Parkinson's disease (PD) shows heterogeneous, evolving brain-morphometry patterns. Modeling these longitudinal trajectories enables mechanistic insight, treatment development, and individualized ‘digital-twin’ forecasting. However, existing methods usually adopt recurrent neural networks and transformer architectures, which rely on discrete, regularly sampled data while struggling to handle irregular and sparse magnetic resonance imaging (MRI) in PD cohorts. Moreover, these methods have difficulty capturing individual heterogeneity including variations in disease onset, progression rate, and symptom severity, which is a hallmark of PD. To address these challenges, we propose CNODE (Conditional Neural ODE), a novel framework for continuous, individualized PD progression forecasting. The core of CNODE is to model morphological brain changes as continuous temporal processes using a neural ODE model. In addition, we jointly learn patient-specific initial time and progress speed to align individual trajectories into a shared progression trajectory. We validate CNODE on the Parkinson's Progression Markers Initiative (PPMI) dataset. Experimental results show that our method outperforms state-of-the-art baselines in forecasting longitudinal PD progression.

Graph Neural Networks (GNNs) and differential equations (DEs) are two rapidly advancing areas of research that have shown remarkable synergy in recent years. GNNs have emerged as powerful tools for learning on graph-structured data, while differential equations provide a principled framework for modeling continuous dynamics across time and space. The intersection of these fields has led to innovative approaches that leverage the strengths of both, enabling applications in physics-informed learning, spatiotemporal modeling, and scientific computing. This survey aims to provide a comprehensive overview of the burgeoning research at the intersection of GNNs and DEs. We will categorize existing methods, discuss their underlying principles, and highlight their applications across domains such as molecular modeling, traffic prediction, and epidemic spreading. Furthermore, we identify open challenges and outline future research directions to advance this interdisciplinary field. A comprehensive paper list is provided at https://github.com/Emory-Melody/Awesome-Graph-NDEs.

Machine Learning (ML) has become ubiquitous, fueling data-driven applications across various organizations. Contrary to the traditional perception of ML in research, ML workflows can be complex, resource-intensive, and time-consuming. Expanding an ML workflow to encompass a wider range of data infrastructure and data types may lead to larger workloads and increased deployment costs. Currently, numerous workflow engines are available (with over ten being widely recognized). This variety poses a challenge for end-users in terms of mastering different engine APIs. While efforts have primarily focused on optimizing ML Operations (MLOps) for a specific workflow engine, current methods largely overlook workflow optimization across different engines. In this work, we design and implement Couler, a system designed for unified ML workflow optimization in the cloud. Our main insight lies in the ability to generate an ML workflow using natural language (NL) descriptions. We integrate Large Language Models (LLMs) into workflow generation, and provide a unified programming interface for various workflow engines. This approach alleviates the need to understand various workflow engines' APIs. Moreover, Couler enhances workflow computation efficiency by introducing automated caching at multiple stages, enabling large workflow auto-parallelization and automatic hyperparameters tuning. These enhancements minimize redundant computational costs and improve fault tolerance during deep learning workflow training. Couler is extensively deployed in real-world production scenarios at Ant Group, handling approximately 22k workflows daily, and has successfully improved the CPU/Memory utilization by more than 15% and the workflow completion rate by around 17%.

The fuzzy cognitive map (FCM) is a powerful model for system state prediction and interpretable knowledge representation. Recent years have witnessed the tremendous efforts devoted to enhancing the basic FCM, such as introducing temporal factors, uncertainty or fuzzy rules to improve interpretation, and introducing fuzzy neural networks or wavelets to improve time series prediction. But how to achieve high-precision yet interpretable prediction in cross-domain real-life applications remains a great challenge. In this article, we propose a novel FCM extension called deep FCM (DFCM) for multivariate time series forecasting, in order to take both the advantage of FCM in interpretation and the advantage of deep neural networks in prediction. Specifically, to improve the predictive power, DFCM leverages a fully connected neural network to model connections (relationships) among concepts in a system, and a recurrent neural network to model unknown exogenous factors that have influences on system dynamics. Moreover, to foster model interpretability encumbered by the embedded deep structures, a partial derivative-based approach is proposed to measure the connection strengths between concepts in DFCM. An alternate function gradient descent algorithm is then proposed for parameter inference. The effectiveness of DFCM is validated over four publicly available datasets with the presence of seven baselines. DFCM indeed provides an important clue to building interpretable predictors for real-life applications.