Date/Time : 21 Jan 2026 16:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Kim Jeongho, Kyung Hee University

In this talk, I will present two different topics on numerical methods for solving PDEs.

In the first part, I will focus on the numerical methods for two-dimensional quantum mechanical systems interacting with electromagnetic fields. Precisely, we will discuss finite difference time domain method and time splitting Fourier Pseudospectral methods for Chern-Simons-Schrodinger/Dirac equations. In the second part, I will move on to the adaptive finite difference method for solving the Poisson equation. I will introduce the quad/octree structure on which the Poisson equation is solved. This provides a stable Hodge decomposition step in the projection method for incompressible flow.

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Date/Time : 14 Jan 2026 16:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Li Xiaoli, Shandong University

The magnetization structures in the form of topological solitons have become important research interest following the fabrication of various ferromagnetic materials. In this talk we first present new higher-order implicit-explicit (IMEX) schemes for the LLG equation. These schemes are linear, length preserving, modified energy stable and only require solving one elliptic equation at each time step. We show that numerical solutions of these schemes are uniformly bounded without any restriction on the time step size, and establish rigorous error estimates of orders 1 to 5 in a unified framework. Next we present some recent developments in constructing the linear, length preserving and original energy preserving schemes.

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Date/Time : 09 Jan 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Kuang Yang, Guangdong University of Technology

Complex Langevin (CL) is a computational method to circumvent the numerical sign problem with applications in finite-density quantum chromodynamics and the real-time dynamics of quantum field theories. It has long been known that, depending on the simulated system, CL does not always converge correctly. We study the regularization of the complex Langevin method via augmenting the action with a stabilization term. We also show that, in certain situations, this regularization can introduce biases, and we propose several extensions to mitigate these effects and further enhance accuracy. Several numerical experiments in the lattice field theory are carried out to show the effectiveness of our approaches.

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Date/Time : 12 Dec 2025 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Su Chunmei, Tsinghua University

The quality of the mesh is crucial for simulating curvature flows, as standard approaches may fail due to mesh distortion. We first present a series of high-order parametric finite element methods based on the BGN formulation for solving various types of flows involving curves and surfaces. Extensive numerical experiments demonstrate the anticipated high-order accuracy while maintaining favorable mesh quality throughout the evolution process. Secondly, for flows involving multiple geometric structures, such as surface diffusion—which reduces area while preserving volume—we propose a type of structure-preserving method that incorporates two scalar Lagrange multipliers along with two evolution equations related to area and volume, respectively. These schemes effectively preserve the geometric structure at a fully discrete level. Comprehensive numerical experiments illustrate that our methods achieve the desired temporal accuracy, while simultaneously preserving the geometric structure of the surface diffusion.

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Date/Time : 29 Oct 2025 16:30
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Guo Ling, Shanghai Normal University

Neural networks (NNs) are transforming computational approaches in physics and engineering by enabling new ways to integrate data with mathematical laws. This progress allows us to tackle inverse problems and ill-posed systems that are otherwise intractable using traditional methods. Accurately estimating predictive uncertainty is essential for using these models in complex scientific applications, yet remains a major challenge. In this talk, I will introduce a new framework for uncertainty quantification based on the information bottleneck principle (IB-UQ), designed for scientific machine learning tasks such as deep neural regression and neural operator learning. The framework allows for principled control over the information flow from inputs to outputs, resulting in improved uncertainty estimation. Furthermore, I will present a physics-informed extension of IB-UQ, tailored for solving PDE-related problems with noisy or partial observations. The effectiveness of this approach is demonstrated through several numerical examples, highlighting its potential in both data-driven and physics-constrained settings.

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Date/Time : 10 Oct 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Liu Liu, The Chinese University of Hong Kong

In this talk, we introduce a bi-fidelity algorithm for velocity discretization of Boltzmann-type kinetic equations under multiple scalings. The proposed method employs a simpler and computationally cheaper low-fidelity model to capture a small set of significant velocity points through the greedy approach, then evaluates the high-fidelity model only at these few velocity points and to reconstruct a bi-fidelity surrogate. This method, inspired by its previous application in solving uncertainty quantification problem for kinetic models, integrates a simpler collision term of relaxation type in the low-fidelity model and an asymptotic-preserving scheme in the high-fidelity update step. Both linear Boltzmann under diffusive scaling and the nonlinear full Boltzmann in hyperbolic scaling are discussed. The weak asymptotic-preserving property and empirical error bound estimates are shown. Extensive numerical experiments on Boltzmann problems with smooth or discontinuous initial conditions and under various regimes have been carefully studied, which demonstrates the effectiveness and efficiency of our designed numerical schemes. This is a joint work with Nicolas Crouseilles and Zhen Hao.

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Date/Time : 17 Sep 2025 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Li Yifei, University of Tübingen

In this talk, we present a numerical analysis of the Eyles-King-Styles tumour growth model, a free boundary problem with nontrivial bulk-surface coupling. Unlike existing evolving bulk problems or evolving surface problems, this bulk-surface coupling necessitates H^{1/2}-order analysis on the surface Γ. We establish a comprehensive H^{1/2}(Γ) framework that captures the coupling between the bulk and surface. It enables a rigorous convergence analysis for continuous finite elements of polynomial degree at least 3, yielding optimal-order H^1(Ω)/H^{1/2}(Γ) error bounds.

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Date/Time : 10 Sep 2025 16:30
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Wang Zhongjian, Nanyang Technological University

In this talk I will discuss the role of regularity estimate for viscous Hamilton Jacobi equation in showing the optimal iteration complexity (square root of dimension) of the Diffusion model. In our approach to the optimal bound, we only assume the Gaussian tail assumption, which does not require log-concaveness of the distribution. Our Gaussian tail assumption admits distribution of early stopping setting and scalable to infinite dimensions. More recently, we also provide analysis for Follmer process and show the deterministic heat flow is a Lipschitz change of variable between target and Gaussian under the Gaussian tail assumption.

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Date/Time : 04 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Khoat Than, Hanoi University of Science and Technology

Deep neural networks (DNNs) have driven many of the most significant breakthroughs in artificial intelligence in recent years, fundamentally transforming the way we live and work. Tasks that seemed intractable just a decade ago can now be solved with remarkable accuracy by large-scale DNNs. A central reason for their success lies in their ability to generalize: after learning from a finite training set, DNNs often perform surprisingly well on unseen data. Yet, despite this empirical success, the theoretical foundations of generalization in deep learning remain poorly understood, posing a long-standing challenge.

In this talk, I will provide an overview of recent theoretical advances, many of which, despite their elegance, turn out to yield vacuous or impractical guarantees for modern networks. I will then introduce our new approaches, which establish explicit connections between the local behaviors of a DNN across different regions of the data space, the complexity of the data distribution, and the model’s generalization performance. These results reveal novel structural insights and suggest that such perspectives could bring us closer to resolving one of the most fundamental open problems in deep learning.

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