidelity numerical simulation data, obtained using reliable but expensive classical numerical methods, to predict the temporal evolution up to a certain point, and then simulate numerically again to retrain the model with new information, continuously updating it with fresh data about the flow dynamics. Finally, a generative AI model was studied that, contrary to the hybrid model, captures the small-scale structures characteristic of turbulent flow dynamics. This model also uses dimensional reduction techniques to train on a simplified representation, requiring more data than the hybrid model but less than similar DL models. The results demonstrate that AI-based models can be widely applied in fluid dynamics problems, allowing prediction of the temporal evolution of flows without the high computational cost of current numerical simulation techniques, offering an efficient alternative for predictive modeling of complex fluid systems. RESUMEN Esta tesis se centra en el desarrollo de modelos de orden reducido que combinan técnicas de descomposición modal con arquitecturas de deep learning (DL) para predecir la dinámica de sistemas fluidos a distintos números de Reynolds. El uso de modelos basados en inteligencia artificial (IA) para modelizar sistemas físicos representa un campo actualmente activo en la comunidad académica con amplias aplicaciones industriales. La motivación para estudiar estos modelos se fundamenta en dos ventajas principales: su capacidad altamente no lineal para identificar patrones complejos dentro de bases de datos estructuradas y no estructuradas, y su bajo coste computacional para inferir predicciones tras el entrenamiento. Estas características resultan especialmente atractivas para la comunidad de mecánica de fluidos, que estudia flujos altamente complejos definidos por múltiples estructuras coherentes a distintas escalas espaciotemporales, difíciles de capturar y computacionalmente costosos, siendo en algunos casos inviable una simulación numérica. Sin embargo, estos modelos requieren de una rica y variada base de datos para su entrenamiento, cuya obtención constituye el principal obstáculo en mecánica de fluidos. Los datos precisos solo se consiguen mediante simulaciones numéricas computacionalmente costosas o experimentos con alto coste monetario. Además, cada muestra tiene una alta dimensión espacial, necesitando arquitecturas de DL complejas. Para abordar estos desafíos, se estudió una metodología híbrida que combina descomposición modal con arquitecturas de DL. La descomposición modal reduce la dimensionalidad de las muestras, permitiendo usar arquitecturas más simples y bases de datos reducidas, consumiendo menos recursos computacionales para su entrenamiento que modelos puramente basados en DL. Dado que los modelos basados en IA suelen generar predicciones que divergen rápidamente de la dinámica objetivo, se desarrolló una metodología adaptativa que aprovecha las ventajas del modelo híbrido. Esta permite entrenar inicialmente sobre datos de simulación numérica, usando métodos clásicos fiables pero costosos, para predecir la evolución temporal hasta cierto punto, y luego volver a simular numéricamente para reentrenar el modelo con nueva información, actualizándolo continuamente con datos frescos sobre la dinámica del flujo. Finalmente, se estudió un modelo de IA generativa que, contrariamente al modelo híbrido, captura las escalas más pequeñas de la dinámica del flujo. Este modelo también utiliza técnicas de reducción dimensional para entrenar en una representación simplificada, requiriendo más datos que el modelo híbrido pero menos que modelos DL similares. Los resultados demuestran que los modelos basados en IA pueden aplicarse ampliamente en mecánica de fluidos, permitiendo predecir la evolución temporal de flujos sin el alto coste...