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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Date/Time : 28 Aug 2024 16:30
Venue : S17 #04-05 (SR2)
Speaker : Zhang Xiaolong, Nanyang Technological University & Hunan Normal University

The Logarithmic Schrödinger Equation (LogSE) exhibits rich dynamics and possesses unique properties compared to the standard Schrödinger equation with cubic nonlinearity. However, the logarithmic nonlinear term $f(u)=uln(∣u∣^2)$ presents significant challenges for both numerical solutions and error analysis, primarily due to low regularity and singularity. In this talk, we will characterize this low regularity within suitable fractional Sobolev spaces and derive the first set of error estimates for the time-splitting Fourier spectral methods with initial data of fractional-order regularity. These results are supported by recent regularity estimates for the LogSE from the PDE community and ample numerical evidence.(Joint work with Prof. Li-Lian Wang, NTU)

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Date/Time : 08 May 2024 16:30
Venue : S17 #04-05 (SR2)
Speaker : Junfu Yao, Johns Hopkins University

Minimal surfaces are known as critical points to the area functional. In this talk, I’ll focus on the question of finding minimal surfaces with prescribed behavior at the asymptotic infinity. This is called the asymptotic Plateau problem. I’ll briefly review previous results and present a min-max theory for finding solutions to this problem. As a corollary of the mountain-pass theorem, I’ll also discuss a topological uniqueness result.

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Date/Time : 20 Mar 2024 16:30
Venue : S17 #05-11 (SR5)
Speaker : Jin Zeyu, Peking University

A promising approach to investigating high-dimensional problems is to identify their intrinsically low-dimensional features, which can be achieved through recently developed techniques for effective low-dimensional representation of functions such as machine learning. Based on available finite-dimensional approximate solution manifolds, we propose a novel model reduction framework for kinetic equations. The method employs projections onto tangent bundles of approximate manifolds, naturally resulting in first-order hyperbolic systems. Under certain conditions on the approximate manifolds, the reduced models preserve several crucial properties, including hyperbolicity, conservation laws, entropy dissipation, finite propagation speed, and linear stability. For the first time, we rigorously discuss the relation between the H-theorem of kinetic equations and the linear stability conditions of reduced systems, determining the choice of Riemannian metrics involved in the model reduction. The framework is widely applicable for the model reduction of many models in kinetic theory. Joint work with Ruo Li.

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Date/Time : 13 Mar 2024 16:30
Venue : S17 #05-11 (SR5)
Speaker : Lin Bo, National University of Singapore

The committor function is a central object for quantifying the transitions between metastable states of dynamical systems. Recently, a number of computational methods based on deep neural networks have been developed for computing the high-dimensional committor function. The success of the methods relies on sampling adequate data for the transition, which still is a challenging task for complex systems at low temperatures. This talk will present a deep learning method with two novel adaptive sampling schemes. In the two schemes, the data are generated actively from a modified potential where the bias potential is constructed from the learned committor function. We theoretically show that the data in the two schemes are uniformly distributed along the transition tube. The efficiency of the method is illustrated on high-dimensional systems including the alanine dipeptide and a dimer system immersed in the water box.

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