Mohammadamin Moradi

Mohammadamin Moradi, Shirin Panahi, Erik M. Bollt et al.

Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of elementary mathematical terms. Examples where sparse optimization fails abound, such as the classic Ikeda or optical-cavity map in nonlinear dynamics and a large variety of ecosystems. Exploiting the recently articulated Kolmogorov-Arnold networks, we develop a general model-discovery framework for any dynamical systems including those that do not satisfy the sparsity condition. In particular, we demonstrate non-uniqueness in that a large number of approximate models of the system can be found which generate the same invariant set with the correct statistics such as the Lyapunov exponents and Kullback-Leibler divergence. An analogy to shadowing of numerical trajectories in chaotic systems is pointed out.

Zheng-Meng Zhai, Mohammadamin Moradi, Ling-Wei Kong et al.

Nonlinear tracking control enabling a dynamical system to track a desired trajectory is fundamental to robotics, serving a wide range of civil and defense applications. In control engineering, designing tracking control requires complete knowledge of the system model and equations. We develop a model-free, machine-learning framework to control a two-arm robotic manipulator using only partially observed states, where the controller is realized by reservoir computing. Stochastic input is exploited for training, which consists of the observed partial state vector as the first and its immediate future as the second component so that the neural machine regards the latter as the future state of the former. In the testing (deployment) phase, the immediate-future component is replaced by the desired observational vector from the reference trajectory. We demonstrate the effectiveness of the control framework using a variety of periodic and chaotic signals, and establish its robustness against measurement noise, disturbances, and uncertainties.

Zheng-Meng Zhai, Mohammadamin Moradi, Bryan Glaz et al.

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state observation of the underlying system and tacitly assume adiabatic changes in the parameter. Formulating an inverse problem and exploiting reservoir computing, we develop a model-free and fully data-driven framework to accurately track time-varying parameters from partial state observation in real time. In particular, with training data from a subset of the dynamical variables of the system for a small number of known parameter values, the framework is able to accurately predict the parameter variations in time. Low- and high-dimensional, Markovian and non-Markovian nonlinear dynamical systems are used to demonstrate the power of the machine-learning based parameter-tracking framework. Pertinent issues affecting the tracking performance are addressed.

Mohammadamin Moradi, Zheng-Meng Zhai, Aaron Nielsen et al.

It was recently demonstrated that two machine-learning architectures, reservoir computing and time-delayed feed-forward neural networks, can be exploited for detecting the Earth's anomaly magnetic field immersed in overwhelming complex signals for magnetic navigation in a GPS-denied environment. The accuracy of the detected anomaly field corresponds to a positioning accuracy in the range of 10 to 40 meters. To increase the accuracy and reduce the uncertainty of weak signal detection as well as to directly obtain the position information, we exploit the machine-learning model of random forests that combines the output of multiple decision trees to give optimal values of the physical quantities of interest. In particular, from time-series data gathered from the cockpit of a flying airplane during various maneuvering stages, where strong background complex signals are caused by other elements of the Earth's magnetic field and the fields produced by the electronic systems in the cockpit, we demonstrate that the random-forest algorithm performs remarkably well in detecting the weak anomaly field and in filtering the position of the aircraft. With the aid of the conventional inertial navigation system, the positioning error can be reduced to less than 10 meters. We also find that, contrary to the conventional wisdom, the classic Tolles-Lawson model for calibrating and removing the magnetic field generated by the body of the aircraft is not necessary and may even be detrimental for the success of the random-forest method.

Mohammadamin Moradi, Runyu Jiang, Yingzi Liu et al.

High-dose-rate (HDR) brachytherapy plays a critical role in the treatment of locally advanced cervical cancer but remains highly dependent on manual treatment planning expertise. The objective of this study is to develop a fully automated HDR brachytherapy planning framework that integrates reinforcement learning (RL) and dose-based optimization to generate clinically acceptable treatment plans with improved consistency and efficiency. We propose a hierarchical two-stage autoplanning framework. In the first stage, a deep Q-network (DQN)-based RL agent iteratively selects treatment planning parameters (TPPs), which control the trade-offs between target coverage and organ-at-risk (OAR) sparing. The agent's state representation includes both dose-volume histogram (DVH) metrics and current TPP values, while its reward function incorporates clinical dose objectives and safety constraints, including D90, V150, V200 for targets, and D2cc for all relevant OARs (bladder, rectum, sigmoid, small bowel, and large bowel). In the second stage, a customized Adam-based optimizer computes the corresponding dwell time distribution for the selected TPPs using a clinically informed loss function. The framework was evaluated on a cohort of patients with complex applicator geometries. The proposed framework successfully learned clinically meaningful TPP adjustments across diverse patient anatomies. For the unseen test patients, the RL-based automated planning method achieved an average score of 93.89%, outperforming the clinical plans which averaged 91.86%. These findings are notable given that score improvements were achieved while maintaining full target coverage and reducing CTV hot spots in most cases.

Shirin Panahi, Ling-Wei Kong, Mohammadamin Moradi et al.

Anticipating a tipping point, a transition from one stable steady state to another, is a problem of broad relevance due to the ubiquity of the phenomenon in diverse fields. The steady-state nature of the dynamics about a tipping point makes its prediction significantly more challenging than predicting other types of critical transitions from oscillatory or chaotic dynamics. Exploiting the benefits of noise, we develop a general data-driven and machine-learning approach to predicting potential future tipping in nonautonomous dynamical systems and validate the framework using examples from different fields. As an application, we address the problem of predicting the potential collapse of the Atlantic Meridional Overturning Circulation (AMOC), possibly driven by climate-induced changes in the freshwater input to the North Atlantic. Our predictions based on synthetic and currently available empirical data place a potential collapse window spanning from 2040 to 2065, in consistency with the results in the current literature.