学术报告报告题目：HyDFVM: A region-aware hybrid finite-volume learning framework for hyperbolic conservation laws
报 告 人：邹青松 教授
报告时间：2026年1月13日（星期二）上午10:30-11:30
报告地点： 37号楼3A01
邀 请 人： 刘晓霞 副教授
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数学学院
2026年1月5日
报告摘要：
In recent years, deep learning-based solvers for partial differential equations (PDEs) have emerged as prominent frontier, attracting significant interest across scientific and engineering disciplines. This study present HyDFVM, a hybrid deep learning framework based on finite volume methods for hyperbolic conservation laws with discontinuous solutions. HyDFVM integrates a spatiotemporal deep finite-volume-methods (tDFVM)–type weak residual, which circumvents explicit derivatives and remains well posed across shocks/contact discontinuities, with a gradient-weighted strong-form residual to enforce differential constraints in continuous regions of the solution, together with an adaptive resampling strategy that concentrates training points near evolving discontinuous features. Across six 1D and 2D benchmark problems involving the Burgers and Euler equations, numerical results indicate that HyDFVM not only suppresses spurious oscillations and excessive smearing of sharp features, but also more accurately captures the location and structure of shocks and contact discontinuities than state-of-the-art (SOTA) deep learning methods. In particular, HyDFVM achieves up to three orders of magnitude reduction in relative L2-norm error compared with existing SOTA approaches on Burgers problems and 63–70% error reduction on 1D Euler cases, while maintaining stable training behavior and computational costs comparable to physics-informed baselines.
报告人简介：
邹青松，男，中山大学计算机学院教授，科学计算系主任，广东省计算数学学会理事长, 期刊IJNAM和Mathematics 编委。主要研究方向为偏微分方程数值算法，包括有限体积法和深度学习算法。在包括SIAM J Numer Anal, Math Comp, Numer Math等在内的期刊以及包括IJCAI， AAAI等在内的会议上发表论文90多篇。主持国自然面上多项，科技部科技创新AI2030重大项目课题，国家基金委重大研究计划培育项目，广东省重点项目等，获广东省自然科学二等奖（第一完成人）。