Multi-Scale Graph Learning for Anti-Sparse Downscaling

Water temperature can vary substantially even across short distances within the same sub-watershed. Accurate prediction of stream water temperature at fine spatial resolutions (i.e., fine scales, $\leq$ 1 km) enables precise interventions to maintain water quality and protect aquatic habitats. Although spatiotemporal models have made substantial progress in spatially coarse time series modeling, challenges persist in predicting at fine spatial scales due to the lack of data at that scale.To address the problem of insufficient fine-scale data, we propose a Multi-Scale Graph Learning (MSGL) method. This method employs a multi-task learning framework where coarse-scale graph learning, bolstered by larger datasets, simultaneously enhances fine-scale graph learning. Although existing multi-scale or multi-resolution methods integrate data from different spatial scales, they often overlook the spatial correspondences across graph structures at various scales. To address this, our MSGL introduces an additional learning task, cross-scale interpolation learning, which leverages the hydrological connectedness of stream locations across coarse- and fine-scale graphs to establish cross-scale connections, thereby enhancing overall model performance. Furthermore, we have broken free from the mindset that multi-scale learning is limited to synchronous training by proposing an Asynchronous Multi-Scale Graph Learning method (ASYNC-MSGL). Extensive experiments demonstrate the state-of-the-art performance of our method for anti-sparse downscaling of daily stream temperatures in the Delaware River Basin, USA, highlighting its potential utility for water resources monitoring and management.

Towards efficient quantum algorithms for diffusion probability models

A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as high-resolution images or audio incurs significant computational, energy, and hardware costs. In this work, we introduce efficient quantum algorithms for implementing DPMs through various quantum ODE solvers. These algorithms highlight the potential of quantum Carleman linearization for diverse mathematical structures, leveraging state-of-the-art quantum linear system solvers (QLSS) or linear combination of Hamiltonian simulations (LCHS). Specifically, we focus on two approaches: DPM-solver-$k$ which employs exact $k$-th order derivatives to compute a polynomial approximation of $\epsilon_\theta(x_\lambda,\lambda)$; and UniPC which uses finite difference of $\epsilon_\theta(x_\lambda,\lambda)$ at different points $(x_{s_m}, \lambda_{s_m})$ to approximate higher-order derivatives. As such, this work represents one of the most direct and pragmatic applications of quantum algorithms to large-scale machine learning models, presumably talking substantial steps towards demonstrating the practical utility of quantum computing.