The Effect of Different Optimization Strategies to Physics-Constrained Deep Learning for Soil Moisture Estimation

Soil moisture is a key hydrological parameter that has significant importance to human society and the environment. Accurate modeling and monitoring of soil moisture in crop fields, especially in the root zone (top 100 cm of soil), is essential for improving agricultural production and crop yield with the help of precision irrigation and farming tools. Realizing the full sensor data potential depends greatly on advanced analytical and predictive domain-aware models. In this work, we propose a physics-constrained deep learning (P-DL) framework to integrate physics-based principles on water transport and water sensing signals for effective reconstruction of the soil moisture dynamics. We adopt three different optimizers, namely Adam, RMSprop, and GD, to minimize the loss function of P-DL during the training process. In the illustrative case study, we demonstrate the empirical convergence of Adam optimizers outperforms the other optimization methods in both mini-batch and full-batch training.

Physics-constrained Active Learning for Soil Moisture Estimation and Optimal Sensor Placement

Soil moisture is a crucial hydrological state variable that has significant importance to the global environment and agriculture. Precise monitoring of soil moisture in crop fields is critical to reducing agricultural drought and improving crop yield. In-situ soil moisture sensors, which are buried at pre-determined depths and distributed across the field, are promising solutions for monitoring soil moisture. However, high-density sensor deployment is neither economically feasible nor practical. Thus, to achieve a higher spatial resolution of soil moisture dynamics using a limited number of sensors, we integrate a physics-based agro-hydrological model based on Richards' equation in a physics-constrained deep learning framework to accurately predict soil moisture dynamics in the soil's root zone. This approach ensures that soil moisture estimates align well with sensor observations while obeying physical laws at the same time. Furthermore, to strategically identify the locations for sensor placement, we introduce a novel active learning framework that combines space-filling design and physics residual-based sampling to maximize data acquisition potential with limited sensors. Our numerical results demonstrate that integrating Physics-constrained Deep Learning (P-DL) with an active learning strategy within a unified framework--named the Physics-constrained Active Learning (P-DAL) framework--significantly improves the predictive accuracy and effectiveness of field-scale soil moisture monitoring using in-situ sensors.

Automated Identication of Atrial Fibrillation from Single-lead ECGs Using Multi-branching ResNet

Atrial fibrillation (AF) is the most common cardiac arrhythmia, which is clinically identified with irregular and rapid heartbeat rhythm. AF puts a patient at risk of forming blood clots, which can eventually lead to heart failure, stroke, or even sudden death. It is of critical importance to develop an advanced analytical model that can effectively interpret the electrocardiography (ECG) signals and provide decision support for accurate AF diagnostics. In this paper, we propose an innovative deep-learning method for automated AF identification from single-lead ECGs. We first engage the continuous wavelet transform (CWT) to extract time-frequency features from ECG signals. Then, we develop a convolutional neural network (CNN) structure that incorporates ResNet for effective network training and multi-branching architectures for addressing the imbalanced data issue to process the 2D time-frequency features for AF classification. We evaluate the proposed methodology using two real-world ECG databases. The experimental results show a superior performance of our method compared with traditional deep learning models.

Hierarchical Deep Learning with Generative Adversarial Network for Automatic Cardiac Diagnosis from ECG Signals

Cardiac disease is the leading cause of death in the US. Accurate heart disease detection is of critical importance for timely medical treatment to save patients' lives. Routine use of electrocardiogram (ECG) is the most common method for physicians to assess the electrical activities of the heart and detect possible abnormal cardiac conditions. Fully utilizing the ECG data for reliable heart disease detection depends on developing effective analytical models. In this paper, we propose a two-level hierarchical deep learning framework with Generative Adversarial Network (GAN) for automatic diagnosis of ECG signals. The first-level model is composed of a Memory-Augmented Deep auto-Encoder with GAN (MadeGAN), which aims to differentiate abnormal signals from normal ECGs for anomaly detection. The second-level learning aims at robust multi-class classification for different arrhythmias identification, which is achieved by integrating the transfer learning technique to transfer knowledge from the first-level learning with the multi-branching architecture to handle the data-lacking and imbalanced data issue. We evaluate the performance of the proposed framework using real-world medical data from the MIT-BIH arrhythmia database. Experimental results show that our proposed model outperforms existing methods that are commonly used in current practice.

Physics-constrained Deep Learning for Robust Inverse ECG Modeling

The rapid developments in advanced sensing and imaging bring about a data-rich environment, facilitating the effective modeling, monitoring, and control of complex systems. For example, the body-sensor network captures multi-channel information pertinent to the electrical activity of the heart (i.e., electrocardiograms (ECG)), which enables medical scientists to monitor and detect abnormal cardiac conditions. However, the high-dimensional sensing data are generally complexly structured and realizing the full data potential depends to a great extent on advanced analytical and predictive methods. This paper presents a physics-constrained deep learning (P-DL) framework for high-dimensional inverse ECG modeling. This method integrates the physical laws of the complex system with the advanced deep learning infrastructure for effective prediction of the system dynamics. The proposed P-DL approach is implemented to solve the inverse ECG model and predict the time-varying distribution of electric potentials in the heart from the ECG data measured by the body-surface sensor network. Experimental results show that the proposed P-DL method significantly outperforms existing methods that are commonly used in current practice.