Yadhu Kartha

Chenxi Wu, Min Zhu, Qinyang Tan et al.

Physics-informed neural networks (PINNs) have shown to be an effective tool for solving forward and inverse problems of partial differential equations (PDEs). PINNs embed the PDEs into the loss of the neural network, and this PDE loss is evaluated at a set of scattered residual points. The distribution of these points are highly important to the performance of PINNs. However, in the existing studies on PINNs, only a few simple residual point sampling methods have mainly been used. Here, we present a comprehensive study of two categories of sampling: non-adaptive uniform sampling and adaptive nonuniform sampling. We consider six uniform sampling, including (1) equispaced uniform grid, (2) uniformly random sampling, (3) Latin hypercube sampling, (4) Halton sequence, (5) Hammersley sequence, and (6) Sobol sequence. We also consider a resampling strategy for uniform sampling. To improve the sampling efficiency and the accuracy of PINNs, we propose two new residual-based adaptive sampling methods: residual-based adaptive distribution (RAD) and residual-based adaptive refinement with distribution (RAR-D), which dynamically improve the distribution of residual points based on the PDE residuals during training. Hence, we have considered a total of 10 different sampling methods, including six non-adaptive uniform sampling, uniform sampling with resampling, two proposed adaptive sampling, and an existing adaptive sampling. We extensively tested the performance of these sampling methods for four forward problems and two inverse problems in many setups. Our numerical results presented in this study are summarized from more than 6000 simulations of PINNs. We show that the proposed adaptive sampling methods of RAD and RAR-D significantly improve the accuracy of PINNs with fewer residual points. The results obtained in this study can also be used as a practical guideline in choosing sampling methods.

Yadhu Kartha, Conor Anderson, Jenny Foster et al.

Autism Spectrum Disorder (ASD) is characterized by challenges with social interaction and communication and by restricted or repetitive patterns of thought and behavior, with significant variability in presentation. Approximately a quarter of children with ASD are classified as having profound autism, who often exhibit challenging behaviors, such as self-injurious behavior, aggression, elopement, or pica, that pose serious safety risks and disrupt learning in educational settings. Prior work has applied wearable sensors and machine learning to detect challenging behaviors, but has been largely confined to controlled laboratory environments. This work demonstrates that predicting challenging behavior episodes is feasible in a real-world special education classroom. We collected approximately 110.7 hours of labeled multimodal wearable data comprising accelerometry, electrodermal activity (EDA), and skin temperature from 9 children and young adults aged 10 to 21 years across standard classroom sessions. We fine-tuned state-of-the-art foundation models for multimodal wearable time-series analysis and show that challenging behavior episodes can be predicted up to 10 minutes in advance with an AUC-ROC of 0.78. These results establish a concrete foundation for developing proactive in-class intervention systems that enable teachers to minimize the safety risks of challenging behaviors in special education classrooms