Date/Time : 03 Feb 2025 16:30
Venue : S16 #03-04
Speaker : Lin Bo, Huairou Laboratory

In this talk, I will introduce a flexible and high-order hybridizable discontinuous Galerkin (HDG) scheme with harmonic averaging technique to solve the drift-diffusion model for semiconductor devices. The proposed scheme combines the robustness of the Scharfetter-Gummel method, which is a classical discretization for this model, with the high-order accuracy and hp-flexibility by the HDG scheme. Gradient-based indicators are introduced to utilize the hp-adaptivity. Numerical examples suggest that the proposed scheme does not exhibit oscillations even when applied to heavily doped and sharp PN-junctions.

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Date/Time : 24 Jan 2025 10:00
Venue : S17 #05-11 (SR5)
Speaker : Wu Xinming, Fudan University

In this talk, we propose a finite element method for solving the coupled model of classical drift-diffusion equations and Schrödinger-Poisson equations in simulating a resonant tunneling diode (RTD). The coupling coefficient $\Theta$ and the quantum electron density $n^{\rm qu}$ are defined by weighted integrals of $|\psi_p|^2$ where $\psi_p$ is the wave function of Schrödinger equation for each momentum $p\in\mathbb{R}$. We first prove a growth rate of $|\psi_p|$ as $|p|\to +\infty$. This enables us to truncate the momentum space $\mathbb{R}$ to a bounded interval $[-P,P]$, which corresponds to an energy interval $[0,E_P]$. Based on a posteriori error estimate for computing $\Theta$ and $n^{\rm qu}$, we propose an energy-adaptive algorithm. The algorithm reduces the number of nodes greatly by capturing resonance peaks accurately and adjusting the partition of $[0,E_P]$ adaptively. Numerical experiment for an RTD shows that, based on energy-adaptive grids, the Gummel method for solving the coupled model is robust and can converge in several iterative steps.

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Date/Time : 21 Jan 2025 16:00
Venue : S17 #04-05 (SR2)
Speaker : Yunpeng Shi, University of California, Davis

In this talk, we explore two classical image processing tasks motivated by cryo-electron microscopy imaging: tomographic image denoising and rigid image registration. Both tasks inherently involve operations of 2D rotations, where leveraging specific transforms can significantly enhance the speed and robustness of the algorithms.

In the first part of the talk, I will introduce an unsupervised image denoiser based on estimating the covariance matrix of clean images. A key insight is that if the image manifold is invariant under global in-plane rotations, this symmetry can be exploited to accelerate computations and reduce dimensionality. I will discuss recent advances in fast expansion into steerable bases that allow us to efficiently utilize this rotational symmetry, leading to a thousand fold improvement in the speed of covariance estimation over existing methods. This technique has been successfully applied to joint deconvolution and denoising of large-scale, real-world cryo-EM images.

In the second part, I will present a fast algorithm for aligning images using optimal transport. Our method leverages the sliced Wasserstein distance by computing the 1D Wasserstein distance between radial line projections of input images. By applying a special transform to the frequency domain, we achieve efficient alignment of two L by L images in O(L^2 log L) operations — matching the complexity of alignment using Euclidean distance. I will demonstrate the robustness of our method to translations and deformations.

Finally, I will comment on the practical limitations of both methods and discuss open questions that remain, highlighting areas for future exploration.

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Date/Time : 12 Dec 2024 16:30
Venue : S17 #04-04 (SR3)
Speaker : Huang Jizu, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

In this talk, we propose a novel accuracy-preserved tensor-train (APTT) method to solve the Boltzmann-BGK equation. We use the Crank-Nicolson Leap Frog (CNLF) scheme for temporal discretization, based on which the collision term can be evaluated only once at each time step. A second-order scheme based on the upwind rule is employed for spatial discretization to match the accuracy of the CNLF scheme. At each time step, the linear system is constructed with the tensor-train (TT) format, where the matrix, the right-hand side, and the collision term involved in the linear system are all represented using the low-rank TT format. Based on such a representation, an efficient and effective iterative solver can be implemented for solving the linear system, which can reduce two orders of magnitude in terms of both time and memory costs compared with classical methods. We present a theoretical analysis to show that the proposed APTT method can maintain accuracy and an extensive set of 3D3V Boltzmann-BGK test examples to demonstrate its effectiveness.

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Date/Time : 12 Nov 2024 16:00
Venue : S16 #03-06
Speaker : Cao Yu, Shanghai Jiao Tong University

Quantum dynamical systems are essential models for understanding the time evolution of our nature. The mathematically simplest models in this context are quantum semigroup dynamics. When a system is closed (as special instances), its dynamics are described by Schrödinger’s equation or equivalently, the von Neumann equation. There is growing interest in simulating the time-dependent Schrödinger’s equation using quantum devices due to its applications in quantum adiabatic computing, quantum control theory, and solving partial differential equations (PDEs). We will explore Sambe-Howland’s clock as a unifying framework for addressing time-dependent problems through time-independent techniques. This approach is compatible with both analog and digital quantum computing and can address some unresolved questions in recent studies. On the other hand, in open systems, semigroup dynamics are described by the Lindblad equation, which models the interaction between the system and its environment. In this talk, we will also discuss a family of structure-preserving algorithms for simulating Lindblad equations, which have close connections to designing stochastic and quantum algorithms.

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Date/Time : 30 Oct 2024 16:30
Venue : S17 #05-11 (SR5)
Speaker : Wang Yangshuai, National University of Singapore

The success of molecular simulations hinges on the accuracy and efficiency of force fields. Recently, machine-learned interatomic potentials (MLIPs) have revolutionized the field by bridging the gap between high-accuracy ab initio models and classical force fields. MLIPs have quickly become an essential tool in computational atomic simulations, leading to numerous breakthroughs across various scientific domains. This talk will provide an overview of the latest advancements in MLIPs, with a focus on their applications in materials science. I will start by discussing the Atomic Cluster Expansion (ACE) method, a linear model known for its strong predictive performance in small systems. To address the limitations of linear models, I will introduce MACE, an advanced potential based on ACE and enhanced by Message Passing Neural Networks (MPNN), tailored for complex systems with superior generalization and robustness. The focus will then shift to MACE-MP-0, a pre-trained foundation model built on MACE, highlighting its predictive accuracy and the advantages of fine-tuning across diverse materials applications. I will conclude by discussing future MLIP extensions that could further enhance molecular modeling and simulation in materials science and chemistry.

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Date/Time : 16 Oct 2024 16:30
Venue : S17 #05-11 (SR5)
Speaker : Gu Yejun, Institute of High Performance Computing

Innovations in automated material design demand models that predict both mechanical properties and inherent uncertainties. Traditional deterministic models, reliant on fitting parameters subject to experimental conditions, fall short in addressing these needs. This study introduces a parameter-free statistical methodology tailored for alloy prediction and design. Centered on a data-driven mixed density neural network, our approach uses existing experimental data from traditional alloys to develop a new constitutive rule for the evolution of dislocation density. This methodology allows for predicting the uncertainty in the resulting stress-strain curves and quantifies the relevant microstructures that must be measured experimentally for more of a deterministic prediction. Further, we delve into the origins of uncertainty, identifying and narrowing the gap between experiments and simulations. Our findings highlight potential solutions for bridging experimental-simulation discrepancies and offer a reliable yet efficient path to developing new alloys.

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Date/Time : 11 Sep 2024 16:30
Venue : S17 #06-11 (SR6)
Speaker : Yang Liu, National University of Singapore

Can we build a single large model for a wide range of PDE-related scientific learning tasks? Can this model generalize to new PDEs without any fine-tuning? In-context operator learning and the corresponding model In-Context Operator Networks (ICON) represent an initial exploration of these questions. We present a detailed methodology for solving PDE problems with ICON, and show how a single ICON model can make forward and reverse predictions for different equations with different strides, provided with appropriately designed data prompts. We show positive evidence for the questions above, through a study on 1D scalar nonlinear conservation laws, a family of PDEs with temporal evolution. In particular, we show that an ICON model trained on conservation laws with cubic flux functions can generalize well to some other flux functions of more general forms, without fine-tuning. We will also discuss different theoretical interpretations of in-context learning.

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Date/Time : 04 Sep 2024 16:30
Venue : S17 #06-11 (SR6)
Speaker : Lin Bo, National University of Singapore

This talk focuses on the development of time-dependent regularized 13-moment equations for general elastic collision models within the linear regime. The detailed derivation demonstrates that these proposed equations exhibit super-Burnett order for small Knudsen numbers and feature a symmetric structure. A novel modification to stable boundary conditions is introduced to remove boundary layers. The effectiveness of the model is validated through numerical simulations of channel flows.

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