Vipin Kumar

Yilong Dai, Shengyu Chen, Ziyi Wang et al.

Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the emergence of various physics-aware data-driven approaches, the field still lacks a unified perspective to uncover their relationships, limitations, and appropriate roles in scientific workflows. To this end, we propose a unifying perspective to place two dominant paradigms: Physics-Informed Neural Networks (PINNs) and Neural Operators (NOs), within a shared design space. We organize existing methods from three fundamental dimensions: what is learned, how physical structures are integrated into the learning process, and how the computational load is amortized across problem instances. In this way, many challenges can be best understood as consequences of these structural properties of learning PDEs. By analyzing advances through this unifying view, our survey aims to facilitate the development of reliable learning-based PDE solvers and catalyze a synthesis of physics and data.

Guruprasad Nayak, Rahul Ghosh, Xiaowei Jia et al.

In many applications, finding adequate labeled data to train predictive models is a major challenge. In this work, we propose methods to use group-level binary labels as weak supervision to train instance-level binary classification models. Aggregate labels are common in several domains where annotating on a group-level might be cheaper or might be the only way to provide annotated data without infringing on privacy. We model group-level labels as Class Conditional Noisy (CCN) labels for individual instances and use the noisy labels to regularize predictions of the model trained on the strongly-labeled instances. Our experiments on real-world application of land cover mapping shows the utility of the proposed method in leveraging group-level labels, both in the presence and absence of class imbalance.

Saurabh Agrawal, Saurabh Verma, Anuj Karpatne et al.

Traditional approaches focus on finding relationships between two entire time series, however, many interesting relationships exist in small sub-intervals of time and remain feeble during other sub-intervals. We define the notion of a sub-interval relationship (SIR) to capture such interactions that are prominent only in certain sub-intervals of time. To that end, we propose a fast-optimal guaranteed algorithm to find most interesting SIR relationship in a pair of time series. Lastly, we demonstrate the utility of our method in climate science domain based on a real-world dataset along with its scalability scope and obtain useful domain insights.