arXiv subjects

Chu-Liang Fu

Publications and source records attributed to Chu-Liang Fu.

10 recordsLinked to original sources

arXiv2026

Tensor-Network Finite Elements for Analytic Operator Equations

Operator equations (OEs) underpin quantitative modeling across science and engineering. Finite-element (FE) methods discretize continuous OEs into finite-dimensional algebraic systems, whereas tensor networks (TNs) provide flexible variational representations of correlated discrete systems. Here, we develop a framework that connects FE with TN for analytic OEs. The power of this method comes from its ability to convert highly non-linear partial differential equations into linear matrix equations. In particular, we show that FE discretization induces a hierarchy of multilinear interaction tensors, through which differential, integral, nonlinear, memory, and delay equations can be expressed within a common algebraic structure. The resulting systems are reformulated as weighted-residual optimization problems over TN degrees of freedom. Matrix-product-state calculations for one-dimensional linear and nonlinear diffusion reproduce conventional solutions with controlled error while preserving continuity and Neumann boundary conditions. The framework provides a common variational language for analytic OEs and establishes a direct connection between FE numerical formalism and TN variational algorithms, offering a general foundation for TN-based and quantum-inspired approaches to solving OEs.

math.NA↗

arXiv2026

Probing Non-Equilibrium Grain Boundary Dynamics with XPCS and Domain-Adaptive Machine Learning

Grain-boundary (GB) dynamics control the stability, mechanical, and functional response of nanocrystalline materials, but direct experimental access to their slow non-equilibrium motion has been limited. Here we establish X-ray photon correlation spectroscopy (XPCS), combined with domain-adaptive machine learning, as a quantitative probe of GB dynamics. Temperature- and grain-size-dependent two-time XPCS measurements in nanocrystalline silicon reveal pronounced departures from time-translation invariance, showing that GB relaxation can remain far from equilibrium over experimental timescales. However, direct extraction of quantitative physical information from these high-dimensional, noisy fluctuation maps faces a significant challenge. To overcome this barrier, we develop a semi-supervised learning framework that transfers physical parameter labels from continuum simulations to unlabeled experimental XPCS maps through domain-adaptive representation alignment. This AI-augmented approach enables the extraction of key kinetic parameters, including bulk diffusivity, GB stiffness, and effective GB concentration, directly from experimental XPCS measurements. Our results show how machine learning can transform indirect fluctuation signals into quantitative materials dynamics, providing a general route to study non-equilibrium defect motion in solids.

cond-mat.mtrl-sci↗

arXiv2026

Coupling Lattice Distortion and Cation Disorder to Control Li-ion Transport in Cation-Disordered Rocksalt Oxides

Cation-disordered solids offer a rich chemical landscape where local coordination, lattice responses, and configurational disorder collectively, yet often implicitly, govern ion transport. In cation-disordered rocksalt oxides, Li+ diffusion has conventionally been rationalized by the static 0-transition-metal (0-TM) percolation rule, which assumes an ideal, passive lattice and thus fails to capture experimentally accessible capacities. Here, we show that lattice distortion is an essential, previously overlooked degree of freedom that actively reshapes Li+ percolation networks. By developing a lattice-responsive framework combining Monte Carlo sampling of cation configurations with machine-learning-accelerated molecular dynamics, we quantitatively predict Li+ percolation and electrochemical capacities within 5% of experiment. Our results reveal a causal coupling between lattice distortion and cation short-range order: enhanced local distortions precede and suppress short-range ordering, activating Li+ migration through nominally inaccessible 1-TM channels, fundamentally extending percolation beyond the 0-TM paradigm. Guided by this, we design and synthesize a high-entropy oxide, Li1.2Mn0.2Ti0.2V0.2Mo0.2O2, which exhibits enhanced distortion and achieves a 71.9% Li+ percolation network, surpassing 65.8% in Li1.2Mn0.4Ti0.4O2, delivering 256.3 mAh/g capacity, closely matching our prediction of 255.1 mAh/g. These findings establish lattice distortion as an active control parameter for ion transport, revising percolation concepts and offering a general design principle beyond metal-ion cathodes.

cond-mat.mtrl-sci↗

arXiv2025

Tuning chiral anomaly signature in a Dirac semimetal via fast-ion implantation

Cd$_3$As$_2$ is a prototypical Dirac semimetal that hosts a chiral anomaly and thereby functions as a platform to test high-energy physics hypotheses and to realize energy efficient applications. Here we use a combination of accelerator-based fast ion implantation and theory-driven planning to enhance the negative longitudinal magnetoresistance (NLMR)--a signature of a chiral anomaly--in Nb-doped Cd$_3$As$_2$ thin films. High-energy ion implantation is commonly used to investigate semiconductors and nuclear materials but is rarely employed to study quantum materials. We use electrical transport and transmission electron microscopy to characterize the NLMR and the crystallinity of Nb-doped Cd$_3$As$_2$ thin films. We find surface-doped Nb-Cd$_3$As$_2$ thin films display a maximum NLMR around $B = 7$ T and bulk-doped Nb-Cd$_3$As$_2$ thin films display a maximum NLMR over $B = 9$ T--all while maintaining crystallinity. This is more than a 100% relative enhancement of the maximum NLMR compared to pristine Cd$_3$As$_2$ thin films ($B = 4$ T). Our work demonstrates the potential of high-energy ion implantation as a practical route to realize chiralitronic functionalities in topological semimetals.

cond-mat.mtrl-sci↗

arXiv2025

A Foundation Model for Non-Destructive Defect Identification from Vibrational Spectra

Defects are ubiquitous in solids and strongly influence materials' mechanical and functional properties. However, non-destructive characterization and quantification of defects, especially when multiple types coexist, remain a long-standing challenge. Here we introduce DefectNet, a foundation machine learning model that predicts the chemical identity and concentration of substitutional point defects with multiple coexisting elements directly from vibrational spectra, specifically phonon density-of-states (PDoS). Trained on over 16,000 simulated spectra from 2,000 semiconductors, DefectNet employs a tailored attention mechanism to identify up to six distinct defect elements at concentrations ranging from 0.2% to 25%. The model generalizes well to unseen crystals across 56 elements and can be fine-tuned on experimental data. Validation using inelastic scattering measurements of SiGe alloys and MgB$_2$ superconductor demonstrates its accuracy and transferability. Our work establishes vibrational spectroscopy as a viable, non-destructive probe for point defect quantification in bulk materials, and highlights the promise of foundation models in data-driven defect engineering.

cond-mat.mtrl-sci↗

arXiv2025

AI-Driven Defect Engineering for Advanced Thermoelectric Materials

Thermoelectric materials offer a promising pathway to directly convert waste heat to electricity. However, achieving high performance remains challenging due to intrinsic trade-offs between electrical conductivity, the Seebeck coefficient, and thermal conductivity, which are further complicated by the presence of defects. This review explores how artificial intelligence (AI) and machine learning (ML) are transforming thermoelectric materials design. Advanced ML approaches including deep neural networks, graph-based models, and transformer architectures, integrated with high-throughput simulations and growing databases, effectively capture structure-property relationships in a complex multiscale defect space and overcome the curse of dimensionality. This review discusses AI-enhanced defect engineering strategies such as composition optimization, entropy and dislocation engineering, and grain boundary design, along with emerging inverse design techniques for generating materials with targeted properties. Finally, it outlines future opportunities in novel physics mechanisms and sustainability, highlighting the critical role of AI in accelerating the discovery of thermoelectric materials.

cond-mat.mtrl-sci↗

arXiv2025

AI-driven materials design: a mini-review

Materials design is an important component of modern science and technology, yet traditional approaches rely heavily on trial-and-error and can be inefficient. Computational techniques, enhanced by modern artificial intelligence (AI), have greatly accelerated the design of new materials. Among these approaches, inverse design has shown great promise in designing materials that meet specific property requirements. In this mini-review, we summarize key computational advancements for materials design over the past few decades. We follow the evolution of relevant materials design techniques, from high-throughput forward machine learning (ML) methods and evolutionary algorithms, to advanced AI strategies like reinforcement learning (RL) and deep generative models. We highlight the paradigm shift from conventional screening approaches to inverse generation driven by deep generative models. Finally, we discuss current challenges and future perspectives of materials inverse design. This review may serve as a brief guide to the approaches, progress, and outlook of designing future functional materials with technological relevance.

cond-mat.mtrl-sci↗

arXiv2024

Quantum Theory of X-ray Photon Correlation Spectroscopy

Characterizing quantum materials is essential for understanding their microscopic interactions and advancing quantum technology. X-ray photon correlation spectroscopy (XPCS) with coherent X-ray sources offers access to higher-order correlations, but its theoretical basis, the Siegert relation, is derived from dynamical light scattering with independent classical scatterers, and its validity for XPCS remains unexamined. Here we present a microscopic quantum theory of XPCS derived from elecron-photon interaction Hamiltonians, introducing four configurations tied to distinct fourth-order electron-density correlation functions. We examine the validity of the Siegert relation and derive a generalized Siegert relation. Notably, the Siegert relation breaks down even in non-interacting Fermi gas due to exchange interactions. Furthermore, density matrix renormalization group calculations on 1D Kitaev chain reveal oscillatary signatures that can distinguish topologically trivial phases from topological phases with Majorana zero modes. Our work provides a robust theoretical foundation for XPCS and highlights the value of higher-order correlations in advanced X-ray and neutron sources for probing quantum materials.

cond-mat.mtrl-sci↗

arXiv2024

A Cluster-Based Computational Thermodynamics Framework with Intrinsic Chemical Short-Range Order: Part I. Configurational Contribution

Exploiting Chemical Short-Range Order (CSRO) is a promising avenue for manipulating the properties of alloys. However, existing modeling frameworks are not sufficient to predict CSRO in multicomponent alloys (>3 components) in an efficient and reliable manner. In this work, we developed a hybrid computational thermodynamics framework by combining unique advantages from Cluster Variation Method (CVM) and CALculation of PHAse Diagram (CALPHAD) method. The key is to decompose the cumbersome cluster variables in CVM into fewer site variables of the basic cluster using the Fowler-Yang-Li (FYL) transform, which considerably reduces the number of variables that must be minimized for multicomponent systems. CSRO is incorporated into CALPHAD with a novel cluster-based solution model called FYL-CVM. This new framework brings more physics into CALPHAD while maintaining its practicality and achieves a good balance between accuracy and computational cost. It leverages statistical mechanics to yield a more physical description of configurational entropy and opens the door to cluster-based CALPHAD database development. The application of the FYL-CVM model in a prototype fcc AB alloy demonstrates its capability to correctly reproduce the essential features of the phase diagram and thermodynamic properties. The hybrid CVM-CALPHAD framework represents a new methodology for thermodynamic modeling that enables atomic-scale order to be exploited for materials design.

cond-mat.mtrl-sci↗

arXiv2016

Oscillatory deviations from Matthiessen's rule due to interacting dislocations

We theoretically examine the validity of Matthiessen's rule caused by strong dislocation-dislocation interaction using a fully quantized dislocation field, where its degree of deviation is quantified at arbitrary electron energy, dislocation-electron and dislocation-dislocation distances and interaction strengths. Contrary to intuition, we show that the electron relaxation rate deviates from the Matthiessen's rule in an oscillatory way as a function of inter-dislocation distance, instead of monotonically. This study could serve as a computational tool to investigate the electronic behavior of a highly-dislocated system at a full quantum field theoretical level.

cond-mat.mtrl-sci↗