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We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained.…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…
Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such…
We employ constraints to control the parameter space of deep neural networks throughout training. The use of customized, appropriately designed constraints can reduce the vanishing/exploding gradients problem, improve smoothness of…
This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem is formulated as a reduced-order modeling problem. The…
The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin dynamics that incorporates a distribution-dependent drift, and it naturally arises from the optimization of two-layer neural networks via (noisy) gradient…
This thesis is mainly concerned with state-space approaches for solving deep (temporal) Gaussian process (DGP) regression problems. More specifically, we represent DGPs as hierarchically composed systems of stochastic differential equations…
We introduce a machine-learning-based coarse-grained molecular dynamics (CGMD) model that faithfully retains the many-body nature of the inter-molecular dissipative interactions. Unlike common empirical CG models, the present model is…
Generalized Langevin dynamics (GLD) arise in the modeling of a number of systems, ranging from structured fluids that exhibit a viscoelastic mechanical response, to biological systems, and other media that exhibit anomalous diffusive…
We extend the data-assimilation approach of Ling and Lozano-Dur\'an (AIAA 2025-1280) to develop machine-learning-based subgrid-scale stress (SGS) models for large-eddy simulation (LES) that are consistent with the numerical scheme of the…
State-of-the-art deep learning methods have shown a remarkable capacity to model complex data domains, but struggle with geospatial data. In this paper, we introduce SpaceGAN, a novel generative model for geospatial domains that learns…
Stochastic gradient descent (SGD) and its variants are widely used and highly effective optimization methods in machine learning, especially for neural network training. By using a single datum or a small subset of the data, selected…
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter…
We develop an alternative approach to study the effect of the generic perturbation (in addition to explicitly considering the loss term) in the nonlinear Klein-Gordon equations. By a change of the variables that cancel the dissipation term…
We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…
In this paper, we study a new type of spatial sparse recovery problem, that is to infer the fine-grained spatial distribution of certain density data in a region only based on the aggregate observations recorded for each of its subregions.…
Spatial transcriptomics technologies enable the measurement of gene expression with spatial context, providing opportunities to understand how gene regulatory networks vary across tissue regions. However, existing graphical models focus…
Designing algorithms for solving high-dimensional Bayesian inverse problems directly in infinite-dimensional function spaces - where such problems are naturally formulated - is crucial to ensure stability and convergence as the…
Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…
The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this…