arXiv subjects

Daniel Zhou

Publications and source records attributed to Daniel Zhou.

4 recordsLinked to original sources

arXiv2026

Duality Between Chemical Potential Dynamics and Reaction-Diffusion Systems

Pattern formation in soft, active, and biological matter is described by two ostensibly distinct continuum frameworks: phase-field theories driven by chemical-potential gradients, and mass-conserving reaction-diffusion (McRD) dynamics governed by local interconversion kinetics. Here we establish a constructive, equation-level duality valid in the nonlinear, far-from-equilibrium regime. McRD is the broader class: every chemical-potential theory with conserved order parameters embeds as the slow dynamics on an attracting manifold of an McRD system; conversely, every McRD with attractive nullcline admits an exact chemical-potential representation in the fast-interconversion limit, with the constitutive relation set by the nullcline. The construction resolves the generic non-invertibility of the chemical-potential as a function of density in phase-separating regimes by embedding it as an attracting manifold in an extended two-field description with conserved total density. Gradient stiffness maps faithfully onto an intrinsic reaction-diffusion length set by the auxiliary field, yielding a diagonal-diffusion normal form whose interface profile matches the original Cahn-Hilliard model by construction. The duality yields an explicit dictionary for phase coexistence: the Maxwell equal-area construction is exactly equivalent to the reactive turnover-balance condition. It extends to weakly nonconservative dynamics, unifying reaction-arrested coarsening and mesa splitting, and to multicomponent theories with broken Maxwell symmetry. As a concrete payoff, the dual sharp-interface picture yields a closed-form velocity law for traveling waves in nonreciprocal Cahn-Hilliard dynamics, in quantitative agreement with simulations.

cond-mat.soft↗

arXiv2026

Amortized Bayesian inference for actigraph time sheet data from mobile devices

Mobile data technologies use ``actigraphs'' to furnish information on health variables as a function of a subject's movement. The advent of wearable devices and related technologies has propelled the creation of health databases consisting of human movement data to conduct research on mobility patterns and health outcomes. Statistical methods for analyzing high-resolution actigraph data depend on the specific inferential context, but the advent of Artificial Intelligence (AI) frameworks require that the methods be congruent to transfer learning and amortization. This article devises amortized Bayesian inference for actigraph time sheets. We pursue a Bayesian approach to ensure full propagation of uncertainty and its quantification using a hierarchical dynamic linear model. We build our analysis around actigraph data from the Physical Activity through Sustainable Transport Approaches in Los Angeles (PASTA-LA) study conducted by the Fielding School of Public Health in the University of California, Los Angeles. Apart from achieving probabilistic imputation of actigraph time sheets, we are also able to statistically learn about the time-varying impact of explanatory variables on the magnitude of acceleration (MAG) for a cohort of subjects.

stat.ML↗

arXiv2023

Personalized Search Via Neural Contextual Semantic Relevance Ranking

Existing neural relevance models do not give enough consideration for query and item context information which diversifies the search results to adapt for personal preference. To bridge this gap, this paper presents a neural learning framework to personalize document ranking results by leveraging the signals to capture how the document fits into users' context. In particular, it models the relationships between document content and user query context using both lexical representations and semantic embeddings such that the user's intent can be better understood by data enrichment of personalized query context information. Extensive experiments performed on the search dataset, demonstrate the effectiveness of the proposed method.

cs.IR↗

arXiv2022

Dynamic Bayesian Learning for Spatiotemporal Mechanistic Models

We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary inputs. The emulated learner can then be used to train the system from noisy data achieved by melding information from observed data with the emulated mechanistic system. This joint melding of mechanistic systems employ hierarchical state-space models with Gaussian process regression. Assuming the dynamical system is controlled by a finite collection of inputs, Gaussian process regression learns the effect of these parameters through a number of training runs, driving the stochastic innovations of the spatiotemporal state-space component. This enables efficient modeling of the dynamics over space and time. This article details exact inference with analytically accessible posterior distributions in hierarchical matrix-variate Normal and Wishart models in designing the emulator. This step obviates expensive iterative algorithms such as Markov chain Monte Carlo or variational approximations. We also show how emulation is applicable to large-scale emulation by designing a dynamic Bayesian transfer learning framework. Inference on mechanistic model parameters proceeds using Markov chain Monte Carlo as a post-emulation step using the emulator as a regression component. We demonstrate this framework through solving inverse problems arising in the analysis of ordinary and partial nonlinear differential equations and, in addition, to a black-box computer model generating spatiotemporal dynamics across a graphical model.

stat.ME↗