arXiv subjects

Nan Feng

Publications and source records attributed to Nan Feng.

9 recordsLinked to original sources

arXiv2026

Amortized Variational Inference for Joint Posterior and Predictive Distributions in Bayesian Uncertainty Quantification

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior distribution of model parameters, and then propagating posterior samples through the predictive model via Monte Carlo simulation. This sequential workflow can be computationally demanding, particularly for high-fidelity models such as those governed by partial differential equations. We propose a variational Bayesian framework that directly targets the posterior-predictive distribution and jointly learns variational approximations of both the posterior and the corresponding predictive distribution. The formulation introduces a variational upper bound on the Kullback--Leibler divergence together with moment-based regularization terms. The variational distributions are trained in an amortized manner, shifting computational effort to an offline stage and enabling efficient online inference. Numerical experiments ranging from analytical benchmarks to a finite-element solid mechanics problem demonstrate that the proposed method achieves more accurate predictive distributions than conventional two-stage variational inference, while substantially reducing the cost of online predictive inference.

stat.ML↗

arXiv2025

Predicting performance-related properties of refrigerant based on tailored small-molecule functional group contribution

As current group contribution (GC) methods are mostly proposed for a wide size-range of molecules, applying them to property prediction of small refrigerant molecules could lead to unacceptable errors. In this sense, for the design of novel refrigerants and refrigeration systems, tailoring GC-based models specifically fitted to refrigerant molecules is of great interest. In this work, databases of potential refrigerant molecules are first collected, focusing on five key properties related to the operational efficiency of refrigeration systems, namely normal boiling point, critical temperature, critical pressure, enthalpy of vaporization, and acentric factor. Based on tailored small-molecule groups, the GC method is combined with machine learning (ML) to model these performance-related properties. Following the development of GC-ML models, their performance is analyzed to highlight the potential group-to-property contributions. Additionally, the refrigerant property databases are extended internally and externally, based on which examples are presented to highlight the significance of the developed models.

physics.chem-ph↗

arXiv2025

Finite Strain Robust Topology Optimization Considering Multiple Uncertainties

This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry uncertainties are incorporated within the topology optimization framework and are modeled by random vectors or random fields. A stochastic perturbation method is adopted to quantify uncertainties, and analytical adjoint sensitivities are derived for efficient gradient-based optimization. Moreover, the mesh distortion of low-density elements under finite deformations is handled by an adaptive linear energy interpolation scheme. The proposed robust topology optimization framework is applied to several examples, and the effects of different uncertain sources on the optimized topologies are systematically investigated. As demonstrated, robust designs are less sensitive to the variation of target uncertain sources than deterministic designs. Finally, it is shown that incorporating symmetry-breaking uncertainties in the topology optimization framework promotes stable designs compared to the deterministic counterpart, where -- when no stability constraint is included -- can lead to unstable designs.

cs.CE↗

arXiv2024

Multi-View Empowered Structural Graph Wordification for Language Models

Significant efforts have been dedicated to integrating the powerful Large Language Models (LLMs) with diverse modalities, particularly focusing on the fusion of language, vision and audio data. However, the graph-structured data, which is inherently rich in structural and domain-specific knowledge, has not yet been gracefully adapted to LLMs. Existing methods either describe the graph with raw text, suffering the loss of graph structural information, or feed Graph Neural Network (GNN) embeddings into LLMs at the cost of losing explainable prompt semantics. To bridge this gap, we introduce an end-to-end modality-aligning framework for LLM-graph alignment: Dual-Residual Vector Quantized-Variational AutoEncoder, namely Dr.E. Our approach is purposefully designed to facilitate token-level alignment with LLMs, enabling an effective translation of the intrinsic `language' of graphs into comprehensible natural language. We also manage to enhance LLMs' more robust structural understanding of graphs by incorporating multiple views of the central nodes based on their surrounding nodes at various distances. Our experimental evaluations on standard graph tasks demonstrate competitive performance against other state-of-the-art (SOTA) approaches. Additionally, our framework ensures certain visual interpretability, efficiency, and robustness, marking the promising successful endeavor to achieve token-level alignment between LLMs and GNNs. Our code is available at: https://github.com/Timothy914/Dr.E.

cs.CL↗

arXiv2024

Phase transitions in typical fluorite-type ferroelectrics

While ferroelectric hafnia ($\mathrm{HfO_2}$) has become a technically important material for microelectronics, the physical origin of its ferroelectricity remains poorly understood. The tetragonal $P4_2/nmc$ phase is commonly assigned as its paraelectric mother phase but has no soft mode at the Brillouin zone center. In this work, we propose that the paraelectric-ferroelectric transition in hafnia-like $Pca2_1$ ferroelectric family can be described by a $Pcca$-$Pca2_1$ transition, where the $Pcca$ mother phase will evolve into either the $Pca2_1$ ferroelectric phase or the centrosymmetric $P2_1/c$ monoclinic phase, depending on the strain conditions. The $Pcca$ phase is directly linked to both phases in the context of continuous phase transition. Hafnia is regarded as a special case of this family, in that it has accidental atomic degeneracy because all anions are oxygen. The theory is also correlated to the seven-coordination theory that explains the ferroelectricity in hafnia from a chemical perspective. In addition, the strain conditions to promote the ferroelectric phase in hafnia are discussed.

cond-mat.mtrl-sci↗

arXiv2023

Bi-discriminator Domain Adversarial Neural Networks with Class-Level Gradient Alignment

Unsupervised domain adaptation aims to transfer rich knowledge from the annotated source domain to the unlabeled target domain with the same label space. One prevalent solution is the bi-discriminator domain adversarial network, which strives to identify target domain samples outside the support of the source domain distribution and enforces their classification to be consistent on both discriminators. Despite being effective, agnostic accuracy and overconfident estimation for out-of-distribution samples hinder its further performance improvement. To address the above challenges, we propose a novel bi-discriminator domain adversarial neural network with class-level gradient alignment, i.e. BACG. BACG resorts to gradient signals and second-order probability estimation for better alignment of domain distributions. Specifically, for accuracy-awareness, we first design an optimizable nearest neighbor algorithm to obtain pseudo-labels of samples in the target domain, and then enforce the backward gradient approximation of the two discriminators at the class level. Furthermore, following evidential learning theory, we transform the traditional softmax-based optimization method into a Multinomial Dirichlet hierarchical model to infer the class probability distribution as well as samples uncertainty, thereby alleviating misestimation of out-of-distribution samples and guaranteeing high-quality classes alignment. In addition, inspired by contrastive learning, we develop a memory bank-based variant, i.e. Fast-BACG, which can greatly shorten the training process at the cost of a minor decrease in accuracy. Extensive experiments and detailed theoretical analysis on four benchmark data sets validate the effectiveness and robustness of our algorithm.

cs.CV↗

arXiv2021

On the Application of Data-Driven Deep Neural Networks in Linear and Nonlinear Structural Dynamics

The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations, for given input (harmonic) excitations. In particular, the focus is on the development of efficient network architectures using fully-connected, sparsely-connected, and convolutional network layers, and on the corresponding training strategies that can provide a balance between the overall network complexity and prediction accuracy in the target dataspaces. For linear dynamics, sparsity patterns of the weight matrix in the network layers are used to construct convolutional DNNs with sparse layers. For nonlinear dynamics, it is shown that sparsity in network layers is lost, and efficient DNNs architectures with fully-connected and convolutional network layers are explored. A transfer learning strategy is also introduced to successfully train the proposed DNNs, and various loading factors that influence the network architectures are studied. It is shown that the proposed DNNs can be used as effective and accurate surrogates for predicting linear and nonlinear dynamical responses under harmonic loadings.

cs.LG↗

arXiv2020

Computational frameworks for homogenization and multiscale stability analyses of nonlinear periodic metamaterials

This paper presents a consistent computational framework for multiscale 1st order finite strain homogenization and stability analyses of rate-independent solids with periodic microstructures. Based on the principle of multiscale virtual power, the homogenization formulation is built on a priori discretized microstructure, and algorithms for computing the matrix representations of the homogenized stresses and tangent moduli are consistently derived. The homogenization results lose their validity at the onset of 1st bifurcation, which can be computed from multiscale stability analysis. The multiscale instabilities include: a) microscale structural instability which is calculated by Bloch wave analysis; and b) macroscale material instability which is calculated by rank-1 convexity checks on the homogenized tangent moduli. Details on the implementation of the Bloch wave analysis are provided, including the selection of the wave vector space and the retrieval of the real-valued buckling mode from the complex-valued Bloch wave. Three methods are detailed for solving the resulted constrained eigenvalue problem - two condensation methods and a null-space based projection method. Both implementations of the homogenization and stability analyses are validated using numerical examples including hyperelastic and elastoplastic metamaterials. Various microscale buckling phenomena are also demonstrated by examining several representative metamaterial examples. Aligned with theoretical results, the numerical results show that the microscopic long wavelength buckling can be equivalently detected by the loss of rank-1 convexity of the homogenized tangent moduli.

cs.CE↗

arXiv2018

Possible structural origin of superconductivity in Sr-doped Bi2Se3

Doping bismuth selenide (Bi2Se3) with elements such as copper and strontium (Sr) can induce superconductivity, making the doped materials interesting candidates to explore potential topological superconducting behaviors. It was thought that the superconductivity of doped Bi2Se3 was induced by dopant atoms intercalated in van der Waals gaps. However, several experiments have shown that the intercalation of dopant atoms may not necessarily make doped Bi2Se3 superconducting. Thus, the structural origin of superconductivity in doped Bi2Se3 remains an open question. Herein, we combined material synthesis and characterization, high-resolution transmission electron microscopy, and first-principles calculations to study the doping structure of Sr-doped Bi2Se3. We found that the emergence of superconductivity is strongly related with n-type dopant atoms. Atomic-level energy-dispersive X-ray mapping revealed various n-type Sr dopants that occupy intercalated and interstitial positions. First-principles calculations showed that the formation energy of a specific interstitial Sr doping position depends strongly on Sr doping level. This site changes from a metastable position at low Sr doping level to a stable position at high Sr doping level. The calculation results explain why quenching is necessary to obtain superconducting samples when the Sr doping level is low and also why slow furnace cooling can yield superconducting samples when the Sr doping level is high. Our findings suggest that Sr atoms doped at interstitial locations, instead of those intercalated in van der Waals gaps, are most likely to be responsible for the emergence of superconductivity in Sr-doped Bi2Se3.

cond-mat.supr-con↗