arXiv subjects

Samuel S. P. Shen

Publications and source records attributed to Samuel S. P. Shen.

8 recordsLinked to original sources

arXiv2026

Diffusion-Based Rollouts as a Stabilization Mechanism for Long-Horizon Environmental Forecasting

Extending forecast lead times while maintaining predictive skill remains a major challenge in environmental forecasting. We investigate diffusion-based rollouts as a stabilization mechanism for recursive forecasting using low-dimensional water-level time series and high-dimensional precipitation fields. Across both modalities, diffusion suppresses recursive error growth, with the largest stabilization occurring where deterministic rollouts are most unstable. However, stabilization does not guarantee forecast fidelity. In the water-level experiments, forecasts progressively lose event-level fidelity as the rollout loses access to external predictive information, and trajectory-level comparisons show that diffusion can remain numerically stable while contracting toward central values and exhibiting reduced variability. In the precipitation experiments, which retain conditioning from numerical weather prediction throughout the rollout, diffusion better preserves spatial organization and event-detection skill. Together, these contrasting experiments indicate that diffusion can control recursive error amplification, while its practical benefit also depends on the predictive information available to constrain future evolution.

cs.LG↗

arXiv2026

OFFER (One-Figure-Facilitates-Every-Relationship)for Trigonometric Functions

This article describes an approach that uses a single figure to illustrate all six trigonometric functions, their fundamental identities, and the law of cosines. We name this method OFFER (one-figure-facilitates-every-relationship) for the convenience of mathematics teaching. The article also describes the SPORT (story-picture-observe-review-tell) approach to effective mathematics learning.

math.GM↗

arXiv2025

A Diffusion-Based Framework for High-Resolution Precipitation Forecasting over CONUS

Accurate precipitation forecasting is essential for hydrometeorological risk management, especially for anticipating extreme rainfall that can lead to flash flooding and infrastructure damage. This study introduces a diffusion-based deep learning (DL) framework that systematically compares three residual prediction strategies differing only in their input sources: (1) a fully data-driven model using only past observations from the Multi-Radar Multi-Sensor (MRMS) system, (2) a corrective model using only forecasts from the High-Resolution Rapid Refresh (HRRR) numerical weather prediction system, and (3) a hybrid model integrating both MRMS and selected HRRR forecast variables. By evaluating these approaches under a unified setup, we provide a clearer understanding of how each data source contributes to predictive skill over the Continental United States (CONUS). Forecasts are produced at 1-km spatial resolution, beginning with direct 1-hour predictions and extending to 12 hours using autoregressive rollouts. Performance is evaluated using both CONUS-wide and region-specific metrics that assess overall performance and skill at extreme rainfall thresholds. Across all lead times, our DL framework consistently outperforms the HRRR baseline in pixel-wise and spatiostatistical metrics. The hybrid model performs best at the shortest lead time, while the HRRR-corrective model outperforms others at longer lead times, maintaining high skill through 12 hours. To assess reliability, we incorporate calibrated uncertainty quantification tailored to the residual learning setup. These gains, particularly at longer lead times, are critical for emergency preparedness, where modest increases in forecast horizon can improve decision-making. This work advances DL-based precipitation forecasting by enhancing predictive skill, reliability, and applicability across regions.

cs.LG↗

arXiv2025

Robustness Test for AI Forecasting of Hurricane Florence Using FourCastNetv2 and Random Perturbations of the Initial Condition

Understanding the robustness of a weather forecasting model with respect to input noise or different uncertainties is important in assessing its output reliability, particularly for extreme weather events like hurricanes. In this paper, we test sensitivity and robustness of an artificial intelligence (AI) weather forecasting model: NVIDIAs FourCastNetv2 (FCNv2). We conduct two experiments designed to assess model output under different levels of injected noise in the models initial condition. First, we perturb the initial condition of Hurricane Florence from the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) dataset (September 13-16, 2018) with varying amounts of Gaussian noise and examine the impact on predicted trajectories and forecasted storm intensity. Second, we start FCNv2 with fully random initial conditions and observe how the model responds to nonsensical inputs. Our results indicate that FCNv2 accurately preserves hurricane features under low to moderate noise injection. Even under high levels of noise, the model maintains the general storm trajectory and structure, although positional accuracy begins to degrade. FCNv2 consistently underestimates storm intensity and persistence across all levels of injected noise. With full random initial conditions, the model generates smooth and cohesive forecasts after a few timesteps, implying the models tendency towards stable, smoothed outputs. Our approach is simple and portable to other data-driven AI weather forecasting models.

cs.LG↗

arXiv2025

Democracy of AI Numerical Weather Models: An Example of Global Forecasting with FourCastNetv2 Made by a University Research Lab Using GPU

This paper demonstrates the feasibility of democratizing AI-driven global weather forecasting models among university research groups by leveraging Graphics Processing Units (GPUs) and freely available AI models, such as NVIDIA's FourCastNetv2. FourCastNetv2 is an NVIDIA's advanced neural network for weather prediction and is trained on a 73-channel subset of the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) dataset at single levels and different pressure levels. Although the training specifications for FourCastNetv2 are not released to the public, the training documentation of the model's first generation, FourCastNet, is available to all users. The training had 64 A100 GPUs and took 16 hours to complete. Although NVIDIA's models offer significant reductions in both time and cost compared to traditional Numerical Weather Prediction (NWP), reproducing published forecasting results presents ongoing challenges for resource-constrained university research groups with limited GPU availability. We demonstrate both (i) leveraging FourCastNetv2 to create predictions through the designated application programming interface (API) and (ii) utilizing NVIDIA hardware to train the original FourCastNet model. Further, this paper demonstrates the capabilities and limitations of NVIDIA A100's for resource-limited research groups in universities. We also explore data management, training efficiency, and model validation, highlighting the advantages and challenges of using limited high-performance computing resources. Consequently, this paper and its corresponding GitHub materials may serve as an initial guide for other university research groups and courses related to machine learning, climate science, and data science to develop research and education programs on AI weather forecasting, and hence help democratize the AI NWP in the digital economy.

cs.LG↗

arXiv2014

Calculus from a Statistics Perspective

This paper provides an approach to establishing the calculus method from the concept of mean, i.e., average. This approach is from a statistics perspective and can help calculus learners understand calculus ideas and analyze a function defined by data or sampling values from a given function, rather than an explicit mathematical formula. The basics of this approach are two averages: arithmetic mean and graphic mean. The arithmetic mean is used to define integral. Area is used to interpret the meaning of an integral. Antiderivative is introduced from integral, and derivative-antiderivative pair is introduced as a mathematical operation entity. The graphic mean is an average speed in an interval and is used to interpret the meaning of a derivative.

math.HO↗

arXiv2014

DD Calculus

This paper introduces DD calculus and describes the basic calculus concepts of derivative and integral in a direct and non-traditional way, without limit definition: Derivative is computed from the point-slope equation of a tangent line and integral is defined as the height increment of a curve. This direct approach to calculus has three distinct features: (i) it defines derivative and (definite) integral without using limits, (ii) it defines derivative and antiderivative simultaneously via a derivative-antiderivative (DA) pair, and (iii) it posits the fundamental theorem of calculus as a natural corollary of the definitions of derivative and integral. The first D in DD calculus attributes to Descartes for his method of tangents and the second D to DA-pair. The DD calculus, or simply direct calculus, makes many traditional notations and procedures unnecessary, a plus when introducing calculus to the non-mathematics majors. It has few intermediate procedures, which can help dispel the mystery of calculus as perceived by the general public. The materials in this paper are intended for use in a two-hour introductory lecture on calculus.

math.HO↗

arXiv2002

A Dynamic Approach to Characterizing Termination of General Logic Programs

We present a new characterization of termination of general logic programs. Most existing termination analysis approaches rely on some static information about the structure of the source code of a logic program, such as modes/types, norms/level mappings, models/interargument relations, and the like. We propose a dynamic approach which employs some key dynamic features of an infinite (generalized) SLDNF-derivation, such as repetition of selected subgoals and recursive increase in term size. We also introduce a new formulation of SLDNF-trees, called generalized SLDNF-trees. Generalized SLDNF-trees deal with negative subgoals in the same way as Prolog and exist for any general logic programs.

cs.LO↗