arXiv subjects

Senwei Liang

Publications and source records attributed to Senwei Liang.

At least 19 recordsLinked to original sources

arXiv2026

Data-Efficient and Interpretable Classification of Circulating Tumor Cell Phenotypes in Microfluidic Devices via Deep Learning

Accurate classification of circulating tumor cell (CTC) phenotypes can provide valuable information for assessing metastatic potential. Label free microfluidic devices provide a hydrodynamic obstacle course that transforms subtle biophysical characteristics of CTCs, including size and deformability, into distinct kinematic trajectories. However, the highly nonlinear fluid structure interactions governing these trajectories make the inverse problem of inferring cellular phenotype from trajectory data analytically intractable. While deep neural networks (DNNs) have emerged as a powerful approach for addressing this inverse problem, their effectiveness is constrained by the limited availability of trajectory data and the lack of physical interpretability. To address these challenges, we propose an interpretable and data efficient DNN framework for trajectory based CTC classification. To mitigate the scarcity of data, we develop Subsequence (SubSeq), a targeted augmentation strategy that randomly extracts informative local trajectory segments during training to promote learning from localized patterns. We further apply Gradient Weighted Class Activation Mapping to identify the trajectory features and physical regions of the microfluidic device that drive model predictions. Experimental results demonstrate that SubSeq improves classification accuracy over the evaluated baseline and augmentation methods. Furthermore, interpretability analysis suggests that localized trajectory segments contain substantial biophysical information relevant to accurate classification. This provides justification for SubSeq and also highlights the redundancy of full-length trajectories. More broadly, the proposed framework views microfluidic geometries as physical encoders of cellular mechanical properties, providing mechanistic insights that may inform the future design of diagnostic devices.

cs.LG↗

arXiv2025

H-FEX: A Symbolic Learning Method for Hamiltonian Systems

Hamiltonian systems describe a broad class of dynamical systems governed by Hamiltonian functions, which encode the total energy and dictate the evolution of the system. Data-driven approaches, such as symbolic regression and neural network-based methods, provide a means to learn the governing equations of dynamical systems directly from observational data of Hamiltonian systems. However, these methods often struggle to accurately capture complex Hamiltonian functions while preserving energy conservation. To overcome this limitation, we propose the Finite Expression Method for learning Hamiltonian Systems (H-FEX), a symbolic learning method that introduces novel interaction nodes designed to capture intricate interaction terms effectively. Our experiments, including those on highly stiff dynamical systems, demonstrate that H-FEX can recover Hamiltonian functions of complex systems that accurately capture system dynamics and preserve energy over long time horizons. These findings highlight the potential of H-FEX as a powerful framework for discovering closed-form expressions of complex dynamical systems.

cs.LG↗

arXiv2025

Identifying Unknown Stochastic Dynamics via Finite expression methods

Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a combination of deterministic and stochastic terms. However, these models usually lack interpretability and have difficulty generalizing beyond their training domain. This paper introduces the Finite Expression Method (FEX), a symbolic learning approach designed to derive interpretable mathematical representations of the deterministic component of SDEs. For the stochastic component, we integrate FEX with advanced generative modeling techniques to provide a comprehensive representation of SDEs. The numerical experiments on linear, nonlinear, and multidimensional SDEs demonstrate that FEX generalizes well beyond the training domain and delivers more accurate long-term predictions compared to neural network-based methods. The symbolic expressions identified by FEX not only improve prediction accuracy but also offer valuable scientific insights into the underlying dynamics of the systems, paving the way for new scientific discoveries.

cs.LG↗

arXiv2025

QuGStep: Refining Step Size Selection in Gradient Estimation for Variational Quantum Algorithms

Variational quantum algorithms (VQAs) offer a promising approach to solving computationally demanding problems by combining parameterized quantum circuits with classical optimization. Estimating probabilistic outcomes on quantum hardware requires repeated measurements (shots). However, in practice, the limited shot budget introduces significant noise in the evaluation of the objective function. Gradient estimation in VQAs often relies on the finite-difference, which evaluates the noisy objective function at perturbed circuit parameter values. The accuracy of this estimation is highly dependent on the choice of step size for these perturbations. An inappropriate step size can exacerbate the impact of noise, causing inaccurate gradient estimates and hindering the classical optimization in VQAs. This paper proposes QuGStep, an algorithm that addresses the challenge of determining the appropriate step size for finite-difference gradient estimation under a shot budget. QuGStep is grounded in a theorem that proves the optimal step size, which accounts for the shot budget, minimizes the error bound in gradient estimation using finite differences. Numerical experiments approximating the ground state energy of several molecules demonstrate that QuGStep can identify the appropriate step size for the given shot budget to obtain effective gradient estimation. Notably, the step size identified by QuGStep achieved convergence to the ground state energy with over 94% fewer shots compared to using a default step size (i.e., step size of 0.01). These findings highlight the potential of QuGStep to improve the practical deployment and scalability of quantum computing technologies.

quant-ph↗

arXiv2025

Robust Multimodal Learning for Ophthalmic Disease Grading via Disentangled Representation

This paper discusses how ophthalmologists often rely on multimodal data to improve diagnostic accuracy. However, complete multimodal data is rare in real-world applications due to a lack of medical equipment and concerns about data privacy. Traditional deep learning methods typically address these issues by learning representations in latent space. However, the paper highlights two key limitations of these approaches: (i) Task-irrelevant redundant information (e.g., numerous slices) in complex modalities leads to significant redundancy in latent space representations. (ii) Overlapping multimodal representations make it difficult to extract unique features for each modality. To overcome these challenges, the authors propose the Essence-Point and Disentangle Representation Learning (EDRL) strategy, which integrates a self-distillation mechanism into an end-to-end framework to enhance feature selection and disentanglement for more robust multimodal learning. Specifically, the Essence-Point Representation Learning module selects discriminative features that improve disease grading performance. The Disentangled Representation Learning module separates multimodal data into modality-common and modality-unique representations, reducing feature entanglement and enhancing both robustness and interpretability in ophthalmic disease diagnosis. Experiments on multimodal ophthalmology datasets show that the proposed EDRL strategy significantly outperforms current state-of-the-art methods.

cs.CV↗

arXiv2025

Exploring the Nexus of Many-Body Theories through Neural Network Techniques: the Tangent Model

In this paper, we present a physically informed neural network representation of the effective interactions associated with coupled-cluster downfolding models to describe chemical systems and processes. The neural network representation not only allows us to evaluate the effective interactions efficiently for various geometrical configurations of chemical systems corresponding to various levels of complexity of the underlying wave functions, but also reveals that the bare and effective interactions are related by a tangent function of some latent variables. We refer to this characterization of the effective interaction as a tangent model. We discuss the connection between this tangent model for the effective interaction with the previously developed theoretical analysis that examines the difference between the bare and effective Hamiltonians in the corresponding active spaces.

quant-ph↗

arXiv2024

Learning Epidemiological Dynamics via the Finite Expression Method

Modeling and forecasting the spread of infectious diseases is essential for effective public health decision-making. Traditional epidemiological models rely on expert-defined frameworks to describe complex dynamics, while neural networks, despite their predictive power, often lack interpretability due to their ``black-box" nature. This paper introduces the Finite Expression Method, a symbolic learning framework that leverages reinforcement learning to derive explicit mathematical expressions for epidemiological dynamics. Through numerical experiments on both synthetic and real-world datasets, FEX demonstrates high accuracy in modeling and predicting disease spread, while uncovering explicit relationships among epidemiological variables. These results highlight FEX as a powerful tool for infectious disease modeling, combining interpretability with strong predictive performance to support practical applications in public health.

cs.LG↗

arXiv2024

Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Method

In this paper, we introduce a new finite expression method (FEX) to solve high-dimensional partial integro-differential equations (PIDEs). This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel method of parameter grouping is proposed to reduce the number of coefficients in high-dimensional function approximation; 2) A Taylor series approximation method is implemented to significantly improve the computational efficiency and accuracy of the evaluation of the integral terms of PIDEs. The new FEX based method, denoted FEX-PG to indicate the addition of the parameter grouping (PG) step to the algorithm, provides both high accuracy and interpretable numerical solutions, with the outcome being an explicit equation that facilitates intuitive understanding of the underlying solution structures. These features are often absent in traditional methods, such as finite element methods (FEM) and finite difference methods, as well as in deep learning-based approaches. To benchmark our method against recent advances, we apply the new FEX-PG to solve benchmark PIDEs in the literature. In high-dimensional settings, FEX-PG exhibits strong and robust performance, achieving relative errors on the order of single precision machine epsilon.

math.NA↗

arXiv2024

Effective Many-body Interactions in Reduced-Dimensionality Spaces Through Neural Network Models

Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head-on. Therefore, developing reduced dimensionality representations that encapsulate complex correlation effects in many-body systems is crucial to advance the understanding of these complicated problems. However, a numerical evaluation of these predictive models can still be associated with a significant computational overhead. To address this challenge, in this paper, we discuss a combined framework that integrates recent advances in the development of active-space representations of coupled cluster (CC) downfolded Hamiltonians with neural network approaches. The primary objective of this effort is to train neural networks to eliminate the computationally expensive steps required for evaluating hundreds or thousands of Hugenholtz diagrams, which correspond to multidimensional tensor contractions necessary for evaluating a many-body form of downfolded/effective Hamiltonians. Using small molecular systems (the H2O and HF molecules) as examples, we demonstrate that training neural networks employing effective Hamiltonians for a few nuclear geometries of molecules can accurately interpolate/ extrapolate their forms to other geometrical configurations characterized by different intensities of correlation effects. We also discuss differences between effective interactions that define CC downfolded Hamiltonians with those of bare Hamiltonians defined by Coulomb interactions in the active spaces.

quant-ph↗

arXiv2024

Artificial-Intelligence-Driven Shot Reduction in Quantum Measurement

Variational Quantum Eigensolver (VQE) provides a powerful solution for approximating molecular ground state energies by combining quantum circuits and classical computers. However, estimating probabilistic outcomes on quantum hardware requires repeated measurements (shots), incurring significant costs as accuracy increases. Optimizing shot allocation is thus critical for improving the efficiency of VQE. Current strategies rely heavily on hand-crafted heuristics requiring extensive expert knowledge. This paper proposes a reinforcement learning (RL) based approach that automatically learns shot assignment policies to minimize total measurement shots while achieving convergence to the minimum of the energy expectation in VQE. The RL agent assigns measurement shots across VQE optimization iterations based on the progress of the optimization. This approach reduces VQE's dependence on static heuristics and human expertise. When the RL-enabled VQE is applied to a small molecule, a shot reduction policy is learned. The policy demonstrates transferability across systems and compatibility with other wavefunction ansatzes. In addition to these specific findings, this work highlights the potential of RL for automatically discovering efficient and scalable quantum optimization strategies.

quant-ph↗

arXiv2023

Learning nonlinear integral operators via Recurrent Neural Networks and its application in solving Integro-Differential Equations

In this paper, we propose using LSTM-RNNs (Long Short-Term Memory-Recurrent Neural Networks) to learn and represent nonlinear integral operators that appear in nonlinear integro-differential equations (IDEs). The LSTM-RNN representation of the nonlinear integral operator allows us to turn a system of nonlinear integro-differential equations into a system of ordinary differential equations for which many efficient solvers are available. Furthermore, because the use of LSTM-RNN representation of the nonlinear integral operator in an IDE eliminates the need to perform a numerical integration in each numerical time evolution step, the overall temporal cost of the LSTM-RNN-based IDE solver can be reduced to $O(n_T)$ from $O(n_T^2)$ if a $n_T$-step trajectory is to be computed. We illustrate the efficiency and robustness of this LSTM-RNN-based numerical IDE solver with a model problem. Additionally, we highlight the generalizability of the learned integral operator by applying it to IDEs driven by different external forces. As a practical application, we show how this methodology can effectively solve the Dyson's equation for quantum many-body systems.

cs.LG↗

arXiv2023

Optimizing Shot Assignment in Variational Quantum Eigensolver Measurement

The rapid progress in quantum computing has opened up new possibilities for tackling complex scientific problems. Variational quantum eigensolver (VQE) holds the potential to solve quantum chemistry problems and achieve quantum advantages. However, the measurement step within the VQE framework presents challenges. It can introduce noise and errors while estimating the objective function with a limited measurement budget. Such error can slow down or prevent the convergence of VQE. To reduce measurement error, many repeated measurements are needed to average out the noise in the objective function. By consolidating Hamiltonian terms into cliques, simultaneous measurements can be performed, reducing the overall measurement shot count. However, limited prior knowledge of each clique, such as noise level of measurement, poses a challenge. This work introduces two shot assignment strategies based on estimating the standard deviation of measurements to improve the convergence of VQE and reduce the required number of shots. These strategies specifically target two distinct scenarios: overallocated and underallocated shots. The efficacy of the optimized shot assignment strategy is demonstrated through numerical experiments conducted on a H$_2$ molecule. This research contributes to the advancement of VQE as a practical tool for solving quantum chemistry problems, paving the way for future applications in complex scientific simulations on quantum computers.

quant-ph↗

arXiv2023

Probing reaction channels via reinforcement learning

We propose a reinforcement learning based method to identify important configurations that connect reactant and product states along chemical reaction paths. By shooting multiple trajectories from these configurations, we can generate an ensemble of configurations that concentrate on the transition path ensemble. This configuration ensemble can be effectively employed in a neural network-based partial differential equation solver to obtain an approximation solution of a restricted Backward Kolmogorov equation, even when the dimension of the problem is very high. The resulting solution, known as the committor function, encodes mechanistic information for the reaction and can in turn be used to evaluate reaction rates.

physics.chem-ph↗

arXiv2022

A Generic Shared Attention Mechanism for Various Backbone Neural Networks

The self-attention mechanism has emerged as a critical component for improving the performance of various backbone neural networks. However, current mainstream approaches individually incorporate newly designed self-attention modules (SAMs) into each layer of the network for granted without fully exploiting their parameters' potential. This leads to suboptimal performance and increased parameter consumption as the network depth increases. To improve this paradigm, in this paper, we first present a counterintuitive but inherent phenomenon: SAMs tend to produce strongly correlated attention maps across different layers, with an average Pearson correlation coefficient of up to 0.85. Inspired by this inherent observation, we propose Dense-and-Implicit Attention (DIA), which directly shares SAMs across layers and employs a long short-term memory module to calibrate and bridge the highly correlated attention maps of different layers, thus improving the parameter utilization efficiency of SAMs. This design of DIA is also consistent with the neural network's dynamical system perspective. Through extensive experiments, we demonstrate that our simple yet effective DIA can consistently enhance various network backbones, including ResNet, Transformer, and UNet, across tasks such as image classification, object detection, and image generation using diffusion models.

cs.CV↗

arXiv2022

On Fast Simulation of Dynamical System with Neural Vector Enhanced Numerical Solver

The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a trade-off between accuracy and computational efficiency. To address this challenge, we introduce a deep learning-based corrector called Neural Vector (NeurVec), which can compensate for integration errors and enable larger time step sizes in simulations. Our extensive experiments on a variety of complex dynamical system benchmarks demonstrate that NeurVec exhibits remarkable generalization capability on a continuous phase space, even when trained using limited and discrete data. NeurVec significantly accelerates traditional solvers, achieving speeds tens to hundreds of times faster while maintaining high levels of accuracy and stability. Moreover, NeurVec's simple-yet-effective design, combined with its ease of implementation, has the potential to establish a new paradigm for fast-solving differential equations based on deep learning.

cs.CE↗

arXiv2022

The Lottery Ticket Hypothesis for Self-attention in Convolutional Neural Network

Recently many plug-and-play self-attention modules (SAMs) are proposed to enhance the model generalization by exploiting the internal information of deep convolutional neural networks (CNNs). In general, previous works ignore where to plug in the SAMs since they connect the SAMs individually with each block of the entire CNN backbone for granted, leading to incremental computational cost and the number of parameters with the growth of network depth. However, we empirically find and verify some counterintuitive phenomena that: (a) Connecting the SAMs to all the blocks may not always bring the largest performance boost, and connecting to partial blocks would be even better; (b) Adding the SAMs to a CNN may not always bring a performance boost, and instead it may even harm the performance of the original CNN backbone. Therefore, we articulate and demonstrate the Lottery Ticket Hypothesis for Self-attention Networks: a full self-attention network contains a subnetwork with sparse self-attention connections that can (1) accelerate inference, (2) reduce extra parameter increment, and (3) maintain accuracy. In addition to the empirical evidence, this hypothesis is also supported by our theoretical evidence. Furthermore, we propose a simple yet effective reinforcement-learning-based method to search the ticket, i.e., the connection scheme that satisfies the three above-mentioned conditions. Extensive experiments on widely-used benchmark datasets and popular self-attention networks show the effectiveness of our method. Besides, our experiments illustrate that our searched ticket has the capacity of transferring to some vision tasks, e.g., crowd counting and segmentation.

cs.CV↗

arXiv2022

Finite Expression Method for Solving High-Dimensional Partial Differential Equations

Designing efficient and accurate numerical solvers for high-dimensional partial differential equations (PDEs) remains a challenging and important topic in computational science and engineering, mainly due to the "curse of dimensionality" in designing numerical schemes that scale in dimension. This paper introduces a new methodology that seeks an approximate PDE solution in the space of functions with finitely many analytic expressions and, hence, this methodology is named the finite expression method (FEX). It is proved in approximation theory that FEX can avoid the curse of dimensionality. As a proof of concept, a deep reinforcement learning method is proposed to implement FEX for various high-dimensional PDEs in different dimensions, achieving high and even machine accuracy with a memory complexity polynomial in dimension and an amenable time complexity. An approximate solution with finite analytic expressions also provides interpretable insights into the ground truth PDE solution, which can further help to advance the understanding of physical systems and design postprocessing techniques for a refined solution.

math.NA↗

arXiv2021

Stationary Density Estimation of It\^o Diffusions Using Deep Learning

In this paper, we consider the density estimation problem associated with the stationary measure of ergodic It\^o diffusions from a discrete-time series that approximate the solutions of the stochastic differential equations. To take an advantage of the characterization of density function through the stationary solution of a parabolic-type Fokker-Planck PDE, we proceed as follows. First, we employ deep neural networks to approximate the drift and diffusion terms of the SDE by solving appropriate supervised learning tasks. Subsequently, we solve a steady-state Fokker-Plank equation associated with the estimated drift and diffusion coefficients with a neural-network-based least-squares method. We establish the convergence of the proposed scheme under appropriate mathematical assumptions, accounting for the generalization errors induced by regressing the drift and diffusion coefficients, and the PDE solvers. This theoretical study relies on a recent perturbation theory of Markov chain result that shows a linear dependence of the density estimation to the error in estimating the drift term, and generalization error results of nonparametric regression and of PDE regression solution obtained with neural-network models. The effectiveness of this method is reflected by numerical simulations of a two-dimensional Student's t distribution and a 20-dimensional Langevin dynamics.

math.NA↗