arXiv subjects

Jin Feng

Publications and source records attributed to Jin Feng.

9 recordsLinked to original sources

arXiv2026

StretchCast: Global-Regional AI Weather Forecasting on Stretched Cubed-Sphere Mesh

Global AI weather forecasting still relies mainly on uniform-resolution models, making it hard to combine regional refinement, two-way regional-global coupling, and affordable training cost. We introduce StretchCast, a global-regional AI forecasting framework built on a variable-resolution stretched cubed-sphere (SCS) mesh that preserves a closed global domain while concentrating resolution over a target region. Within this framework, we develop a one-step predictor, SCS_Base Model, and a rollout-oriented multistep predictor, SCS_FCST4 Model, to test the feasibility of SCS-based forecasting and the benefit of joint multistep training. Experiments use ERA5 with 69 variables over 1998-2022. Because training compute remains limited, this study uses a coarse-resolution proof-of-concept configuration rather than a final high-resolution system. Even with only about 7,776 effective global grid cells and roughly 0.875 degree resolution over the center-refined face, the 23M-parameter SCS_Base Model yields stable multivariate forecasts. With 83M parameters and training cost on the order of hours, SCS_FCST4 Model delivers competitive medium-range anomaly-correlation evolution over the target region after unified reprojection, especially for geopotential height, specific humidity, and part of the lower-tropospheric winds, while maintaining smooth cross-face continuity and realistic multiscale structure in typhoon and spectral analyses. These results support StretchCast as a practical lightweight foundation for global-regional AI weather forecasting.

physics.ao-ph↗

arXiv2025

On a Hamilton-Jacobi PDE theory for hydrodynamic limit of action minimizing collective dynamics

We establish multi-scale convergence theory for a class of Hamilton-Jacobi PDEs in space of probability measures. They arise from context of hydrodynamic limit of N-particle deterministic action minimizing (global) Lagrangian dynamics. From a Lagrangian point of view, this can also be viewed as a limit result on two scale convergence of action minimizing probability-measure-valued paths. However, we focus on the Hamiltonian formulation here mostly. We derive and study convergence of the associated abstract but scalar Hamilton-Jacobi equations, defined in space of probability measures. There is an infinite dimensional singular averaging structure within these equations. We develop an indirect variational approach to apply finite dimensional weak K.A.M. theory to such infinite dimensional setting here. With a weakly interacting particle assumption, the averaging step only involves that of individual particles, which is implicitly but rigorously treated using the weak K.A.M. theory. Consequently, we can close the above mentioned averaging step by identifying limiting Hamiltonian, and arrive at a rigorous convergence result on solutions of the nonlinear PDEs in space of probability measures. In technical development parts of the paper, we devise new viscosity solution techniques regarding projection of equations with a submetry structure in state space, multi-scale convergence for certain abstract Hamilton-Jacobi equations in metric spaces, as well as comparison principles for equations in space of probability measures. The space of probability measure we consider is a special case of Alexandrov metric space with curvature bounded from below. Since some results are better explained in such metric space setting, we also develop some techniques in the general settings which are of independent interests.

math.AP↗

arXiv2025

MARS2 2025 Challenge on Multimodal Reasoning: Datasets, Methods, Results, Discussion, and Outlook

This paper reviews the MARS2 2025 Challenge on Multimodal Reasoning. We aim to bring together different approaches in multimodal machine learning and LLMs via a large benchmark. We hope it better allows researchers to follow the state-of-the-art in this very dynamic area. Meanwhile, a growing number of testbeds have boosted the evolution of general-purpose large language models. Thus, this year's MARS2 focuses on real-world and specialized scenarios to broaden the multimodal reasoning applications of MLLMs. Our organizing team released two tailored datasets Lens and AdsQA as test sets, which support general reasoning in 12 daily scenarios and domain-specific reasoning in advertisement videos, respectively. We evaluated 40+ baselines that include both generalist MLLMs and task-specific models, and opened up three competition tracks, i.e., Visual Grounding in Real-world Scenarios (VG-RS), Visual Question Answering with Spatial Awareness (VQA-SA), and Visual Reasoning in Creative Advertisement Videos (VR-Ads). Finally, 76 teams from the renowned academic and industrial institutions have registered and 40+ valid submissions (out of 1200+) have been included in our ranking lists. Our datasets, code sets (40+ baselines and 15+ participants' methods), and rankings are publicly available on the MARS2 workshop website and our GitHub organization page https://github.com/mars2workshop/, where our updates and announcements of upcoming events will be continuously provided.

cs.CV↗

arXiv2025

A system of Schr\"odinger's problems and functional equations

We propose and study a system of Schr\"odinger's problems and functional equations in probability theory. More precisely, we consider a system of variational problems of relative entropies for probability measures on a Euclidean space with given two endpoint marginals, which can be defined inductively. We also consider an inductively defined system of functional equations, which are Euler's equations for our variational problems. These are generalizations of Schr\"odinger's problem and functional equation. % in probability theory. We prove the existence and uniqueness of solutions to our functional equations, % up to a multiplicative function, from which we show the existence and uniqueness of a minimizer of our variational problem. Our problem gives an approach for a stochastic optimal transport analog of the Knothe--Rosenblatt rearrangement via a variational problem point of view.

math.PR↗

arXiv2024

Leadsee-Precip: A Deep Learning Diagnostic Model for Precipitation

Recently, deep-learning weather forecasting models have surpassed traditional numerical models in terms of the accuracy of meteorological variables. However, there is considerable potential for improvements in precipitation forecasts, especially for heavy precipitation events. To address this deficiency, we propose Leadsee-Precip, a global deep learning model to generate precipitation from meteorological circulation fields. The model utilizes an information balance scheme to tackle the challenges of predicting heavy precipitation caused by the long-tail distribution of precipitation data. Additionally, more accurate satellite and radar-based precipitation retrievals are used as training targets. Compared to artificial intelligence global weather models, the heavy precipitation from Leadsee-Precip is more consistent with observations and shows competitive performance against global numerical weather prediction models. Leadsee-Precip can be integrated with any global circulation model to generate precipitation forecasts. But the deviations between the predicted and the ground-truth circulation fields may lead to a weakened precipitation forecast, which could potentially be mitigated by further fine-tuning based on the predicted circulation fields.

physics.ao-ph↗

arXiv2023

W-MAE: Pre-trained weather model with masked autoencoder for multi-variable weather forecasting

Weather forecasting is a long-standing computational challenge with direct societal and economic impacts. This task involves a large amount of continuous data collection and exhibits rich spatiotemporal dependencies over long periods, making it highly suitable for deep learning models. In this paper, we apply pre-training techniques to weather forecasting and propose W-MAE, a Weather model with Masked AutoEncoder pre-training for weather forecasting. W-MAE is pre-trained in a self-supervised manner to reconstruct spatial correlations within meteorological variables. On the temporal scale, we fine-tune the pre-trained W-MAE to predict the future states of meteorological variables, thereby modeling the temporal dependencies present in weather data. We conduct our experiments using the fifth-generation ECMWF Reanalysis (ERA5) data, with samples selected every six hours. Experimental results show that our W-MAE framework offers three key benefits: 1) when predicting the future state of meteorological variables, the utilization of our pre-trained W-MAE can effectively alleviate the problem of cumulative errors in prediction, maintaining stable performance in the short-to-medium term; 2) when predicting diagnostic variables (e.g., total precipitation), our model exhibits significant performance advantages over FourCastNet; 3) Our task-agnostic pre-training schema can be easily integrated with various task-specific models. When our pre-training framework is applied to FourCastNet, it yields an average 20% performance improvement in Anomaly Correlation Coefficient (ACC).

cs.LG↗

arXiv2021

A Hamilton-Jacobi PDE associated with hydrodynamic fluctuations from a nonlinear diffusion equation

We study a class of Hamilton-Jacobi partial differential equations in the space of probability measures. In the first part of this paper, we prove comparison principles (implying uniqueness) for this class. In the second part, we establish the existence of a solution and give a representation using a family of partial differential equations with control. A large part of our analysis exploits special structures of the Hamiltonian, which might look mysterious at first sight. However, we show that this Hamiltonian structure arises naturally as limit of Hamiltonians of microscopical models. Indeed, in the third part of this paper, we informally derive the Hamiltonian studied before, in a context of fluctuation theory on the hydrodynamic scale. The analysis is carried out for a specific model of stochastic interacting particles in gas kinetics, namely a version of the Carleman model. We use a two-scale averaging method on Hamiltonians defined in the space of probability measures to derive the limiting Hamiltonian.

math.AP↗

arXiv2012

Small-time asymptotics for fast mean-reverting stochastic volatility models

In this paper, we study stochastic volatility models in regimes where the maturity is small, but large compared to the mean-reversion time of the stochastic volatility factor. The problem falls in the class of averaging/homogenization problems for nonlinear HJB-type equations where the "fast variable" lives in a noncompact space. We develop a general argument based on viscosity solutions which we apply to the two regimes studied in the paper. We derive a large deviation principle, and we deduce asymptotic prices for out-of-the-money call and put options, and their corresponding implied volatilities. The results of this paper generalize the ones obtained in Feng, Forde and Fouque [SIAM J. Financial Math. 1 (2010) 126-141] by a moment generating function computation in the particular case of the Heston model.

q-fin.PR↗

arXiv2006

Large deviation for diffusions and Hamilton--Jacobi equation in Hilbert spaces

Large deviation for Markov processes can be studied by Hamilton--Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the transformed generators exists. Such limit induces a Hamilton--Jacobi equation. Second, we show that a strong form of uniqueness (the comparison principle) holds for the limit equation. Finally, we verify an exponential compact containment estimate. The large deviation principle then follows from the above three verifications. This paper illustrates such a method applied to a class of Hilbert-space-valued small diffusion processes. The examples include stochastically perturbed Allen--Cahn, Cahn--Hilliard PDEs and a one-dimensional quasilinear PDE with a viscosity term. We prove the comparison principle using a variant of the Tataru method. We also discuss different notions of viscosity solution in infinite dimensions in such context.

math.PR↗