arXiv subjects

Mengyang Gu

Publications and source records attributed to Mengyang Gu.

At least 19 recordsLinked to original sources

arXiv2026

GNet: A scalable and flexible Gaussian process network with nonparametric neurons

We develop GNet, a scalable and flexible Gaussian process network with nonparametric activation functions modeled by Gaussian processes. To reduce computational and storage costs, we introduce the jointly inverse Kalman filter, a fast algorithm together with closed-form expressions of gradients for accelerating model training and predictions without the need to form covariance matrices. Using a unified optimization setting, GNet shows competitive performance across a diverse range of test problems, including predicting nonlinear functions, nonparametric regression of real-world data, and predicting one-body direct correlation functions with high-dimensional inputs in classical density function theory. The strong performance of GNet, accelerated by the jointly inverse Kalman filter, suggests broad applicability to large-scale predictive modeling with substantially reduced computational and storage costs.

stat.ME↗

arXiv2026

Model-free estimation in scattering analysis of microscopy

The mean squared displacement (MSD) of particles or probes is commonly estimated from microscopy videos using particle tracking approaches, which rely on tuning parameters manually, and are often unstable over the entire lag time range, especially in dense or low-contrast situations. In this work, we propose model-free ab initio uncertainty quantification (MF-AIUQ), a model-free method for scattering analysis of microscopy video based on a probabilistic framework, which estimates MSD without isolating particles and linking their trajectories. Based on the relationship between the intermediate scattering function (ISF) and the MSD derived from the cumulant theorem, MF-AIUQ estimates the MSD values by the marginal maximum likelihood estimator. To reduce the computational cost, the likelihood function is approximated by a subset of Fourier-transformed intensities. These intensities are equally spaced at the logarithmic values of Fourier basis functions and lag time points. We found that the ISF is smooth in this logarithmic input space, and the information of the ISF can be captured by this subset of inputs. We examine the method through simulation studies covering several representative stochastic processes and three experimental systems: a Newtonian fluid for evaluating performance in optically dense and bright-field settings, a gelation system with an evolving MSD shape, and snail mucin, a viscoelastic biopolymer, for modulus estimation. Across these studies, MF-AIUQ provides smooth and stable MSD estimates over the full lag time range and serves as a useful complementary approach in settings where particle tracking is unreliable or a parametric model of MSD is unavailable or unverifiable.

stat.AP↗

arXiv2026

Accessible pore geometry governs tracer diffusion in crowded environments

Tracer diffusion in crowded environments is central to many biological and soft matter systems, but quantitative frameworks for linking tracer motion to environmental structure remain limited, and the co-dependence among geometric variables that facilitate or hinder tracer transport is not yet well understood. Here, we study the transport of rigid tracers in suspensions of soft particles and within living cells. Experiments reveal a transition from diffusive to confined motion as the matrix area fraction increases. The observed ensemble-level statistics, including the mean-squared displacements (MSDs), can be reproduced using a minimal simulation. Using simulation outputs, we train a parallel partial Gaussian process (PPGP) model that rapidly predicts MSDs from matrix geometric variables, including area fraction, particle size, and polydispersity. Analysis reveals that tracer transport is primarily governed by accessible pore sizes and that distinct global structures can produce indistinguishable MSDs. While MSDs do not uniquely encode system geometrical parameters, we nevertheless find correspondence between pore size distribution and the ensemble MSDs. By modeling matrix self-diffusivity, the minimal model can also phenomenologically describe MSDs of internalized tracer particles in cells. The framework enables rapid inference of structural properties in crowded environments, including transport in the intracellular environment.

cond-mat.soft↗

arXiv2026

Long-Term Probabilistic Forecast of Vegetation Conditions Using Climate Attributes in the Four Corners Region

Weather conditions can drastically alter the state of crops and rangelands, and in turn, impact the incomes and food security of individuals worldwide. Satellite-based remote sensing offers an effective way to monitor vegetation and climate variables on regional and global scales. The annual peak Normalized Difference Vegetation Index (NDVI), derived from satellite observations, is closely associated with crop development, rangeland biomass, and vegetation growth. Although various machine learning methods have been developed to forecast NDVI over short time ranges, such as one-month-ahead predictions, long-term forecasting approaches, such as one-year-ahead predictions of vegetation conditions, are not yet available. To fill this gap, we develop a two-phase machine learning model to forecast the one-year-ahead peak NDVI over high-resolution grids, using the Four Corners region of the Southwestern United States as a testbed. In phase one, we identify informative climate attributes, including precipitation and maximum vapor pressure deficit, and develop the generalized parallel Gaussian process that captures the relationship between climate attributes and NDVI. In phase two, we forecast these climate attributes using historical data at least one year before the NDVI prediction month, which then serve as inputs to forecast the peak NDVI at each spatial grid. We developed open-source tools that outperform alternative methods for both gross NDVI and grid-based NDVI one-year forecasts, providing information that can help farmers and ranchers make actionable plans a year in advance.

stat.AP↗

arXiv2025

Synergizing chemical and AI communities for advancing laboratories of the future

The development of automated experimental facilities and the digitization of experimental data have introduced numerous opportunities to radically advance chemical laboratories. As many laboratory tasks involve predicting and understanding previously unknown chemical relationships, machine learning (ML) approaches trained on experimental data can substantially accelerate the conventional design-build-test-learn process. This outlook article aims to help chemists understand and begin to adopt ML predictive models for a variety of laboratory tasks, including experimental design, synthesis optimization, and materials characterization. Furthermore, this article introduces how artificial intelligence (AI) agents based on large language models can help researchers acquire background knowledge in chemical or data science and accelerate various aspects of the discovery process. We present three case studies in distinct areas to illustrate how ML models and AI agents can be leveraged to reduce time-consuming experiments and manual data analysis. Finally, we highlight existing challenges that require continued synergistic effort from both experimental and computational communities to address.

stat.AP↗

arXiv2025

Fast phase prediction of charged polymer blends by white-box machine learning surrogates

Compatibilized polymer blends are a complex, yet versatile and widespread category of material. When the components of a binary blend are immiscible, they are typically driven towards a macrophase-separated state, but with the introduction of electrostatic interactions, they can be either homogenized or shifted to microphase separation. However, both experimental and simulation approaches face significant challenges in efficiently exploring the vast design space of charge-compatibilized polymer blends, encompassing chemical interactions, architectural properties, and composition. In this work, we introduce a white-box machine learning approach integrated with polymer field theory to predict the phase behavior of these systems, which is significantly more accurate than conventional black-box machine learning approaches. The random phase approximation (RPA) calculation is used as a testbed to determine polymer phases. Instead of directly predicting the polymer phase output of RPA calculations from a large input space by a machine learning model, we build a parallel partial Gaussian process model to predict the most computationally intensive component of the RPA calculation that only involves polymer architecture parameters as inputs. This approach substantially reduces the computational cost of the RPA calculation across a vast input space with nearly 100% accuracy for out-of-sample prediction, enabling rapid screening of polymer blend charge-compatibilization designs. More broadly, the white-box machine learning strategy offers a promising approach for dramatic acceleration of polymer field-theoretic methods for mapping out polymer phase behavior.

cond-mat.soft↗

arXiv2025

Neural Operators for Forward and Inverse Potential-Density Mappings in Classical Density Functional Theory

Neural operators are capable of capturing nonlinear mappings between infinite-dimensional functional spaces, offering a data-driven approach to modeling complex functional relationships in classical density functional theory (cDFT). In this work, we evaluate the performance of several neural operator architectures in learning the functional relationships between the one-body density profile $\rho(x)$, the one-body direct correlation function $c_1(x)$, and the external potential $V_{ext}(x)$ of inhomogeneous one-dimensional (1D) hard-rod fluids, using training data generated from analytical solutions of the underlying statistical-mechanical model. We compared their performance in terms of the Mean Squared Error (MSE) loss in establishing the functional relationships as well as in predicting the excess free energy across two test sets: (1) a group test set generated via random cross-validation (CV) to assess interpolation capability, and (2) a newly constructed dataset for leave-one-group CV to evaluate extrapolation performance. Our results show that FNO achieves the most accurate predictions of the excess free energy, with the squared ReLU activation function outperforming other activation choices. Among the DeepONet variants, the Residual Multiscale Convolutional Neural Network (RMSCNN) combined with a trainable Gaussian derivative kernel (GK-RMSCNN-DeepONet) demonstrates the best performance. Additionally, we applied the trained models to solve for the density profiles at various external potentials and compared the results with those obtained from the direct mapping $V_{ext} \mapsto \rho$ with neural operators, as well as with Gaussian Process Regression (GPR) combined with Active Learning by Error Control (ALEC), which has shown strong performance in previous studies.

physics.chem-ph↗

arXiv2025

Unsupervised cell segmentation by fast Gaussian Processes

Cell boundary information is crucial for analyzing cell behaviors from time-lapse microscopy videos. Existing supervised cell segmentation tools, such as ImageJ, require tuning various parameters and rely on restrictive assumptions about the shape of the objects. While recent supervised segmentation tools based on convolutional neural networks enhance accuracy, they depend on high-quality labeled images, making them unsuitable for segmenting new types of objects not in the database. We developed a novel unsupervised cell segmentation algorithm based on fast Gaussian processes for noisy microscopy images without the need for parameter tuning or restrictive assumptions about the shape of the object. We derived robust thresholding criteria adaptive for heterogeneous images containing distinct brightness at different parts to separate objects from the background, and employed watershed segmentation to distinguish touching cell objects. Both simulated studies and real-data analysis of large microscopy images demonstrate the scalability and accuracy of our approach compared with the alternatives.

stat.AP↗

arXiv2025

Prior distributions for Gaussian processes in computer model emulation and calibration

This article discusses prior distributions for the parameters of Gaussian processes (GPs) that are widely used as surrogate models to emulate expensive computer simulations. The parameters typically involve mean parameters, a variance parameter, and correlation parameters. These parameters are often estimated by maximum likelihood (MLE). In some scenarios, however, the MLE can be unstable, particularly when the number of simulation runs is small, and some Bayesian estimators display better properties. We introduce default Bayesian priors for the parameters of GPs with isotropic and separable correlation functions for emulating computer simulations with both scalar-valued and vector-valued outputs. We also summarize recent developments of Bayesian priors for calibrating computer models by field or experimental observations. Finally, we review software packages for computer model emulation and calibration.

stat.ME↗

arXiv2025

Fast data inversion for high-dimensional Ornstein-Uhlenbeck processes from noisy measurements

In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can be either fixed or estimated. We utilize an orthogonal factor loading matrix that avoids computing the inversion of the posterior covariance matrix at each time of the Kalman filter, and derive closed-form expressions in an expectation-maximization algorithm for parameter estimation, which substantially reduces the computational complexity without approximation. Our approach has several applications, including noise filtering for high-dimensional time series, estimating nonseparable covariance structure between different time series, and estimating latent physical processes from real-world measurements. Extensive simulated studies illustrate higher accuracy and scalability of our approach compared to alternatives. Furthermore, by applying our method to geodetic measurements to estimate slow slip events from geodetic data in the Cascadia region, our estimated slip better agrees with independently measured seismic data of tremor events. The substantial acceleration from our method enables the use of massive noisy data for geological hazard quantification and other applications.

stat.CO↗

arXiv2024

Mixing, Enhanced Dissipation and Phase Transition in the Kinetic Vicsek Model

In this paper, we study the kinetic Vicsek model, which serves as a starting point for describing the polarization phenomena observed in the experiments of fibroblasts moving on liquid crystalline substrates. The long-time behavior of the kinetic equation is analyzed, revealing that, within specific parameter regimes, the mixing and enhanced dissipation phenomena stabilize the dynamics and ensure effective information communication among agents. Consequently, the solution exhibits features similar to those of a spatially-homogeneous system. As a result, we confirm the phase transition observed in the agent-based Vicsek model at the kinetic level.

math.AP↗

arXiv2024

The inverse Kalman filter

We introduce the inverse Kalman filter, which enables exact matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with linear computational cost. We integrate the inverse Kalman filter with the conjugate gradient algorithm, which substantially accelerates the computation of matrix inversion for a general form of covariance matrix, where other approximation approaches may not be directly applicable. We demonstrate the scalability and efficiency of the proposed approach through applications in nonparametric estimation of particle interaction functions, using both simulations and cell trajectories from microscopy data.

stat.ME↗

arXiv2024

Learning from landmarks, curves, surfaces, and shapes in Geomstats

We introduce the shape module of the Python package Geomstats to analyze shapes of objects represented as landmarks, curves and surfaces across fields of natural sciences and engineering. The shape module first implements widely used shape spaces, such as the Kendall shape space, as well as elastic spaces of discrete curves and surfaces. The shape module further implements the abstract mathematical structures of group actions, fiber bundles, quotient spaces and associated Riemannian metrics which allow users to build their own shape spaces. The Riemannian geometry tools enable users to compare, average, interpolate between shapes inside a given shape space. These essential operations can then be leveraged to perform statistics and machine learning on shape data. We present the object-oriented implementation of the shape module along with illustrative examples and show how it can be used to perform statistics and machine learning on shape spaces.

cs.GR↗

arXiv2023

Perfecting Liquid-State Theories with Machine Intelligence

Recent years have seen a significant increase in the use of machine intelligence for predicting electronic structure, molecular force fields, and the physicochemical properties of various condensed systems. However, substantial challenges remain in developing a comprehensive framework capable of handling a wide range of atomic compositions and thermodynamic conditions. This perspective discusses potential future developments in liquid-state theories leveraging on recent advancements of functional machine learning. By harnessing the strengths of theoretical analysis and machine learning techniques including surrogate models, dimension reduction and uncertainty quantification, we envision that liquid-state theories will gain significant improvements in accuracy, scalability and computational efficiency, enabling their broader applications across diverse materials and chemical systems.

physics.chem-ph↗

arXiv2023

Probabilistic forecast of nonlinear dynamical systems with uncertainty quantification

Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict new scenarios unobserved before. In this work, we first extend parallel partial Gaussian processes for predicting the vector-valued transition function that links the observations between the current and next time points, and quantify the uncertainty of predictions by posterior sampling. Second, we show the equivalence between the dynamic mode decomposition and the maximum likelihood estimator of the linear mapping matrix in the linear state space model. The connection provides a {probabilistic generative} model of dynamic mode decomposition and thus, uncertainty of predictions can be obtained. Furthermore, we draw close connections between different data-driven models for approximating nonlinear dynamics, through a unified view of generative models. We study two numerical examples, where the inputs of the dynamics are assumed to be known in the first example and the inputs are unknown in the second example. The examples indicate that uncertainty of forecast can be properly quantified, whereas model or input misspecification can degrade the accuracy of uncertainty quantification.

stat.ME↗

arXiv2023

Sequential Kalman filter for fast online changepoint detection in longitudinal health records

This article introduces the sequential Kalman filter, a computationally scalable approach for online changepoint detection with temporally correlated data. The temporal correlation was not considered in the Bayesian online changepoint detection approach due to the large computational cost. Motivated by detecting COVID-19 infections for dialysis patients from massive longitudinal health records with a large number of covariates, we develop a scalable approach to detect multiple changepoints from correlated data by sequentially stitching Kalman filters of subsequences to compute the joint distribution of the observations, which has linear computational complexity with respect to the number of observations between the last detected changepoint and the current observation at each time point, without approximating the likelihood function. Compared to other online changepoint detection methods, simulated experiments show that our approach is more precise in detecting single or multiple changes in mean, variance, or correlation for temporally correlated data. Furthermore, we propose a new way to integrate classification and changepoint detection approaches that improve the detection delay and accuracy for detecting COVID-19 infection compared to other alternatives.

stat.AP↗

arXiv2023

Analyzing Disparity and Temporal Progression of Internet Quality through Crowdsourced Measurements with Bias-Correction

Crowdsourced speedtest measurements are an important tool for studying internet performance from the end user perspective. Nevertheless, despite the accuracy of individual measurements, simplistic aggregation of these data points is problematic due to their intrinsic sampling bias. In this work, we utilize a dataset of nearly 1 million individual Ookla Speedtest measurements, correlate each datapoint with 2019 Census demographic data, and develop new methods to present a novel analysis to quantify regional sampling bias and the relationship of internet performance to demographic profile. We find that the crowdsourced Ookla Speedtest data points contain significant sampling bias across different census block groups based on a statistical test of homogeneity. We introduce two methods to correct the regional bias by the population of each census block group. Whereas the sampling bias leads to a small discrepancy in the overall cumulative distribution function of internet speed in a city between estimation from original samples and bias-corrected estimation, the discrepancy is much smaller compared to the size of the sampling heterogeneity across regions. Further, we show that the sampling bias is strongly associated with a few demographic variables, such as income, education level, age, and ethnic distribution. Through regression analysis, we find that regions with higher income, younger populations, and lower representation of Hispanic residents tend to measure faster internet speeds along with substantial collinearity amongst socioeconomic attributes and ethnic composition. Finally, we find that average internet speed increases over time based on both linear and nonlinear analysis from state space models, though the regional sampling bias may result in a small overestimation of the temporal increase of internet speed.

stat.AP↗

arXiv2023

Ab initio uncertainty quantification in scattering analysis of microscopy

Estimating parameters from data is a fundamental problem, customarily done by minimizing a loss function between a model and observed statistics. In scattering-based analysis, researchers often employ their domain expertise to select a specific range of wave vectors for analysis, a choice that can vary depending on the specific case. We introduce another paradigm that defines a probabilistic generative model from the beginning of data processing and propagates the uncertainty for parameter estimation, termed the ab initio uncertainty quantification (AIUQ). As an illustrative example, we demonstrate this approach with differential dynamic microscopy (DDM) that extracts dynamical information through Fourier analysis at a selected range of wave vectors. We first show that the conventional way of estimation in DDM is equivalent to fitting a temporal variogram in the reciprocal space using a latent factor model. Then we derive the maximum marginal likelihood estimator, which optimally weighs the information at all wave vectors, therefore eliminating the need to select the range of wave vectors. Furthermore, we substantially reduce the computational cost by utilizing the generalized Schur algorithm for Toeplitz covariances without approximation. Simulated studies validate that AIUQ improves estimation accuracy and enables model selection with automated analysis. The utility of AIUQ is also demonstrated by three distinct sets of experiments: first in an isotropic Newtonian fluid, pushing limits of optically dense systems compared to multiple particle tracking; next in a system undergoing a sol-gel transition, automating the determination of gelling points and critical exponent; and lastly, in discerning anisotropic diffusive behavior of colloids in a liquid crystal. These outcomes collectively underscore AIUQ's versatility to capture system dynamics in an efficient and automated manner.

physics.comp-ph↗