arXiv subjects

Tianyu Jin

Publications and source records attributed to Tianyu Jin.

5 recordsLinked to original sources

arXiv2026

Iterative thresholding low-rank time integration for high-dimensional problems

This work analyzes a method for time integration of high-dimensional linear Schrödinger-type problems based on hierarchical tensor approximations. In particular, this method provides a balance between error bounds and associated approximation ranks, using a scheme for iterative refinement with soft thresholding of tensors. The practical performance of the method is illustrated by numerical tests on coupled oscillators.

math.NA↗

arXiv2026

SAGA: Scene-Aware, Goal-Evolving Agents for Long-Horizon Strategy Game Planning

Grand-strategy games such as Civilization pose a distinctive long-horizon planning problem: an agent must divide one shared resource pool among six competing domains -- technology, government, diplomacy, city development, expansion, and military -- under partial observability, with no feedback except a delayed final score. Current LLM agents fall short in three ways: 1) they cannot infer spatial relations from raw coordinates; 2) they allocate resources poorly, because feeding the entire growing state into one prompt and planning all domains in a single output diffuses attention and biases decisions toward urgent events; and 3) they cannot improve, as the delayed score gives no signal within or across games. We present SAGA, an LLM multi-agent framework pairing one mechanism with each weakness: (i) a Map-Semantic Scene Graph turning coordinates into per-entity statements of distance, direction, and threat; (ii) a Tool-Augmented Planner that retrieves only the state a decision needs, cutting the order of magnitude of its input, and issues a separate plan per domain to six specialist controllers, so urgent events do not derail long-term plans; and (iii) a Dual-Horizon Feedback Loop setting short-term goals during play and distilling each game into lessons for the next. On CivRealm, a Civilization-style benchmark, SAGA leads five LLM baselines on mean final score and is the only method significantly ahead of all of them on city development, the first investment baselines sacrifice, with 27% fewer output tokens; with cross-game learning it scores highest after five games, and its fifth game consistently surpasses its first across four maps. Our code is available at https://github.com/Kazecloudk/SAGA-Scene-Aware-Goal-Evolving-Agents-for-Long-Horizon-Strategy-Game-Planning.

cs.AI↗

arXiv2025

Adaptive and hybrid reduced order models to mitigate Kolmogorov barrier in a multiscale kinetic transport equation

In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the underlying scattering effect is not sufficiently strong, the system governed by this equation exhibits transport-dominated behavior. Suffering from the Kolmogorov barrier for transport-dominant problems, classical linear ROMs may become inefficient in this regime. To address this issue, we first develop a piecewise linear ROM by introducing a novel goal-oriented adaptive time partitioning strategy. To avoid local over-refinement or under-refinement, we propose an adaptive coarsening and refinement strategy that remains robust with various initial empirical partitions. Additionally, for problems where a local linear approximation is not sufficiently efficient, we further develop a hybrid ROM, which combines autoencoder-based nonlinear ROMs and piecewise linear ROMs. Compared to previous autoencoder-based ROMs, this hybridized method reduces the offline autoencoder's training cost by only applying it to time intervals that are adaptively identified as the most challenging. Numerical experiments demonstrate that our proposed approaches successfully predict full-order solutions at unseen parameter values with both efficiency and accuracy. To the best of our knowledge, this is the first attempt to address the Kolmogorov barrier for multiscale kinetic transport problems with the coexistence of both transport- and diffusion-dominant behaviors.

math.NA↗

arXiv2025

A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics

The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of larger time steps, and better structure preservation properties. However, this comes at the price of having to solve a nonlinear equation at every time step of the numerical scheme. In this work, we propose a novel deep learning based hybrid Newton's method to accelerate this solution of the nonlinear time step system for stiff time-evolution nonlinear equations. We propose a targeted learning strategy which facilitates robust unsupervised learning in an offline phase and provides a highly efficient initialisation for the Newton iteration leading to consistent acceleration of Newton's method. A quantifiable rate of improvement in Newton's method achieved by improved initialisation is provided and we analyse the upper bound of the generalisation error of our unsupervised learning strategy. These theoretical results are supported by extensive numerical results, demonstrating the efficiency of our proposed neural hybrid solver both in one- and two-dimensional cases.

math.NA↗

arXiv2024

Energy stable neural network for gradient flow equations

We propose an energy stable network (EStable-Net) for solving gradient flow equations. The EStable-Net enables decreasing of a discrete energy along the neural network, which is consistent with the property of the gradient flow equation. The architecture of the neural network EStable-Net is based on the block network structure (Autoflow) in which output of each block can be interpreted as an intermediate state of the evolution process of the equation, and the energy stable property is incorporated in each block, which is easily generalized to include other physical and/or numerical properties. Our EStable-Net is a supervised learning network approach for solving evolution equations which does not depend on the convergence of time step goes to 0, and can be applied generally even when only data is available but the equation is unknown. We also propose a training strategy for supervised learning that employs data of the evolution stages with different nature. The EStable-Net is validated by numerical experimental results based on the Allen-Cahn equation and the Cahn-Hilliard equation in two dimensions.

cs.LG↗