Learning image derived PDE-phenotypes from fMRI data.

This study explored various feature extraction methods for use in automated diagnosis of Attention-Deficit Hyperactivity Disorder (ADHD) from functional Magnetic Resonance Image (fMRI) data. Each participant's data consisted of a resting state fMRI scan as well as phenotypic data (age, gender, handedness, IQ, and site of scanning) from the ADHD-200 dataset. We used machine learning techniques to produce support vector machine (SVM) classifiers that attempted to differentiate between (1) all ADHD patients vs. healthy controls and (2) ADHD combined (ADHD-c) type vs. ADHD inattentive (ADHD-i) type vs. controls. In different tests, we used only the phenotypic data, only the imaging data, or else both the phenotypic and imaging data. For feature extraction on fMRI data, we tested the Fast Fourier Transform (FFT), different variants of Principal Component Analysis (PCA), and combinations of FFT and PCA. PCA variants included PCA over time (PCA-t), PCA over space and time (PCA-st), and kernelized PCA (kPCA-st). Baseline chance accuracy was 64.2% produced by guessing healthy control (the majority class) for all participants. Using only phenotypic data produced 72.9% accuracy on two class diagnosis and 66.8% on three class diagnosis. Diagnosis using only imaging data did not perform as well as phenotypic-only approaches. Using both phenotypic and imaging data with combined FFT and kPCA-st feature extraction yielded accuracies of 76.0% on two class diagnosis and 68.6% on three class diagnosis—better than phenotypic-only approaches. Our results demonstrate the potential of using FFT and kPCA-st with resting-state fMRI data as well as phenotypic data for automated diagnosis of ADHD. These results are encouraging given known challenges of learning ADHD diagnostic classifiers using the ADHD-200 dataset (see Brown et al., 2012).

Simultaneous digital twin identification and signal-noise decomposition through modified generalized sparse identification of nonlinear dynamics

Physics-informed genetic programming for discovery of partial differential equations from scarce and noisy data

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown and need to be estimated from the measurements of the dynamic system in the presence of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from long-range infrared light detection and ranging data. Supplementary materials for this article are available online.

Data-driven modeling has been widely utilized by industry and academia to model the dynamics of many chemical processes. In recent times, sparse identification of nonlinear dynamics (SINDy) is proving to be a promising data-driven modeling approach for identifying sparse and interpretable process models. An important application of developing a process model is to deploy it for real-time prediction purposes. However, a model trained offline is not sufficient to deal with process uncertainties, which are prevalent in chemical processes. This requires an adaptive modeling approach that is capable of identifying and predicting the nonlinear process dynamics on the fly by coping with process uncertainties. Motivated by this, an adaptive modeling framework called online adaptive sparse identification of systems (OASIS) is developed to extend the capabilities of SINDy for accurate and automatic approximation of process models. The OASIS method combines the goodness of SINDy and deep learning for modeling nonlinear process systems and predicting dynamics in real-time. First, SINDy is utilized to identify multiple local process models from historical process data recorded from varying operating conditions. Next, a deep neural network is built using the identified local SINDy models and their training data. The objective of training a deep neural network is to learn the functional relationship between SINDy coefficients and operating conditions, such that when the trained deep neural network is employed online, it will readily provide a suitable local SINDy model based on the current operating conditions. In this chapter, we describe the OASIS algorithm and discuss its implementation on three interesting applications: model predictive control of a continuous stirred tank reactor (CSTR), fault prediction of a polyethylene reactor, and the remaining lifetime estimation of a Li-ion battery.

The SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable challenge. In the present work, we extend a recently proposed model based on nearest-neighbor spatial interactions by one of the authors towards a nonlocal, nonlinear PDE variant of the SIR prototype. We then seek to develop a set of tools that provide insights for this PDE framework. Stationary states and their stability analysis offer a perspective on the early spatial growth of the infection. Evolutionary computational dynamics enable visualization of the spatio-temporal progression of infection and recovery, allowing for an appreciation of the effect of varying parameters of the nonlocal kernel, such as, e.g., its width parameter. These features are explored in both one- and two-dimensional settings. At a model-reduction level, we develop a sequence of interpretable moment-based diagnostics to observe how these reflect the total number of infections, the epidemic’s epicenter, and its spread. Finally, we propose a data-driven methodology based on the sparse identification of nonlinear dynamics (SINDy) to identify approximate closed-form dynamical equations for such quantities. These approaches may pave the way for further spatio-temporal studies, enabling the quantification of epidemics.

Experimental results have shown that anti-cancer therapies, such as radiotherapy and chemotherapy, can modulate the cell cycle and generate cell cycle phase-dependent responses. As a result, obtaining a detailed understanding of the cell cycle is one possible path towards improving the efficacy of many of these therapies. Here, we consider a basic structured partial differential equation (PDE) model for cell progression through the cell cycle, and derive expressions for key quantities, such as the population growth rate and cell phase proportions. These quantities are shown to be periodic and, as such, we compare the PDE model to a corresponding ordinary differential equation (ODE) model in which the parameters are linked by ensuring that the long-term ODE behaviour agrees with the average PDE behaviour. By design, we find that the ODE model does an excellent job of representing the mean dynamics of the PDE model within just a few cell cycles. However, by probing the parameter space we find cases in which this mean behaviour is not a good measure of the PDE population growth. Our analytical comparison of two caricature models (one PDE and one ODE system) provides insight into cases in which the simple ODE model is an appropriate approximation to the PDE model.

A crucial challenge encountered in diverse areas of engineering applications involves speculating the governing equations based upon partial observations. On this basis, a variant of the sparse identification of nonlinear dynamics (SINDy) algorithm is developed. First, the Akaike information criterion (AIC) is integrated to enforce model selection by hierarchically ranking the most informative model from several manageable candidate models. This integration avoids restricting the number of candidate models, which is a disadvantage of the traditional methods for model selection. The subsequent procedure expands the structure of dynamics from ordinary differential equations (ODEs) to partial differential equations (PDEs), while group sparsity is employed to identify the nonconstant coefficients of partial differential equations. Of practical consideration within an integrated frame is data processing, which tends to treat noise separate from signals and tends to parametrize the noise probability distribution. In particular, the coefficients of a species of canonical ODEs and PDEs, such as the Van der Pol, Rössler, Burgers’ and Kuramoto–Sivashinsky equations, can be identified correctly with the introduction of noise. Furthermore, except for normal noise, the proposed approach is able to capture the distribution of uniform noise. In accordance with the results of the experiments, the computational speed is markedly advanced and possesses robustness.

Neuroimaging-based diagnosis could help clinicians in making accurate diagnosis, accessing accurate prognosis, and deciding faster, more effective, and personalized treatment on an individual person basis. In this research work, we aim to develop a neuro-imaging, i.e. functional magnetic resonance imaging (fMRI), based method to detect attention deficit hyper-activity disorder (ADHD), which is a psychiatric disorder categorized by the impulsive nature, lack of attention, and hyper activeness. We utilized fMRI scans as well as personal characteristic features (PCF) data provided as part of ADHD-200 challenge. We aim to train a machine learning classifier by using fMRI and PCF data to classify each participant into one of the following three classes: healthy control (HC), combined-type ADHD (ADHD-C), or inattentive-type ADHD (ADHD-I). We used participants’ PCF and fMRI data separately, and then evaluated the combined use of both the datasets in detecting different classes. Support vector machine classifier with linear kernel was used for the training. The experiments were conducted under two different configurations: (i) 2-way configuration where classification was conducted between HC and ADHD (ADHD-C+ADHD-I) patients, and between ADHD-C and ADHD-I, and (ii) 3-way configuration where data of all the categories (HC, ADHD-C and ADHD-I) was combined together for classification. The 2-way classification approach achieved the diagnostic accuracy of 86.52% and 82.43% in distinguishing HC from ADHD patients, and ADHD-C and ADHD-I, respectively. The 3-way classification revealed classification success rate of 78.59% when both fMRI and PCF data were used together. These results demonstrate the importance of utilizing fMRI data and PCF for the detection of psychiatric disorders.

Attention deficit hyperactivity disorder (ADHD) is a neurological disorder that develops over time and is typified by impulsivity, hyperactivity, and attention deficiency. There have been noticeable changes in the patterns of brain activity in recent studies using functional magnetic resonance imaging (fMRI). Particularly in the prefrontal cortex. Machine learning algorithms show promise in distinguishing ADHD subtypes based on these neurobiological signatures. However, the inherent heterogeneity of ADHD complicates consistent classification, while small sample sizes limit the generalizability of findings. Additionally, methodological variability across studies contributes to inconsistent results, and the opaque nature of machine learning models hinders the understanding of underlying mechanisms. We suggest a novel deep learning architecture to overcome these issues by combining spatio-temporal feature extraction and classification through a hierarchical residual convolutional noise reduction autoencoder (HRCNRAE) and a 3D convolutional gated memory unit (GMU). This framework effectively reduces spatial dimensions, captures key temporal and spatial features, and utilizes a sigmoid classifier for robust binary classification. Our methodology was rigorously validated on the ADHD-200 dataset across five sites, demonstrating enhancements in diagnostic accuracy ranging from 1.26% to 9.6% compared to existing models. Importantly, this research represents the first application of a 3D Convolutional GMU for diagnosing ADHD with fMRI data. The improvements highlight the efficacy of our architecture in capturing complex spatio-temporal features, paving the way for more accurate and reliable ADHD diagnoses.

Objective To investigate the characteristics of brain function in children with attentiondeficit hyperactivity disorder(ADHD)in resting state using functional magnetic resonance imaging(fMRI).Methods Fifteen healty school children and 14 children with ADHD were experienced resting-state fMRI scans,A regional homogeneity (ReHo)approach was used to analyze blood oxygen level-dependent fMRI (BOLD-fMRI)data in resting state.The fMRI data were processed with software SPM2 and REST 1.2.Results Compared with controls.ADHD showed decreased ReHo in bilateral inferior parietal lobule (Z=3.73,Z=3.34),bilateral cuneus(Z=3.42,Z=3.86),left middle frontal gyrus(Z=3.24),left middle temporal gyrus(Z=3.24),left precuneus(Z=3.45),right insula(Z=3.09)and risht cerebellum (Z=3.42),and increased ReHo in the bilateral inferior frontal gyrus(Z=3.19,Z=2.93).Conclusion Compared with the normal controls,children with ADHD children may have abnormal neural activity in several brain regions which are related to execution control,attention and default mode network. Key words: Attention deficit disorder with hyperactivity; Magnetic resonance imaging; Resting state; Regional homogeneity

IntroductionThe moment quantities associated with the nonlinear Schrödinger equation offer important insights into the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment quantities are amenable to both analytical and numerical treatments.MethodsIn this paper, we present a data-driven approach associated with the “Sparse Identification of Nonlinear Dynamics” (SINDy) to capture the evolution behaviors of such moment quantities numerically.Results and DiscussionOur method is applied first to some well-known closed systems of ordinary differential equations (ODEs) which describe the evolution dynamics of relevant moment quantities. Our examples are, progressively, of increasing complexity and our findings explore different choices within the SINDy library. We also consider the potential discovery of coordinate transformations that lead to moment system closure. Finally, we extend considerations to settings where a closed analytical form of the moment dynamics is not available.

In this study, boundary control of a flexible manipulator is developed on the basis of the dynamic, partial differential equation (PDE) model. One of the main contributions is that the high gain observer is first applied to the PDE model of a flexible manipulator instead of measuring link velocity and end actuator velocity. In addition, using singular perturbation approach the PDE model is divided into two simpler subsystems to simplify the control design. Based on the proposed observer and decoupled PDE model, a sliding mode boundary control is designed to regulate angular position and suppress elastic vibration simultaneously. Numerical simulations demonstrate the effectiveness of the proposed scheme.

Efficacy of novel Summation-based Synergetic Artificial Neural Network in ADHD diagnosis

In recent years, increasing attention has been paid to Attention Deficit Hyperactivity Disorder (ADHD) as one of the most common neurobehavioral diseases in school-age children. In this paper, sparse representation is used as an effective tool to analyze the corresponding functional brain connectivities from functional MRI data. Two diagnosis models, i.e., ADHD and healthy control models, are employed to deal with the ADHD patients and control subjects. In these models, we learn the feature spaces of ADHD and control components adaptively via dictionary learning. Moreover, we also perform an energy operation as a penalty term in the models, which forces the feature energy of subjects minimized in the wrong feature spaces. Following these models, we carefully design a framework for ADHD classification, where more sophisticated methods are adopted including synthetic minority oversampling technique and SVM. In the experiments on ADHD-200 dataset, our method can achieve a remarkable accuracy compared with several state-of-the-art classification methods.