arXiv subjects

Ziyu Xie

Publications and source records attributed to Ziyu Xie.

6 recordsLinked to original sources

arXiv2026

Dynamical one-from-many quantum metrology: Sum rule and matrix-free precision bound

Practical quantum single-parameter estimation is rarely a pristine task; it almost invariably involves nuisance parameters, casting it as a one-from-many problem. Existing approaches to this problem rely on multi-parameter metrology, reducing the matrix quantum Cramér-Rao bound to obtain scalar quantum precision limits. However, these methods are often hampered by the demanding inversion of the quantum Fisher information (QFI) matrix and the requisite choice of a weight matrix, and they break down when the QFI matrix becomes singular. Here, we show that for dynamical one-from-many estimation, a previously overlooked sum rule connecting the QFI about all model parameters to the QFI about time necessitates including the latter to consider an augmented QFI matrix while simultaneously rendering it inherently singular--precisely the scenario where conventional approaches fail. To meet this challenge, we derive a tight, matrix-free quantum precision bound that involves only scalar quantities, offers broad applicability, and subsumes existing results as special cases. Validated in both unitary and noisy settings, our findings provide a refined operational framework for practical quantum single-parameter metrology.

quant-ph↗

arXiv2023

Functional PCA and Deep Neural Networks-based Bayesian Inverse Uncertainty Quantification with Transient Experimental Data

Inverse UQ is the process to inversely quantify the model input uncertainties based on experimental data. This work focuses on developing an inverse UQ process for time-dependent responses, using dimensionality reduction by functional principal component analysis (PCA) and deep neural network (DNN)-based surrogate models. The demonstration is based on the inverse UQ of TRACE physical model parameters using the FEBA transient experimental data. The measurement data is time-dependent peak cladding temperature (PCT). Since the quantity-of-interest (QoI) is time-dependent that corresponds to infinite-dimensional responses, PCA is used to reduce the QoI dimension while preserving the transient profile of the PCT, in order to make the inverse UQ process more efficient. However, conventional PCA applied directly to the PCT time series profiles can hardly represent the data precisely due to the sudden temperature drop at the time of quenching. As a result, a functional alignment method is used to separate the phase and amplitude information of the transient PCT profiles before dimensionality reduction. DNNs are then trained using PC scores from functional PCA to build surrogate models of TRACE in order to reduce the computational cost in Markov Chain Monte Carlo sampling. Bayesian neural networks are used to estimate the uncertainties of DNN surrogate model predictions. In this study, we compared four different inverse UQ processes with different dimensionality reduction methods and surrogate models. The proposed approach shows an improvement in reducing the dimension of the TRACE transient simulations, and the forward propagation of inverse UQ results has a better agreement with the experimental data.

stat.ML↗

arXiv2021

Bayesian Inverse Uncertainty Quantification of a MOOSE-based Melt Pool Model for Additive Manufacturing Using Experimental Data

Additive manufacturing (AM) technology is being increasingly adopted in a wide variety of application areas due to its ability to rapidly produce, prototype, and customize designs. AM techniques afford significant opportunities in regard to nuclear materials, including an accelerated fabrication process and reduced cost. High-fidelity modeling and simulation (M\&S) of AM processes is being developed in Idaho National Laboratory (INL)'s Multiphysics Object-Oriented Simulation Environment (MOOSE) to support AM process optimization and provide a fundamental understanding of the various physical interactions involved. In this paper, we employ Bayesian inverse uncertainty quantification (UQ) to quantify the input uncertainties in a MOOSE-based melt pool model for AM. Inverse UQ is the process of inversely quantifying the input uncertainties while keeping model predictions consistent with the measurement data. The inverse UQ process takes into account uncertainties from the model, code, and data while simultaneously characterizing the uncertain distributions in the input parameters--rather than merely providing best-fit point estimates. We employ measurement data on melt pool geometry (lengths and depths) to quantify the uncertainties in several melt pool model parameters. Simulation results using the posterior uncertainties have shown improved agreement with experimental data, as compared to those using the prior nominal values. The resulting parameter uncertainties can be used to replace expert opinions in future uncertainty, sensitivity, and validation studies.

stat.AP↗

arXiv2021

Towards Improving the Predictive Capability of Computer Simulations by Integrating Inverse Uncertainty Quantification and Quantitative Validation with Bayesian Hypothesis Testing

The Best Estimate plus Uncertainty (BEPU) approach for nuclear systems modeling and simulation requires that the prediction uncertainty must be quantified in order to prove that the investigated design stays within acceptance criteria. A rigorous Uncertainty Quantification (UQ) process should simultaneously consider multiple sources of quantifiable uncertainties: (1) parameter uncertainty due to randomness or lack of knowledge; (2) experimental uncertainty due to measurement noise; (3) model uncertainty caused by missing/incomplete physics and numerical approximation errors, and (4) code uncertainty when surrogate models are used. In this paper, we propose a comprehensive framework to integrate results from inverse UQ and quantitative validation to provide robust predictions so that all these sources of uncertainties can be taken into consideration. Inverse UQ quantifies the parameter uncertainties based on experimental data while taking into account uncertainties from model, code and measurement. In the validation step, we use a quantitative validation metric based on Bayesian hypothesis testing. The resulting metric, called the Bayes factor, is then used to form weighting factors to combine the prior and posterior knowledge of the parameter uncertainties in a Bayesian model averaging process. In this way, model predictions will be able to integrate the results from inverse UQ and validation to account for all available sources of uncertainties. This framework is a step towards addressing the ANS Nuclear Grand Challenge on "Simulation/Experimentation" by bridging the gap between models and data.

stat.CO↗

arXiv2021

A Comprehensive Survey of Inverse Uncertainty Quantification of Physical Model Parameters in Nuclear System Thermal-Hydraulics Codes

Uncertainty Quantification (UQ) is an essential step in computational model validation because assessment of the model accuracy requires a concrete, quantifiable measure of uncertainty in the model predictions. The concept of UQ in the nuclear community generally means forward UQ (FUQ), in which the information flow is from the inputs to the outputs. Inverse UQ (IUQ), in which the information flow is from the model outputs and experimental data to the inputs, is an equally important component of UQ but has been significantly underrated until recently. FUQ requires knowledge in the input uncertainties which has been specified by expert opinion or user self-evaluation. IUQ is defined as the process to inversely quantify the input uncertainties based on experimental data. This review paper aims to provide a comprehensive and comparative discussion of the major aspects of the IUQ methodologies that have been used on the physical models in system thermal-hydraulics codes. IUQ methods can be categorized by three main groups: frequentist (deterministic), Bayesian (probabilistic), and empirical (design-of-experiments). We used eight metrics to evaluate an IUQ method, including solidity, complexity, accessibility, independence, flexibility, comprehensiveness, transparency, and tractability. Twelve IUQ methods are reviewed, compared, and evaluated based on these eight metrics. Such comparative evaluation will provide a good guidance for users to select a proper IUQ method based on the IUQ problem under investigation.

stat.AP↗

arXiv2011

Nearest Prime Simplicial Complex for Object Recognition

The structure representation of data distribution plays an important role in understanding the underlying mechanism of generating data. In this paper, we propose nearest prime simplicial complex approaches (NSC) by utilizing persistent homology to capture such structures. Assuming that each class is represented with a prime simplicial complex, we classify unlabeled samples based on the nearest projection distances from the samples to the simplicial complexes. We also extend the extrapolation ability of these complexes with a projection constraint term. Experiments in simulated and practical datasets indicate that compared with several published algorithms, the proposed NSC approaches achieve promising performance without losing the structure representation.

cs.LG↗