Abstract : Materials modeling and simulation is essential in underpinning the discovery and synthesis of new materials and chemicals with novel functionalities in various key areas like energy and biomedicine. Materials science provides a rich source of problems in computational mathematics. Meanwhile, mathematicians are crucial to address fundamental questions with a solid theoretical foundation. The overarching goal of this minisymposium is to promote academic exchanges and collaborations among researchers working in the exciting and rapidly developing field of mathematics in materials science, especially focusing on the mathematical theory in complex materials as well as the applications of state-of-art machine-learning techniques.
[04090] A framework for a generalization analysis of MLIPs
Format : Online Talk on Zoom
Author(s) :
Yangshuai Wang (University of British Columbia)
Abstract : I will talk about an analytical (as opposed to statistical) approach to demonstrate the generalization of MLIPs and its application on simulating crystalline defects, explaining how the choice of training data and the accuracy of the fit to that training data affect the accuracy of predictions on materials properties.
[04086] A Finite Element Configuration Interaction Method for Wigner Localization
Format : Online Talk on Zoom
Author(s) :
Xue Quan (Beijing Normal University)
Huajie Chen (Beijing Normal University)
Abstract : This work proposes a numerical algorithm to study the Wigner localization phenomenon which carefully treats the many-body correlations. The main features are three-fold: (i) a finite element discretization of the one-body space such that the sharp localization can be captured; (ii) a good initial state obtained by exploiting the strongly correlated limit; and (iii) a selected configuration interaction method by choosing the Slater determinants from (stochastic) gradients.
[05440] Equivariant Tensor Network Potentials
Format : Talk at Waseda University
Author(s) :
Max Hodapp (Materials Center Leoben)
Alexander Shapeev (Skoltech)
Abstract : The computational cost of many state-of-the-art machine-learning interatomic (MLIPs) potentials increases exponentially with the number of atomic features. Low-rank tensor networks can overcome exponential growth in complexity, however, it is often not easy to encode the model symmetries. Here, we propose a formalism for rank-efficient equivariant tensor networks (ETNs) that remain invariant under actions of SO(3), and, using ETNs, develop a new class of MLIPs that demonstrate superior performance over existing MLIPs.
[04136] Planewave approximation for electronic structure calculation of incommensurate systems
Format : Talk at Waseda University
Author(s) :
Ting Wang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences )
Abstract : Incommensurate structures come from stacking the single layers of low-dimensional materials on top of one another with misalignment, such as a twist in orientation. While these structures are of significant physical interest, they pose many theoretical challenges due to the loss of periodicity. Under the planewave framework, we provide a numerical scheme to compute the electronic structure of incommensurate systems based on density functional theory.
[04088] DeePN2: A Deep Learning-Based Non-Newtonian Hydrodynamic Model
Format : Talk at Waseda University
Author(s) :
Lidong Fang (Michigan State University)
Pei Ge (Michigan State University)
Lei Zhang (Shanghai Jiao Tong University)
Weinan E (Peking University)
Huan Lei (Michigan State University)
Abstract : A longstanding problem in the modeling of non-Newtonian hydrodynamics of polymeric flows is the availability of reliable and interpretable hydrodynamic models that faithfully encode the underlying microscale polymer dynamics. The main complication arises from the long polymer relaxation time, the complex molecular structure, and the heterogeneous interaction. DeePN2, a deep learning-based non-Newtonian hydrodynamic model, has been proposed and has shown some success in systematically passing the micro-scale structural mechanics information to the macro-scale hydrodynamics for suspensions with simple polymer conformation and bond potential. The model retains a multi-scaled nature by mapping the polymer configurations into a set of symmetry-preserving macro-scale features. The extended constitutive laws for these macro-scale features can be directly learned from the kinetics of their micro-scale counterparts. In this paper, we develop DeePN2 using more complex micro-structural models. We show that DeePN2 can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention.
[04357] Numerical Analysis of Structural Green's Function in Multiple Scattering Theory
Format : Talk at Waseda University
Author(s) :
Xiaoxu Li (Beijing Normal University)
Huajie Chen (Beijing Normal University)
Abstract : This work studies the multiple scattering theory, also called Green's function method, in the electronic structure calculations of disordered systems from a mathematical perspective. By analyzing the structural Green's function, which can be viewed as the representation of Green's function in some basis, we will (a) improve the space truncation way to accelerate model convergence; (b) establish a mathematical analysis framework for Green's function and provide a prior error estimate; (c) design two linear-scaling algorithms with systematically controllable error.
[04087] Variational Monte Carlo from a Continuous Viewpoint
Format : Talk at Waseda University
Author(s) :
Juerong Feng (Beijing Normal University)
Huajie Chen (Beijing Normal University)
Abstract : We study the variational Monte Carlo (VMC) method for quantum many-body problems based on data-driven wavefunction ansatz. We present a continuous stochastic gradient flow formulation for the VMC algorithm and show the large-time asymptotics with an explicit decay bound in terms of the many-body Hamiltonian and the wavefunction parameterization. In particular, we perform a careful analysis of the interactions between the approximation error of the ground state wavefunction and the generalization error of the sampling.
