LC-SVD-DLinear: A low-cost physics-based hybrid machine learning model for data forecasting using sparse measurements

This article introduces a novel methodology that integrates singular value decomposition (SVD) with a shallow linear neural network for forecasting high resolution fluid mechanics data. The method, termed LC-SVD-DLinear, combines a low-cost variant of singular value decomposition (LC-SVD) with the DLinear architecture, which decomposes the input features-specifically, the temporal coefficients-into trend and seasonality components, enabling a shallow neural network to capture the non-linear dynamics of the temporal data. This methodology uses under-resolved data, which can either be input directly into the hybrid model or downsampled from high resolution using two distinct techniques provided by the methodology. Working with under-resolved cases helps reduce the overall computational cost. Additionally, we present a variant of the method, LC-HOSVD-DLinear, which combines a low-cost version of the high-order singular value decomposition (LC-HOSVD) algorithm with the DLinear network, designed for high-order data. These approaches have been validated using two datasets: first, a numerical simulation of three-dimensional flow past a circular cylinder at $Re = 220$; and second, an experimental dataset of turbulent flow passing a circular cylinder at $Re = 2600$. The combination of these datasets demonstrates the robustness of the method. The forecasting and reconstruction results are evaluated through various error metrics, including uncertainty quantification. The work developed in this article will be included in the next release of ModelFLOWs-app

EigenHearts: Cardiac Diseases Classification Using EigenFaces Approach

In the realm of cardiovascular medicine, medical imaging plays a crucial role in accurately classifying cardiac diseases and making precise diagnoses. However, the field faces significant challenges when integrating data science techniques, as a significant volume of images is required for these techniques. As a consequence, it is necessary to investigate different avenues to overcome this challenge. In this contribution, we offer an innovative tool to conquer this limitation. In particular, we delve into the application of a well recognized method known as the EigenFaces approach to classify cardiac diseases. This approach was originally motivated for efficiently representing pictures of faces using principal component analysis, which provides a set of eigenvectors (aka eigenfaces), explaining the variation between face images. As this approach proven to be efficient for face recognition, it motivated us to explore its efficiency on more complicated data bases. In particular, we integrate this approach, with convolutional neural networks (CNNs) to classify echocardiography images taken from mice in five distinct cardiac conditions (healthy, diabetic cardiomyopathy, myocardial infarction, obesity and TAC hypertension). Performing a preprocessing step inspired from the eigenfaces approach on the echocardiography datasets, yields sets of pod modes, which we will call eigenhearts. To demonstrate the proposed approach, we compare two testcases: (i) supplying the CNN with the original images directly, (ii) supplying the CNN with images projected into the obtained pod modes. The results show a substantial and noteworthy enhancement when employing SVD for pre-processing, with classification accuracy increasing by approximately 50%.

A Novel Data Augmentation Tool for Enhancing Machine Learning Classification: A New Application of the Higher Order Dynamic Mode Decomposition for Improved Cardiac Disease Identification

In this work, a data-driven, modal decomposition method, the higher order dynamic mode decomposition (HODMD), is combined with a convolutional neural network (CNN) in order to improve the classification accuracy of several cardiac diseases using echocardiography images. The HODMD algorithm is used first as feature extraction technique for the echocardiography datasets, taken from both healthy mice and mice afflicted by different cardiac diseases (Diabetic Cardiomyopathy, Obesity, TAC Hypertrophy and Myocardial Infarction). A total number of 130 echocardiography datasets are used in this work. The dominant features related to each cardiac disease were identified and represented by the HODMD algorithm as a set of DMD modes, which then are used as the input to the CNN. In a way, the database dimension was augmented, hence HODMD has been used, for the first time to the authors knowledge, for data augmentation in the machine learning framework. Six sets of the original echocardiography databases were hold out to be used as unseen data to test the performance of the CNN. In order to demonstrate the efficiency of the HODMD technique, two testcases are studied: the CNN is first trained using the original echocardiography images only, and second training the CNN using a combination of the original images and the DMD modes. The classification performance of the designed trained CNN shows that combining the original images with the DMD modes improves the results in all the testcases, as it improves the accuracy by up to 22%. These results show the great potential of using the HODMD algorithm as a data augmentation technique.

Intercepting Unauthorized Aerial Robots in Controlled Airspace Using Reinforcement Learning

The proliferation of unmanned aerial vehicles (UAVs) in controlled airspace presents significant risks, including potential collisions, disruptions to air traffic, and security threats. Ensuring the safe and efficient operation of airspace, particularly in urban environments and near critical infrastructure, necessitates effective methods to intercept unauthorized or non-cooperative UAVs. This work addresses the critical need for robust, adaptive systems capable of managing such threats through the use of Reinforcement Learning (RL). We present a novel approach utilizing RL to train fixed-wing UAV pursuer agents for intercepting dynamic evader targets. Our methodology explores both model-based and model-free RL algorithms, specifically DreamerV3, Truncated Quantile Critics (TQC), and Soft Actor-Critic (SAC). The training and evaluation of these algorithms were conducted under diverse scenarios, including unseen evasion strategies and environmental perturbations. Our approach leverages high-fidelity flight dynamics simulations to create realistic training environments. This research underscores the importance of developing intelligent, adaptive control systems for UAV interception, significantly contributing to the advancement of secure and efficient airspace management. It demonstrates the potential of RL to train systems capable of autonomously achieving these critical tasks.

Automatic Cardiac Pathology Recognition in Echocardiography Images Using Higher Order Dynamic Mode Decomposition and a Vision Transformer for Small Datasets

Heart diseases are the main international cause of human defunction. According to the WHO, nearly 18 million people decease each year because of heart diseases. Also considering the increase of medical data, much pressure is put on the health industry to develop systems for early and accurate heart disease recognition. In this work, an automatic cardiac pathology recognition system based on a novel deep learning framework is proposed, which analyses in real-time echocardiography video sequences. The system works in two stages. The first one transforms the data included in a database of echocardiography sequences into a machine-learning-compatible collection of annotated images which can be used in the training stage of any kind of machine learning-based framework, and more specifically with deep learning. This includes the use of the Higher Order Dynamic Mode Decomposition (HODMD) algorithm, for the first time to the authors' knowledge, for both data augmentation and feature extraction in the medical field. The second stage is focused on building and training a Vision Transformer (ViT), barely explored in the related literature. The ViT is adapted for an effective training from scratch, even with small datasets. The designed neural network analyses images from an echocardiography sequence to predict the heart state. The results obtained show the superiority of the proposed system and the efficacy of the HODMD algorithm, even outperforming pretrained Convolutional Neural Networks (CNNs), which are so far the method of choice in the literature.

Exploring the efficacy of a hybrid approach with modal decomposition over fully deep learning models for flow dynamics forecasting

Fluid dynamics problems are characterized by being multidimensional and nonlinear, causing the experiments and numerical simulations being complex, time-consuming and monetarily expensive. In this sense, there is a need to find new ways to obtain data in a more economical manner. Thus, in this work we study the application of time series forecasting to fluid dynamics problems, where the aim is to predict the flow dynamics using only past information. We focus our study on models based on deep learning that do not require a high amount of data for training, as this is the problem we are trying to address. Specifically in this work we have tested three autoregressive models where two of them are fully based on deep learning and the other one is a hybrid model that combines modal decomposition with deep learning. We ask these models to generate $200$ time-ahead predictions of two datasets coming from a numerical simulation and experimental measurements, where the latter is characterized by being turbulent. We show how the hybrid model generates more reliable predictions in the experimental case, as it is physics-informed in the sense that the modal decomposition extracts the physics in a way that allows us to predict it.

A predictive physics-aware hybrid reduced order model for reacting flows

In this work, a new hybrid predictive Reduced Order Model (ROM) is proposed to solve reacting flow problems. This algorithm is based on a dimensionality reduction using Proper Orthogonal Decomposition (POD) combined with deep learning architectures. The number of degrees of freedom is reduced from thousands of temporal points to a few POD modes with their corresponding temporal coefficients. Two different deep learning architectures have been tested to predict the temporal coefficients, based on recursive (RNN) and convolutional (CNN) neural networks. From each architecture, different models have been created to understand the behavior of each parameter of the neural network. Results show that these architectures are able to predict the temporal coefficients of the POD modes, as well as the whole snapshots. The RNN shows lower prediction error for all the variables analyzed. The model was also found capable of predicting more complex simulations showing transfer learning capabilities.

Forecasting through deep learning and modal decomposition in multi-phase concentric jets

This work presents a set of neural network (NN) models specifically designed for accurate and efficient fluid dynamics forecasting. In this work, we show how neural networks training can be improved by reducing data complexity through a modal decomposition technique called higher order dynamic mode decomposition (HODMD), which identifies the main structures inside flow dynamics and reconstructs the original flow using only these main structures. This reconstruction has the same number of samples and spatial dimension as the original flow, but with a less complex dynamics and preserving its main features. We also show the low computational cost required by the proposed NN models, both in their training and inference phases. The core idea of this work is to test the limits of applicability of deep learning models to data forecasting in complex fluid dynamics problems. Generalization capabilities of the models are demonstrated by using the same neural network architectures to forecast the future dynamics of four different multi-phase flows. Data sets used to train and test these deep learning models come from Direct Numerical Simulations (DNS) of these flows.

A Novel Data-Driven Method for the Analysis and Reconstruction of Cardiac Cine MRI

Cardiac cine magnetic resonance imaging (MRI) can be considered the optimal criterion for measuring cardiac function. This imaging technique can provide us with detailed information about cardiac structure, tissue composition and even blood flow. This work considers the application of the higher order dynamic mode decomposition (HODMD) method to a set of MR images of a heart, with the ultimate goal of identifying the main patterns and frequencies driving the heart dynamics. A novel algorithm based on singular value decomposition combined with HODMD is introduced, providing a three-dimensional reconstruction of the heart. This algorithm is applied (i) to reconstruct corrupted or missing images, and (ii) to build a reduced order model of the heart dynamics.

Higher Order Dynamic Mode Decomposition: from Fluid Dynamics to Heart Disease Analysis

In this work, we study in detail the performance of Higher Order Dynamic Mode Decomposition (HODMD) technique when applied to echocardiography images. HODMD is a data-driven method generally used in fluid dynamics and in the analysis of complex non-linear dynamical systems modeling several complex industrial applications. In this paper we apply HODMD, for the first time to the authors knowledge, for patterns recognition in echocardiography, specifically, echocardiography data taken from several mice, either in healthy conditions or afflicted by different cardiac diseases. We exploit the HODMD advantageous properties in dynamics identification and noise cleaning to identify the relevant frequencies and coherent patterns for each one of the diseases. The echocardiography datasets consist of video loops taken with respect to a long axis view (LAX) and a short axis view (SAX), where each video loop covers at least three cardiac cycles, formed by (at most) 300 frames each (called snapshots). The proposed algorithm, using only a maximum quantity of 200 snapshots, was able to capture two branches of frequencies, representing the heart rate and respiratory rate. Additionally, the algorithm provided a number of modes, which represent the dominant features and patterns in the different echocardiography images, also related to the heart and the lung. Six datasets were analyzed: one echocardiography taken from a healthy subject and five different sets of echocardiography taken from subjects with either Diabetic Cardiomyopathy, Obesity, SFSR4 Hypertrophy, TAC Hypertrophy or Myocardial Infarction. The results show that HODMD is robust and a suitable tool to identify characteristic patterns able to classify the different pathologies studied.