arXiv subjects

Tianchi Li

Publications and source records attributed to Tianchi Li.

4 recordsLinked to original sources

arXiv2026

Guiding LLM-based Loop Invariant Synthesis via Feedback on Local Reasoning Errors

We propose a novel framework that provides constructive feedback to an LLM in the "guess-and-check" paradigm by formally verifying its own thinking process and detecting local reasoning errors. We apply this framework to the loop invariant synthesis problem. We prompt the model to produce a step-by-step natural language proof justifying its thinking process for the failed verification condition of its generated loop invariants. Then, we use an LLM to translate the reasoning steps into first-order logic implications, which can be checked automatically. An invalid implication pinpoints the exact logical flaw in the LLM's thinking process, which we then use to construct targeted feedback for refinement. We have implemented our approach in a tool called LORIS and evaluated it on a main benchmark suite of 460 C programs and an additional benchmark suite of 50 C programs each of which involves non-linear properties. On the main benchmark suite, LORIS solved 445 of the programs, and achieved an overall success rate of $93.1\%$. LORIS also demonstrates robustness on the challenging non-linear benchmark suite.

cs.PL↗

arXiv2026

High-fidelity level-set modeling of polycrystalline grain growth

Accurate modeling of polycrystalline microstructure evolution under strong crystallographic heterogeneities remains a major challenge for full-field numerical methods at the mesoscopic scale. In this work, we present a high-fidelity level-set framework for capillarity-driven grain growth in polycrystals with highly-heterogeneous, disorientation-dependent grain boundary energies. The novel framework represents a polycrystalline extension of our level-set formulation, previously developed and validated using a single triple junction benchmark case. In-depth comparisons with three established level-set models demonstrate that the proposed method yields the most energetically-consistent evolution of grain statistics, disorientation distribution function, and triple junction dihedral angles. Accuracy and robustness are maintained across the entire heterogeneity spectrum. To the best of our knowledge, this approach delivers the highest-fidelity front-capturing level-set modeling of grain growth based on Mullins' mean curvature flow theory, paving the way for state-of-the-art digital twins for annealing applications.

cond-mat.mtrl-sci↗

arXiv2025

An accurate and robust level-set formulation for multiple junction kinetics

The front-capturing Level-Set (LS) method is widely employed in academia and industry to model grain boundary (GB) migration during the microstructure evolution of polycrystalline materials under thermo-mechanical treatments. During capillarity-driven grain growth, the conventional mean curvature flow equation, $\vec{v} = - \mu \gamma \kappa \vec{n}$, is used to compute the GB normal migration velocity. Over recent decades, extensive efforts have been made to incorporate polycrystalline heterogeneity into this framework. However, despite increased complexity and computational costs, these approaches have yet to achieve fully satisfactory performance. This paper introduces a simple yet robust LS formulation that accurately captures multiple junction kinetics, even with extreme GB energy ratios. Validation against existing analytical solutions highlights the method's accuracy and efficiency. This novel approach offers significant potential for advancing the study of highly heterogeneous interface systems.

cs.CE↗

arXiv2023

Siloxane molecules: Nonlinear elastic behavior and fracture characteristics

Fracture phenomena in soft materials span multiple length- and timescales. This poses a major challenge in computational modeling and predictive materials design. To pass quantitatively from molecular- to continuum scales, a precise representation of the material response at the molecular level is vital. Here, we derive the nonlinear elastic response and fracture characteristics of individual siloxane molecules using molecular dynamics (MD) studies. For short chains, we find deviations from classical scalings for both the effective stiffness and mean chain rupture times. A simple model of a non-uniform chain of Kuhn segments captures the observed effect and agrees well with MD data. We find that the dominating fracture mechanism depends on the applied force scale in a non-monotonic fashion. This analysis suggests that common polydimethylsiloxane (PDMS) networks fail at crosslinking points. Our results can be readily lumped into coarse-grained models. Although focusing on PDMS as a model system, our study presents a general procedure to pass beyond the window of accessible rupture times in MD studies employing mean first passage time theory, which can be exploited for arbitrary molecular systems.

cond-mat.soft↗