This project aims to develop the mathematical foundations for a digital twin (DT) system for individuals with autism spectrum disorder (ASD), focusing on dynamic modeling, prediction, uncertainty quantification, and treatment or intervention recommendation through DT-based optimization. ASD is characterized by challenges in social interaction, communication, and behavior, such as difficulties in forming relationships, understanding nonverbal cues, speech development, repetitive behaviors, and sensory sensitivities. The project will create a unified system integrating clinical and neuro-developmental data, analyzed using a DT healthcare paradigm. The DT technology will enable individualized models, and its predictive capabilities will allow healthcare providers to anticipate progression and adjust treatment or intervention proactively. Additionally, the continuous feedback loop from real-time data will enhance therapeutic outcomes. The developed methods and theories will have broader applicability to other medical areas, improving healthcare efficiency, reducing system burdens, and informing public health strategies. This will ultimately enhance care and promote community well-being. The project will also develop quality cyberinfrastructure to share algorithms, data, and open-source software with the community. Furthermore, the investigators plan to expand scientific impacts through collaborating with medical experts and industry scientists, training undergraduate and graduate students, and integrating research findings into course development.<br/><br/>The project will develop a DT framework by modeling brain activities with a unified data structure, linked to behavioral characteristics and interventions aligned with individuals' neuro-developmental processes. This system will integrate multimodal and multi-source data related to human health and development. It will establish foundational models for training and generating synthetic data from DT models, enabling personalized predictions of progression and uncertainty quantification through novel interdisciplinary approaches. The DT system consists of four research modules: (1) Develop computational models based on conditional variational auto-encoders (CVAE) and longitudinal CVAE to analyze brain activities, integrate diverse imaging data, and model neurodevelopmental processes. (2) Create a novel bilevel formulation for multi-distribution fine-tuning techniques on pretrained foundational models and a fast algorithm to learn from heterogeneous data sources to predict ASD outcomes. (3) Develop a model-free conformal prediction procedure to ensemble predictions from multiple models obtained with different modalities and progression simulations, integrating various types of uncertainties into one framework. (4) Develop a DT-based reinforcement learning framework to recommend personalized treatment/intervention plans that significantly improve online learning efficiency and clinical outcomes. The project will address challenges such as multimodality and multi-source data, high-dimensional features, dynamic progression of ASD symptoms, brain functional connectivity, and the need for personalized intervention or treatment recommendations and uncertainty quantification.<br/><br/>This project is jointly funded by the Division of Mathematical Sciences, the OAC Cyberinfrastructure for Sustained Scientific Innovation (CSSI) program, and the CBET Engineering of Biomedical Systems program.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.