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This paper presents the first scientific application of local time-stepping (LTS) schemes in the Model for Prediction Across Scales-Ocean (MPAS-O). We use LTS schemes in a single-layer, global ocean model that predicts the storm surge…

The Courant-Friedrichs-Lewy (CFL) condition is a well known, necessary condition for the stability of explicit time-stepping schemes that effectively places a limit on the size of the largest admittable time-step for a given problem. We…

Numerical solutions of hyperbolic partial differential equations(PDEs) are ubiquitous in science and engineering. Method of lines is a popular approach to discretize PDEs defined in spacetime, where space and time are discretized…

This paper describes a localized algorithm for the topological simplification of scalar data, an essential pre-processing step of topological data analysis (TDA). Given a scalar field f and a selection of extrema to preserve, the proposed…

Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any…

The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps,…

Test-Time Scaling (TTS) is an important method for improving the performance of Large Language Models (LLMs) by using additional computation during the inference phase. However, current studies do not systematically analyze how policy…

Correlated time series (CTS) forecasting plays an essential role in many practical applications, such as traffic management and server load control. Many deep learning models have been proposed to improve the accuracy of CTS forecasting.…

Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGrote09}, a leapfrog based explicit local time-stepping…

Multivariate time series forecasting has seen widely ranging applications in various domains, including finance, traffic, energy, and healthcare. To capture the sophisticated temporal patterns, plenty of research studies designed complex…

Unconditionally stable time stepping schemes are useful and often practically necessary for advancing parabolic operators in multi-scale systems. However, serious accuracy problems may emerge when taking time steps that far exceed the…

Test-Time Scaling (TTS) has proven effective in improving the performance of Large Language Models (LLMs) during inference. However, existing research has overlooked the efficiency of TTS from a latency-sensitive perspective. Through a…

Test-time scaling (TTS) has recently emerged as a promising direction to exploit the hidden reasoning capabilities of pre-trained large language models (LLMs). However, existing scaling methods narrowly focus on the compute-optimal…

Test-time scaling (TTS) -- the dynamic allocation of compute during inference -- is a promising direction for improving reasoning in large language models (LLMs). However, a systematic comparison of well-known TTS strategies under identical…

Despite the enormous success of Hamiltonian Monte Carlo and related Markov Chain Monte Carlo (MCMC) methods, sampling often still represents the computational bottleneck in scientific applications. Availability of parallel resources can…

Water demand is a highly important variable for operational control and decision making. Hence, the development of accurate forecasts is a valuable field of research to further improve the efficiency of water utilities. Focusing on…

Parallel test-time scaling (TTS) is a pivotal approach for enhancing large language models (LLMs), typically by sampling multiple token-based chains-of-thought in parallel and aggregating outcomes through voting or search. Recent advances…

We derived a number of numerical methods to treat biomolecular systems with multiple time scales. Based on the splitting of the operators associated with the slow-varying and fast-varying forces, new multiple time-stepping (MTS) methods are…

Mixed precision training (MPT) is becoming a practical technique to improve the speed and energy efficiency of training deep neural networks by leveraging the fast hardware support for IEEE half-precision floating point that is available in…

Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny time-step across the entire computational domain when using…