Publications

We prove that all the criteria proposed in the literature to identify a Chern band hosting exact fractional Chern insulating ground states, in fact, describe an equivalence with a lowest Landau level defined in curved space under a non-uniform magnetic field. In addition, we design an operational test for the most general instance of such lowest Landau level mapping, which only relies on the computationally inexpensive evaluation of Bloch wavefunctions' derivatives. Our work clarifies the common origin of various Chern-idealness criteria, proves that these criteria exhaust all possible lowest Landau levels, and hints at classes of Chern bands that may posses interesting phases beyond Landau level physics.

Strong light-matter interactions as realized in an optical cavity provide a tantalizing opportunity to control the properties of condensed matter systems. Inspired by experimental advances in cavity quantum electrodynamics and the fabrication and control of two-dimensional magnets, we investigate the fate of a quantum critical antiferromagnet coupled to an optical cavity field. Using unbiased quantum Monte Carlo simulations, we compute the scaling behavior of the magnetic structure factor and other observables. While the position and universality class are not changed by a single cavity mode, the critical fluctuations themselves obtain a sizable enhancement, scaling with a fractional exponent that defies expectations based on simple perturbation theory. The scaling exponent can be understood using a generic scaling argument, based on which we predict that the effect may be even stronger in other universality classes. Our microscopic model is based on realistic parameters for two-dimensional magnetic quantum materials and the effect may be within the range of experimental detection.

We present an approach to interface branching random walks with Markov chain Monte Carlo sampling, and to switch seamlessly between the two. The approach is discussed in the context of auxiliary-field quantum Monte Carlo (AFQMC) but is applicable to other Monte Carlo calculations or simulations. In AFQMC, the formulation of branching random walks along imaginary-time is needed to realize a constraint to control the sign or phase problem. The constraint is derived from an exact gauge condition, and is in practice implemented approximately with a trial wave function or trial density matrix, which can break exactness in the algorithm. We use the generalized Metropolis algorithm to sample a selected portion of the imaginary-time path after it has been produced by the branching random walk. This interfacing allows a constraint release to follow seamlessly from the constrained-path sampling, which can reduce the systematic error from the latter. It also provides a way to improve the computation of correlation functions and observables that do not commute with the Hamiltonian. We illustrate the method in atoms and molecules, where improvements in accuracy can be clearly quantified and near-exact results are obtained. We also discuss the computation of the variance of the Hamiltonian and propose a convenient way to evaluate it stochastically without changing the scaling of AFQMC.

High-harmonic generation (HHG) in liquids is opening new opportunities for attosecond light sources and attosecond time-resolved studies of dynamics in the liquid phase. In gas-phase HHG, few-cycle pulses are routinely used to create isolated attosecond pulses and to extend the cut-off energy. Here, we study the properties of HHG in liquids, including water and several alcohols, by continuously tuning the pulse duration of a mid-infrared driver from the multi- to the sub-two-cycle regime. Similar to the gas phase, we observe the transition from discrete odd-order harmonics to continuous extreme-ultraviolet emission. However, the cut-off energy is shown to be entirely independent of the pulse duration. This observation is confirmed by ab-initio simulations of HHG in large clusters. Our results support the notion that the cut-off energy is a fundamental property of the liquid, independent of the driving-pulse properties. Combined with the recently reported wavelength-independence of the cutoff, these results confirm the direct sensitivity of HHG to the mean-free paths of slow electrons in liquids. Our results additionally imply that few-cycle mid-infrared laser pulses are suitable drivers for generating isolated attosecond pulses from liquids.

High-harmonic spectroscopy (HHS) is a nonlinear all-optical technique with inherent attosecond temporal resolution, which has been applied successfully to a broad variety of systems in the gas phase and solid state. Here, we extend HHS to the liquid phase, and uncover the mechanism of high-harmonic generation (HHG) for this phase of matter. Studying HHG over a broad range of wavelengths and intensities, we show that the cut-off (E

https://arxiv.org/abs/2211.04241

Incomplete labels are common in multi-task learning for biomedical applications due to several practical difficulties, e.g., expensive annotation efforts by experts, limit of data collection, different sources of data. A naive approach to enable joint learning for partially labeled data is adding self-supervised learning for tasks without ground truths by augmenting an input image and forcing the multi-task model to return the same outputs for both the input and augmented images. However, the partially labeled setting can result in imbalanced learning of tasks since not all tasks are trainable with ground truth supervisions for each data sample. In this work, we propose a multi-task curriculum learning method tailored for partially labeled data. For balanced learning of tasks, our multitask curriculum prioritizes less performing tasks during training by setting different supervised learning frequencies for each task. We demonstrate that our method outperforms standard approaches on one biomedical and two natural image datasets. Furthermore, our learning method with partially labeled data performs better than the standard multi-task learning methods with fully labeled data for the same number of annotations.

Blastomere instance segmentation is important for analyzing embryos’ abnormality. To measure the accurate shapes and sizes of blastomeres, their amodal segmentation is necessary. Amodal instance segmentation aims to recover an object’s complete silhouette even when the object is not fully visible. For each detected object, previous methods directly regress the target mask from input features. However, images of an object under different amounts of occlusion should have the same amodal mask output, making it harder to train the regression model. To alleviate the problem, we propose to classify input features into intermediate shape codes and recover complete object shapes. First, we pre-train the Vector Quantized Variational Autoencoder (VQ-VAE) model to learn these discrete shape codes from ground truth amodal masks. Then, we incorporate the VQ-VAE model into the amodal instance segmentation pipeline with an additional refinement module. We also detect an occlusion map to integrate occlusion information with a backbone feature. As such, our network faithfully detects bounding boxes of amodal objects. On an internal embryo cell image benchmark, the proposed method outperforms previous state-of-the-art methods. To show generalizability, we show segmentation results on the public KINS natural image benchmark. Our method would enable accurate measurement of blastomeres in In Vitro Fertilization (IVF) clinics, potentially increasing the IVF success rate.

Function approximation has been an indispensable component in modern reinforcement learning algorithms designed to tackle problems with large state spaces in high dimensions. This paper reviews recent results on error analysis for these reinforcement learning algorithms in linear or nonlinear approximation settings, emphasizing approximation error and estimation error/sample complexity. We discuss various properties related to approximation error and present concrete conditions on transition probability and reward function under which these properties hold true. Sample complexity analysis in reinforcement learning is more complicated than in supervised learning, primarily due to the distribution mismatch phenomenon. With assumptions on the linear structure of the problem, numerous algorithms in the literature achieve polynomial sample complexity with respect to the number of features, episode length, and accuracy, although the minimax rate has not been achieved yet. These results rely on the $L^∞$ and UCB estimation of estimation error, which can handle the distribution mismatch phenomenon. The problem and analysis become substantially more challenging in the setting of nonlinear function approximation, as both $L^∞$ and UCB estimation are inadequate for bounding the error with a favorable rate in high dimensions. We discuss additional assumption necessary to address the distribution mismatch and derive meaningful results for nonlinear RL problems.

Developing robust constitutive models is a fundamental and longstanding problem for accelerating the simulation of complicated physics. Machine learning provides promising tools to construct constitutive models based on various calibration data. In this work, we propose a neural operator to develop nonlocal constitutive models for tensorial quantities through a vector-cloud neural network with equivariance (VCNN-e). The VCNN-e respects all the invariance properties desired by constitutive models, faithfully reflects the region of influence in physics, and is applicable to different spatial resolutions. By design, the model guarantees that the predicted tensor is invariant to the frame translation and ordering (permutation) of the neighboring points. Furthermore, it is equivariant to the frame rotation, i.e., the output tensor co-rotates with the coordinate frame. We evaluate the VCNN-e by using it to emulate the Reynolds stress transport model for turbulent flows, which directly computes the Reynolds stress tensor to close the Reynolds-averaged Navier--Stokes (RANS) equations. The evaluation is performed in two situations: (1) emulating the Reynolds stress model through synthetic data generated from the Reynolds stress transport equations with closure models, and (2) predicting the Reynolds stress by learning from data generated from direct numerical simulations. Such a priori evaluations of the proposed network pave the way for developing and calibrating robust and nonlocal, non-equilibrium closure models for the RANS equations.