arXiv subjects

Zhihang Xu

Publications and source records attributed to Zhihang Xu.

12 recordsLinked to original sources

arXiv2026

Thickness-Driven Superconductor-Insulator Transition in (Cu,C)-1234 and Proximity-Induced Superconductivity Recovery in (Cu,C)-1234/YBCO Heterostructure

Superconducting proximity effect and related thickness-driven property evolution remain an important issue in understanding high temperature superconductors. Among proximity systems, superconductor-superconductor (S-S') is special for the existence of intrinsic superconductivity in both materials. Such platform allows the different superconducting orders to compete, couple and reconstruct at the interface. In this paper, (Cu,C)-1234/YBCO heterostructure grown on LAO (001) with fixed thickness of bottom YBCO layer as 150 nm and varied thickness of top (Cu,C)-1234 layer as 188nm, 87 nm, 18nm and estimated 1.2 nm were fabricated and component films were preserved. Electrical transport characterization indicated that as the thickness decrease the (Cu,C)-1234 film degrades and underwent the superconductor-insulator transition (SIT) from thicker to less than 18 nm. In contrast, superconductivity is re-established in transport measurements when the insulating (Cu,C)-1234 layer is coupled to superconducting YBCO As the (Cu,C)-1234 thickness is further reduced to approximately 1.2 nm, the recovered superconductivity is strongly suppressed. The observed thickness dependence is consistent with a scenario in which interfacial coupling restores superconductivity over a finite thickness range before increasing disorder and dimensional confinement dominate in the two-dimensional limit. This work establishes a promising platform for investigating interfacial coupling between cuprate superconductors and provides new insight into the superconducting proximity effect in high-temperature superconducting heterostructures.

cond-mat.supr-con↗

arXiv2026

I-MCHM: Interface Multicontinuum Homogenization for Multiscale Elliptic Problems

We introduce an interface multicontinuum homogenization method (I-MCHM) for high-contrast elliptic problems whose subdomains may have distinct microscopic patterns and unequal numbers of continua. Multicontinuum models upscale microscopic fields to macroscopic continuum quantities; here the continua are the high- and low-permeability regions, and the macroscopic variables are the corresponding local averages of the fine-scale solution on observing cells of size $H_\epsilon$. Although the fine-scale solution is continuous across a material interface, these macroscopic continuum fields need not coincide on the interface. Moreover, when adjacent subdomains retain different numbers of continua, a one-to-one coarse transmission condition cannot be defined. Standard subdomain-wise multicontinuum homogenization therefore determines the bulk equations but leaves the interaction among these coarse variables unspecified. I-MCHM closes this gap by constructing two-sided constrained local bases on interface neighborhoods and assembling a coarse bilinear form with bulk cut-cell integrals and interface-segment corrections over the subdomain adjacency graph, without prescribing a pointwise transmission law. Numerical experiments on straight, curved, and triple-junction geometries, including continuum-coupling ablations and unequal continuum counts, demonstrate the accuracy of the resulting upscaled model.

math.NA↗

arXiv2026

Parametrization of subgrid scales in long-term simulations of the shallow-water equations using machine learning and convex limiting

We present a method for parametrizing sub-grid processes in the Shallow Water equations. We define coarse variables and local spatial averages and use a feed-forward neural network to learn sub-grid fluxes. Our method results in a local parametrization that uses a four-point computational stencil, which has several advantages over globally coupled parametrizations. We demonstrate numerically that our method improves energy balance in long-term turbulent simulations and also accurately reproduces individual solutions. The long-term simulations refer to numerical studies where a fluid flow is simulated over a duration long enough to reach a statistical steady state. The neural network parametrization can be easily combined with flux limiting to reduce oscillations near shocks. More importantly, our method provides reliable parametrizations, even in dynamical regimes that are not included in the training data.

physics.flu-dyn↗

arXiv2026

Numerical Methods for Solving Nonlinearly Coupled Poisson Equations in Dual-Continuum Modeled Porous Electrodes

Porous electrodes are widely used in electrochemical systems, where accurately determining electric potentials, particularly overpotentials, is essential for understanding electrode behavior. At the macroscopic scale, porous electrodes are typically modeled using a dual-continuum approach, treating the porous solid phase and the liquid electrolyte as spatially superimposed domains. Determining potential distributions requires solving two Poisson equations that are nonlinearly coupled through Butler-Volmer kinetics under galvanostatic and potentiostatic operating modes. Under galvanostatic operation, these equations form an underconstrained singular system due to all-Neumann boundary conditions, posing numerical challenges. This paper systematically presents numerical methods for solving nonlinearly coupled Poisson equations in dual-continuum porous electrodes, with a particular focus on galvanostatic solutions. We mathematically establish solution uniqueness in terms of the potential difference between the electrode and electrolyte (or overpotential), as well as the individual potentials up to a shared constant shift. To resolve the nonuniqueness of the solution, we introduce three numerical approaches: (1) Lagrange Constrained Method (LCM), (2) Dirichlet Substitution Method (DSM), and (3) Global Constraining Method (GCM), where GCM enables solving the overpotential without imposing an explicit system reference potential. Additionally, we develop both decoupled and fully coupled nonlinear solution strategies and evaluate their computational performance in both homogeneous and heterogeneous conductivity cases. The presented numerical methods are general for addressing similar underconstrained nonlinear systems. A Python implementation is provided at https://github.com/harrywang1129/porous_electrode_solver.

math.NA↗

arXiv2026

An ILUES-based adaptive Gaussian process method for multimodal Bayesian inverse problems

Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are computationally expensive. This challenge is further compounded when the posterior distribution is multimodal. To address this issue, we propose a Gaussian process (GP)-based method to indirectly build surrogates for the forward model. Specifically, the unnormalized posterior density is expressed as a product of an auxiliary density and an exponential GP surrogate. Iteratively, the auxiliary density converges to the posterior distribution, starting from an arbitrary initial density. However, the efficiency of GP regression is highly influenced by the quality of the training data. Therefore, we utilize the iterative local updating ensemble smoother (ILUES) to generate high-quality samples that are concentrated in regions with high posterior probability. Subsequently, based on the surrogate model and mode information extracted using a clustering method, Markov chain Monte Carlo (MCMC) with a Gaussian mixed (GM) proposal is used to draw samples from the auxiliary density. Through numerical examples, we demonstrate that the proposed method can accurately and efficiently represent the posterior with a limited number of forward simulations.

stat.CO↗

arXiv2025

Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs

While deep learning has achieved remarkable success in solving partial differential equations (PDEs), it still faces significant challenges, particularly when the PDE solutions have low regularity or singularities. To address these issues, we propose the Weak TransNet (WTN) method, based on a Petrov-Galerkin formulation, for solving elliptic PDEs in this work, though its framework may extend to other classes of equations. Specifically, the neural feature space defined by TransNet (Zhang et al., 2023) is used as the trial space, while the test space is composed of radial basis functions. Since the solution is expressed as a linear combination of trial functions, the coefficients can be determined by minimizing the weak PDE residual via least squares. Thus, this approach could help mitigate the challenges of non-convexity and ill-conditioning that often arise in neural network training. Furthermore, the WTN method is extended to handle problems whose solutions exhibit multiscale features or possess sharp variations. Several numerical experiments are presented to demonstrate the robustness and efficiency of the proposed methods.

math.NA↗

arXiv2024

Billion-Fold Enhancement of Room-Temperature Ionic Conductivity in h-RMnO3/YSZ Heterostructures via Electric-Field-Assisted Oxygen Deficiency Engineering

Oxide heterostructures provide versatile platforms for manipulating electronic and ionic conductive states. In this study, we demonstrate a remarkable billion-fold enhancement in room-temperature ionic conductivity within h-RMnO3/YSZ heterostructures, achieved through electric-field-assisted oxygen deficiency engineering. This enhancement is closely linked to substantial oxygen depletion in YSZ and is tunable by varying the thickness of the h-RMnO3 film layer and the applied voltage bias. Our findings underscore the critical importance of interfacial design and vacancy control in enhancing ionic transport capabilities, paving the way for advanced applications in low-temperature energy harvesting, storage, and conversion technologies.

cond-mat.mtrl-sci↗

arXiv2023

MuLanTTS: The Microsoft Speech Synthesis System for Blizzard Challenge 2023

In this paper, we present MuLanTTS, the Microsoft end-to-end neural text-to-speech (TTS) system designed for the Blizzard Challenge 2023. About 50 hours of audiobook corpus for French TTS as hub task and another 2 hours of speaker adaptation as spoke task are released to build synthesized voices for different test purposes including sentences, paragraphs, homographs, lists, etc. Building upon DelightfulTTS, we adopt contextual and emotion encoders to adapt the audiobook data to enrich beyond sentences for long-form prosody and dialogue expressiveness. Regarding the recording quality, we also apply denoise algorithms and long audio processing for both corpora. For the hub task, only the 50-hour single speaker data is used for building the TTS system, while for the spoke task, a multi-speaker source model is used for target speaker fine tuning. MuLanTTS achieves mean scores of quality assessment 4.3 and 4.5 in the respective tasks, statistically comparable with natural speech while keeping good similarity according to similarity assessment. The excellent and similarity in this year's new and dense statistical evaluation show the effectiveness of our proposed system in both tasks.

eess.AS↗

arXiv2023

A domain-decomposed VAE method for Bayesian inverse problems

Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and high-dimensional parameterization of priors. This paper proposes a domain-decomposed variational auto-encoder Markov chain Monte Carlo (DD-VAE-MCMC) method to tackle these challenges simultaneously. Through partitioning the global physical domain into small subdomains, the proposed method first constructs local deterministic generative models based on local historical data, which provide efficient local prior representations. Gaussian process models with active learning address the domain decomposition interface conditions. Then inversions are conducted on each subdomain independently in parallel and in low-dimensional latent parameter spaces. The local inference solutions are post-processed through the Poisson image blending procedure to result in an efficient global inference result. Numerical examples are provided to demonstrate the performance of the proposed method.

stat.ML↗

arXiv2022

Domain-decomposed Bayesian inversion based on local Karhunen-Loève expansions

In many Bayesian inverse problems the goal is to recover a spatially varying random field. Such problems are often computationally challenging especially when the forward model is governed by complex partial differential equations (PDEs). The challenge is particularly severe when the spatial domain is large and the unknown random field needs to be represented by a high-dimensional parameter. In this paper, we present a domain-decomposed method to attack the dimensionality issue and the method decomposes the spatial domain and the parameter domain simultaneously. On each subdomain, a local Karhunen-Lo`eve (KL) expansion is constructed, and a local inversion problem is solved independently in a parallel manner, and more importantly, in a lower-dimensional space. After local posterior samples are generated through conducting Markov chain Monte Carlo (MCMC) simulations on subdomains, a novel projection procedure is developed to effectively reconstruct the global field. In addition, the domain decomposition interface conditions are dealt with an adaptive Gaussian process-based fitting strategy. Numerical examples are provided to demonstrate the performance of the proposed method.

math.NA↗

arXiv2022

Deep neural network based adaptive learning for switched systems

In this paper, we present a deep neural network based adaptive learning (DNN-AL) approach for switched systems. Currently, deep neural network based methods are actively developed for learning governing equations in unknown dynamic systems, but their efficiency can degenerate for switching systems, where structural changes exist at discrete time instants. In this new DNN-AL strategy, observed datasets are adaptively decomposed into subsets, such that no structural changes within each subset. During the adaptive procedures, DNNs are hierarchically constructed, and unknown switching time instants are gradually identified. Especially, network parameters at previous iteration steps are reused to initialize networks for the later iteration steps, which gives efficient training procedures for the DNNs. For the DNNs obtained through our DNN-AL, bounds of the prediction error are established. Numerical studies are conducted to demonstrate the efficiency of DNN-AL.

cs.LG↗

arXiv2021

DelightfulTTS: The Microsoft Speech Synthesis System for Blizzard Challenge 2021

This paper describes the Microsoft end-to-end neural text to speech (TTS) system: DelightfulTTS for Blizzard Challenge 2021. The goal of this challenge is to synthesize natural and high-quality speech from text, and we approach this goal in two perspectives: The first is to directly model and generate waveform in 48 kHz sampling rate, which brings higher perception quality than previous systems with 16 kHz or 24 kHz sampling rate; The second is to model the variation information in speech through a systematic design, which improves the prosody and naturalness. Specifically, for 48 kHz modeling, we predict 16 kHz mel-spectrogram in acoustic model, and propose a vocoder called HiFiNet to directly generate 48 kHz waveform from predicted 16 kHz mel-spectrogram, which can better trade off training efficiency, modelling stability and voice quality. We model variation information systematically from both explicit (speaker ID, language ID, pitch and duration) and implicit (utterance-level and phoneme-level prosody) perspectives: 1) For speaker and language ID, we use lookup embedding in training and inference; 2) For pitch and duration, we extract the values from paired text-speech data in training and use two predictors to predict the values in inference; 3) For utterance-level and phoneme-level prosody, we use two reference encoders to extract the values in training, and use two separate predictors to predict the values in inference. Additionally, we introduce an improved Conformer block to better model the local and global dependency in acoustic model. For task SH1, DelightfulTTS achieves 4.17 mean score in MOS test and 4.35 in SMOS test, which indicates the effectiveness of our proposed system

cs.SD↗