arXiv subjects

Zhao Ding

Publications and source records attributed to Zhao Ding.

9 recordsLinked to original sources

arXiv2026

Building a physics-aware AI ecosystem for solid-state hydrogen storage materials

Hydrogen storage remains a central bottleneck for scalable hydrogen energy systems due to the multiscale and coupled nature of the thermodynamics, kinetics, and microstructural evolution of hydrogen storage materials (HSMs). Although artificial intelligence (AI) has accelerated materials discovery, current approaches remain constrained by fragmented data, limited physical consistency, and weak integration with experimental validation. Here, we propose a unified framework that integrates coherent data infrastructure, physics-grounded modeling, and AI-driven inverse design within a closed-loop discovery paradigm. By embedding physical constraints and experimental feedback, this approach enables adaptive, physically consistent optimization, thereby establishing a pathway toward autonomous, digital-twin-enabled discovery of HSMs.

cond-mat.mtrl-sci↗

arXiv2024

Nonlinear Assimilation via Score-based Sequential Langevin Sampling

This paper introduces score-based sequential Langevin sampling (SSLS), a novel approach to nonlinear data assimilation within a recursive Bayesian filtering framework. The proposed method decomposes the assimilation process into alternating prediction and update steps, using dynamic models for state prediction and incorporating observational data via score-based Langevin Monte Carlo during the updates. To overcome inherent challenges in highly non-log-concave posterior sampling, we integrate an annealing strategy into the update mechanism. Theoretically, we establish convergence guarantees for SSLS in total variation (TV) distance, yielding concrete insights into the algorithm's error behavior with respect to key hyperparameters. Crucially, our derived error bounds demonstrate the asymptotic stability of SSLS, guaranteeing that local posterior sampling errors do not accumulate indefinitely over time. Extensive numerical experiments across challenging scenarios, including high-dimensional systems, strong nonlinearity, and sparse observations, highlight the robust performance of the proposed method. Furthermore, SSLS effectively quantifies the uncertainty associated with state estimates, rendering it particularly valuable for reliable error calibration.

math.NA↗

arXiv2024

Characteristic Learning for Provable One Step Generation

We propose the characteristic generator, an one-step generative model that combines the sampling efficiency of generative adversarial networks (GANs) with the training stability of flow-based models. The proposed model is based on characteristics along which probability-density transport is governed by ordinary differential equations (ODEs). Specifically, we first estimate the underlying velocity field and numerically solve the probability-flow ODE using an exponential integrator, thereby obtaining discrete approximations of the characteristic trajectories. We then train a deep neural network to approximate these trajectories, yielding a one-step transport map from a Gaussian prior to the target distribution. Theoretically, we analyze the errors introduced by velocity-field estimation, numerical discretization, and characteristic approximation, and establish a nonasymptotic convergence rate in the Wasserstein-2 distance under mild assumptions on the data distribution. Moreover, under a low-dimensional linear-subspace assumption, we show that the convergence rate depends on the intrinsic data dimension rather than the potentially much larger ambient dimension, demonstrating the model's ability to alleviate the curse of dimensionality. Experiments on synthetic and real-world datasets show that the characteristic generator produces high-quality, high-resolution samples using only one or a few neural-network evaluations.

cs.LG↗

arXiv2024

Deep conditional distribution learning via conditional F\"ollmer flow

We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional F\"ollmer Flow. Starting from a standard Gaussian distribution, the proposed flow could approximate the target conditional distribution very well when the time is close to 1. For effective implementation, we discretize the flow with Euler's method where we estimate the velocity field nonparametrically using a deep neural network. Furthermore, we also establish the convergence result for the Wasserstein-2 distance between the distribution of the learned samples and the target conditional distribution, providing the first comprehensive end-to-end error analysis for conditional distribution learning via ODE flow. Our numerical experiments showcase its effectiveness across a range of scenarios, from standard nonparametric conditional density estimation problems to more intricate challenges involving image data, illustrating its superiority over various existing conditional density estimation methods.

stat.ML↗

arXiv2024

Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network

We propose SDORE, a Semi-supervised Deep Sobolev Regressor, for the nonparametric estimation of the underlying regression function and its gradient. SDORE employs deep ReQU neural networks to minimize the empirical risk with gradient norm regularization, allowing the approximation of the regularization term by unlabeled data. Our study includes a thorough analysis of the convergence rates of SDORE in $L^{2}$-norm, achieving the minimax optimality. Further, we establish a convergence rate for the associated plug-in gradient estimator, even in the presence of significant domain shift. These theoretical findings offer valuable insights for selecting regularization parameters and determining the size of the neural network, while showcasing the provable advantage of leveraging unlabeled data in semi-supervised learning. To the best of our knowledge, SDORE is the first provable neural network-based approach that simultaneously estimates the regression function and its gradient, with diverse applications such as nonparametric variable selection. The effectiveness of SDORE is validated through an extensive range of numerical simulations.

stat.ML↗

arXiv2023

Sampling via F\"ollmer Flow

We introduce a novel unit-time ordinary differential equation (ODE) flow called the preconditioned F\"{o}llmer flow, which efficiently transforms a Gaussian measure into a desired target measure at time 1. To discretize the flow, we apply Euler's method, where the velocity field is calculated either analytically or through Monte Carlo approximation using Gaussian samples. Under reasonable conditions, we derive a non-asymptotic error bound in the Wasserstein distance between the sampling distribution and the target distribution. Through numerical experiments on mixture distributions in 1D, 2D, and high-dimensional spaces, we demonstrate that the samples generated by our proposed flow exhibit higher quality compared to those obtained by several existing methods. Furthermore, we propose leveraging the F\"{o}llmer flow as a warmstart strategy for existing Markov Chain Monte Carlo (MCMC) methods, aiming to mitigate mode collapses and enhance their performance. Finally, thanks to the deterministic nature of the F\"{o}llmer flow, we can leverage deep neural networks to fit the trajectory of sample evaluations. This allows us to obtain a generator for one-step sampling as a result.

stat.ME↗

arXiv2023

Offline Reinforcement Learning with Imbalanced Datasets

The prevalent use of benchmarks in current offline reinforcement learning (RL) research has led to a neglect of the imbalance of real-world dataset distributions in the development of models. The real-world offline RL dataset is often imbalanced over the state space due to the challenge of exploration or safety considerations. In this paper, we specify properties of imbalanced datasets in offline RL, where the state coverage follows a power law distribution characterized by skewed policies. Theoretically and empirically, we show that typically offline RL methods based on distributional constraints, such as conservative Q-learning (CQL), are ineffective in extracting policies under the imbalanced dataset. Inspired by natural intelligence, we propose a novel offline RL method that utilizes the augmentation of CQL with a retrieval process to recall past related experiences, effectively alleviating the challenges posed by imbalanced datasets. We evaluate our method on several tasks in the context of imbalanced datasets with varying levels of imbalance, utilizing the variant of D4RL. Empirical results demonstrate the superiority of our method over other baselines.

cs.LG↗

arXiv2020

Highly Anisotropic Electronic and Mechanical Properties of Monolayer and Bilayer As2S3

Anisotropic materials, with orientation-dependent properties, have attracted more and more attention due to their compelling tunable and flexible performance in electronic and optomechanical devices. So far, two-dimensional (2D) black phosphorus shows the largest known anisotropic behavior, which is highly desired for synaptic and neuromorphic devices, multifunctional directional memories, and even polarization-sensitive photodetector, whereas it is unstable at ambient conditions. Recently, 2D few-layered As2S3 with superior chemical stability was successfully exfoliated in experiments. However, the electronic and mechanical properties of monolayer and bilayer As2S3 is still lacking. Here, we report the large anisotropic electronic and mechanical properties of As2S3 systems through first-principles calculations and general angle-dependent Hooke's law. Monolayer and bilayer As2S3 exhibit anisotropic factors of Young's modulus of 3.15 and 3.32, respectively, which are larger than the black phosphorous with experimentally confirmed and an anisotropic factor of 2. This study provides an effective route to flexible orientation-dependent nanoelectronics, nanomechanics, and offers implications in promoting related experimental investigations.

cond-mat.mtrl-sci↗

arXiv2020

Robust Decoding from Binary Measurements with Cardinality Constraint Least Squares

The main goal of 1-bit compressive sampling is to decode $n$ dimensional signals with sparsity level $s$ from $m$ binary measurements. This is a challenging task due to the presence of nonlinearity, noises and sign flips. In this paper, the cardinality constraint least square is proposed as a desired decoder. We prove that, up to a constant $c$, with high probability, the proposed decoder achieves a minimax estimation error as long as $m \geq \mathcal{O}( s\log n)$. Computationally, we utilize a generalized Newton algorithm (GNA) to solve the cardinality constraint minimization problem with the cost of solving a least squares problem with small size at each iteration. We prove that, with high probability, the $\ell_{\infty}$ norm of the estimation error between the output of GNA and the underlying target decays to $\mathcal{O}(\sqrt{\frac{\log n }{m}}) $ after at most $\mathcal{O}(\log s)$ iterations. Moreover, the underlying support can be recovered with high probability in $\mathcal{O}(\log s)$ steps provided that the target signal is detectable. Extensive numerical simulations and comparisons with state-of-the-art methods are presented to illustrate the robustness of our proposed decoder and the efficiency of the GNA algorithm.

cs.IT↗