报告题目：FrFNO:Injecting the analytic Mittag-Leffler propagator into a resolution-robust neural operator for space-time fractional PDEs

报告人：庞国飞（东南大学）

报告时间：2026年10月29日（周四）14:00-16:00

报告地点：江宁校区乐学楼1118

主办单位：91麻豆 水力学与流体力学研究所

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报告简介：

Fractional partial differential equations couple a memory-dependent time derivative with a nonlocal fractional Laplacian, and their repeated solution under varying fractional orders, initial data, or diffusivity fields is computationally expensive. Neural operators offer a fast surrogate, but standard architectures must relearn the dominant linear fractional evolution from data. We propose the Fractional Fourier Neural Operator (FrFNO), a resolution-robust conditional operator. It injects the analytic Mittag--Leffler response of the frozen linear part as a once-precomputed, resolution-independent propagator table, and trains a spectral convolutional network only on the residual induced by variable coefficients and nonlinear advection, conditioned continuously on both fractional orders. The central theoretical result is that under zero-shot super-resolution the injected propagator fills the out-of-band modes that a standard Fourier neural operator sets to zero, replacing the out-of-band full-field tail by the smaller residual tail (a K-independent constant-factor reduction under weak perturbation). On a nonlinear two-dimensional space--time fractional Burgers problem FrFNO achieves the lowest relative L^2 error among six baselines (FNO, PINO, PDNO, CNO, DeepONet, U-Net) at the training resolution and under zero-shot super-resolution, yields the smallest spectral phase error, and remains the best at the integer-order limit. The same construction extends to coupled fractional systems such as fractional Allen-Cahn and Navier--Stokes equations.

报告人简介：

庞国飞，东南大学数学学院副研究员。研究课题涉及计算数学与计算力学，研究方向为统计机器学习应用及其数学理论、科学计算中的机器学习方法、智能流体等。目前已在SIAM Journal on Scientific Computing、Journal of Computational Physics、Nature Machine Intelligence和Physics of Fluids等计算数学/力学和机器学习领域的期刊上发表论文30余篇，Google总引用9000余次。主持完成国家自然基金一项，教育部重点实验室开放基金项目两项，GF项目1项，参与国家面上一项、江苏省面上项目一项。 讲授面上本科生课程《数学建模与数学实验》、数学学院本科生专业课《数据结构与算法》《机器学习》。获评东南大学2024“全校最受欢迎老师（提名）”、东南大学2025届最受毕业生欢迎教师、东南大学优秀班主任标兵等称号，获得江苏省高校第十一届数学基础课教师授课竞赛一等奖。