Fall 2026 Schedule

Friday 2:00 pm - 3:15 pm (CST)

Location: 2122 STEM-AG

For any questions or requests, please contact Zezhong Zhang (zez0002@auburn.edu)

Week 1: 

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Week 2: 

Date and time: Aug 28 (Friday) 2:00 pm - 3:15 pm @ 2122 STEM-AG

Speaker: Shu Liu (Florida State University)

Title: A Natural Primal-Dual Gradient Method for Adversarial Neural Network Training for Solving Partial Differential Equations

Abstract: Computing high-dimensional PDEs remains an important yet challenging problem in computational mathematics. We propose a scalable deep learning–based algorithm for solving PDEs that integrates preconditioned gradient methods with adversarial training. We reformulate the problem as an inf–sup saddle-point problem and apply the Primal–Dual Hybrid Gradient algorithm. To enhance efficiency and stability, we introduce suitable preconditioning operators into the proximal steps of the PDHG algorithm, which leads to a natural gradient ascent–descent scheme for updating neural network parameters. The resulting natural gradients are evaluated using the Krylov subspace method (MINRES), allowing the inversion of preconditioning matrices to be handled through matrix–vector products. Convergence guarantees are established for time-continuous formulation of the algorithm when applied to linear equations, particularly elliptic PDEs in divergence form. We further validate the proposed method on a broad range of linear and nonlinear PDEs across varying dimensions. Numerical results demonstrate that our approach is both efficient and robust, exhibiting more stable convergence and higher accuracy than benchmark deep learning–based solvers.

Week 3 

Date and time: Sep 4 (Friday) 2:00 pm - 3:15 pm @ 2122 STEM-AG

Speaker: Xuenan Li (Purdue University)

Title: Pseudo-magnetism in a strained discrete honeycomb lattice

Abstract: Slowly-varying nonuniform strain in honeycomb media can generate an effective pseudo-magnetic field, even though the underlying medium is non-magnetic. This phenomenon was first discovered in graphene and later in photonic crystals, and other physical settings. In this talk, I will start from a discrete nearest-neighbor tight-binding model for a nonuniformly strained honeycomb medium. I will then show how this model leads to a continuum magnetic Dirac Hamiltonian that describes wave packets concentrated near a Dirac point of the undeformed structure. I will focus on unidirectional deformations with bounded gradients that preserve translation invariance along the armchair direction. In this setting, we prove the existence of eigenmodes that behave like plane waves along the armchair direction and are strongly localized in the transverse direction, together with quantitative correction estimates. These results apply to deformations that produce an approximately constant pseudo-magnetic field perpendicular to the plane. They also lead to nearly flat bands and, as a consequence, a very high density of states. These analytical results are also supported by numerical simulations of the corresponding deformations. This is joint work with Michael I. Weinstein.

Week 4: 

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Week 5: 

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Week 6: 

Date and time: Sep 25 (Friday) 2:00 pm - 3:15 pm @ 2122 STEM-AG

Speaker: Ruoyu Hu (Auburn University)

Title: Advanced Filtering and Data Assimilation for Partially Observed Dynamical Systems: From State Estimation to Control

Abstract: Data assimilation combines model predictions with noisy or partial observations to estimate the evolving state of a dynamical system. In this talk, I will discuss the Ensemble Score Filter (EnSF), a training-free score-based method for nonlinear and high-dimensional data assimilation. Applications include two-phase flow in porous media under uncertain permeability and real-data energy-consumption forecasting with a pretrained black-box forward model. I will then turn to a recent extension from state estimation to control in power-grid applications. Using a customized transmission-network simulator, we study how load uncertainty affects heuristic and reinforcement-learning controllers, and whether EnSF-based load correction can improve downstream grid operation. Together, these examples illustrate how modern data assimilation methods can connect state estimation, forecast correction, and sequential decision-making in partially observed dynamical systems.

Week 7: (Cancelled)

Date and time: Oct 2 (Friday) 2:00 pm - 3:15 pm @ 2122 STEM-AG

Speaker: Chunmei Wang (University of Florida)

Title: TBD

Abstract: TBD

Week 8: 

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Week 9: 

Date and time: Oct 16 (Friday) 2:00 pm - 3:15 pm @ 2122 STEM-AG

Speaker: Yiran Wang (The University of Alabama)

Title: Multiscale Modeling, Fast Solvers, and Scientific Machine Learning for Flow and Transport in Heterogeneous Media

Abstract: Complex flow and transport phenomena in heterogeneous media pose major challenges for both classical numerical simulation and modern data-driven modeling. In this talk, I will present my work on multiscale modeling and fast computational methods for PDEs, and discuss how these ideas can be integrated with scientific machine learning to construct efficient and reliable models for high-dimensional, parameter-dependent systems. I will highlight methodologies that combine multiscale structure, reduced-order representations, and physics-based constraints to accelerate simulation while maintaining fidelity to the underlying dynamics. I will then describe how these ideas extend naturally to operator learning and inverse problems, where one seeks to learn solution operators or recover hidden parameters from limited and noisy observations. The overall goal is to develop mathematically grounded, computationally efficient, and physically interpretable learning frameworks for PDEs arising in flow and transport. I will conclude with future directions on multiscale operator modeling, adaptive discretization, and data-driven discovery of effective models, with potential applications to porous media, transport processes, and other complex systems.

Week 10: 

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Week 11: 

Date and time: Oct 30 (Friday) 2:00 pm - 3:15 pm @ 2122 STEM-AG

Speaker: Xiaoliang Wan (Louisiana State University)

Title: Deep Adaptive Sampling for Neural PDE Solvers

Abstract: Neural PDE solvers rely on finite sets of random training samples, and their numerical accuracy can suffer when the sampling distribution does not reflect the structure of the solution. Uniform sampling may place too few points in small regions containing sharp features. A common adaptive strategy selects informative points from a large uniform candidate pool, but it remains constrained by that pool: critical regions may receive too few candidates, and the candidates within them may not adequately cover the most informative features. In this talk, we present deep adaptive sampling (DAS) and adversarial adaptive sampling (AAS), which update the sampling distribution and generate new points as training proceeds. We discuss these methods for physics-informed neural networks and describe how adaptive sampling also applies to deep BSDE and variational solvers. Applications include elliptic equations with sharp peaks, parametric cavity flow, committor functions for rare transitions, and a Hamilton–Jacobi–Bellman equation. Numerical results illustrate improvements in accuracy and sample efficiency.

Week 12: 

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Week 13: 

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Week 14: 

Speaker: Jiangyu Yu

Title: TBD

Abstract: TBD

Week 15: 

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Week 16: 

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