arXiv subjects

Liangrong Peng

Publications and source records attributed to Liangrong Peng.

16 recordsLinked to original sources

arXiv2025

Epidemic dynamics in physical-information-social multilayer networks

During epidemic outbreaks, information dissemination enhances individual protection, while social institutions influence the transmission through measures like government interventions, media campaigns, and hospital resource allocation. Here we develop a tripartite physical-information-social epidemic model and derive the corresponding kinetic equations in different scales by using the Microscopic Markov Chain Approach and mean-field approximations. The basic reproduction number and epidemic thresholds are explicitly derived by the next generation matrix method. Our results reveal that (1) active information exchange curbs disease transmission, (2) earlier and stronger government responses reduce the epidemic size, and (3) stronger governmental influence on media and hospitals further decreases disease transmission, particularly in hospital nodes. In fixed community structures, groups with frequent physical contact but weak information access (e.g., students) exhibit higher infection rates. For diverse communities, weaker physical layer heterogeneity but stronger information layer heterogeneity (e.g., high internet penetration in rural areas) inhibits epidemic outbreaks. These findings offer valuable insights for epidemic prevention and control strategies.

physics.soc-ph↗

arXiv2025

Thermodynamics of Chemical Reactions in Open Systems Reduced by PEA and QSSA

Previous studies have primarily focused on the nonequilibrium thermodynamics of chemical reaction networks (CRNs) occurring in closed systems. In contrast, CRNs in open systems exhibit much richer nonequilibrium phenomena due to sustained matter and energy exchange. Here, we bridge the quantitative relationships between essential thermodynamic quantities -- including the steady state, enthalpy, intrinsic Gibbs free energy, and entropy production rate -- in original mass-action equations and their PEA- or QSSA-reduced counterparts for open CRNs. Our analysis demonstrates that the thermodynamic structure, especially the second law of thermodynamics, of the full CRNs may not be preserved in reduced models when algebraic relations are imposed. Specifically, PEA-reduced models lose monotonicity in the intrinsic Gibbs free energy, whereas QSSA retains this property. These theoretical findings are further validated through analytical and numerical studies of two archetypal open systems: the Michaelis-Menten reactions and the phosphorylation-dephosphorylation cycle (PdPC). Our results provide a systematic framework for evaluating the fidelity of reduced models.

physics.chem-ph↗

arXiv2024

MEP-Net: Generating Solutions to Scientific Problems with Limited Knowledge by Maximum Entropy Principle

Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions from data. This paper proposes a novel neural network architecture, the MEP-Net, which combines the MEP with neural networks to generate probability distributions from moment constraints. We also provide a comprehensive overview of the fundamentals of the maximum entropy principle, its mathematical formulations, and a rigorous justification for its applicability for non-equilibrium systems based on the large deviations principle. Through fruitful numerical experiments, we demonstrate that the MEP-Net can be particularly useful in modeling the evolution of probability distributions in biochemical reaction networks and in generating complex distributions from data.

stat.ML↗

arXiv2024

Thermodynamics for Reduced Models of Breakable Amyloid Filaments Based on Maximum Entropy Principle

Amyloid filaments are associated with neurodegenerative diseases such as Alzheimer's and Parkinson's. Simplified models of amyloid aggregation are crucial because the original mass-action equations involve numerous variables, complicating analysis and understanding. While dynamical aspects of simplified models have been widely studied, their thermodynamic properties are less understood. In this study, we explore the Maximum Entropy Principle (MEP)-reduced models, initially developed for dynamical analysis, from a brand-new thermodynamic perspective. Analytical expressions along with numerical simulations demonstrate that the discrete MEP-reduced model strictly retains laws of thermodynamics, which holds true even when filament lengths transit from discrete values to continuous real numbers. Our findings not only clarify the thermodynamic consistency between the MEP-reduced models and the original models of amyloid filaments for the first time, but also suggest avenues for future research into the model-reduction thermodynamics.

physics.bio-ph↗

arXiv2023

A data-driven analysis on the mediation effect of compartment models between control measures and COVID-19 epidemics

We make a retrospective review on various control measures taken by 127 countries/territories during the first wave of COVID-19 pandemic until July 7, 2020, and evaluate their impacts on the epidemic dynamics quantitatively. The SEIR-QD model, as a representative for general compartment models, is used to fit the epidemic data, enabling the extraction of crucial model parameters and dynamical features. The mediation effect of the SEIR-QD model is revealed by using the mediation analysis with structure equation modeling for multiple mediators operating in parallel. The inherent impacts of these control policies on the transmission dynamics of COVID-19 epidemics are clarified, and compared with results derived from both multiple linear regression and neural-network-based nonlinear regression. Through this data-driven analysis, the mediation effect of compartment models is confirmed, which provides a better understanding on the intrinsic correlations among the strength of control measures and the dynamical features of COVID-19 epidemics.

q-bio.PE↗

arXiv2023

Thermodynamics for Reduced Models of Chemical Reactions by PEA and QSSA

Partial equilibrium approximation (PEA) and quasi-steady-state approximation (QSSA) are two classical methods for reducing complex macroscopic chemical reactions into simple computable ones. Previous studies mainly focus on the accuracy of solutions before and after applying model reduction. While, in this paper we start from a thermodynamic view, and try to establish a quantitative connection on the essential thermodynamic quantities, like entropy production rate, free energy dissipation rate and entropy flow rate, between the original reversible chemical mass-action equations and the reduced models by either PEA or QSSA. Our results reveal that the PEA and QSSA do not necessarily preserve the nice thermodynamic structure of the original full model during the reduction procedure (e.g. the loss of non-negativity of free energy dissipation rate), especially when adopting the algebraic relations in replace of differential equations. These results are further validated though the application to Michaelis-Menten reactions analytically and numerically as a prototype. We expect our study would motivate a re-examination on the effectiveness of various model reduction or approximation methods from a new perspective of non-equilibrium thermodynamics.

physics.chem-ph↗

arXiv2022

Towards Optimal Control of Amyloid Fibrillation

EGCG, as a representative of amyloid inhibitors, has shown a promising ability against Abeta fibrillation by directly degradating the mature fibrils. Most previous studies have been focusing on its functional mechanisms, meanwhile its optimal dosage has been seldom considered. To solve this critical issue, we refer to the generalized Logistics model for amyloid fibrillation and inhibition and adopt the optimal control theory to balance the effectiveness and cost (or toxicity) of inhibitors. The optimal control trajectory of inhibitors is analytically solved, based on which the influence of model parameters, the difference between the optimal control strategy and several traditional drug dosing strategies are systematically compared and validated through experiments. Our results will shed light on the rational usage of amyloid inhibitors in clinic.

physics.med-ph↗

arXiv2021

Rational evaluation of various epidemic models based on the COVID-19 data of China

In this paper, based on the Akaike information criterion, root mean square error and robustness coefficient, a rational evaluation of various epidemic models/methods, including seven empirical functions, four statistical inference methods and five dynamical models, on their forecasting abilities is carried out. With respect to the outbreak data of COVID-19 epidemics in China, we find that before the inflection point, all models fail to make a reliable prediction. The Logistic function consistently underestimates the final epidemic size, while the Gompertz's function makes an overestimation in all cases. Towards statistical inference methods, the methods of sequential Bayesian and time-dependent reproduction number are more accurate at the late stage of an epidemic. And the transition-like behavior of exponential growth method from underestimation to overestimation with respect to the inflection point might be useful for constructing a more reliable forecast. Compared to ODE-based SIR, SEIR and SEIR-AHQ models, the SEIR-QD and SEIR-PO models generally show a better performance on studying the COVID-19 epidemics, whose success we believe could be attributed to a proper trade-off between model complexity and fitting accuracy. Our findings not only are crucial for the forecast of COVID-19 epidemics, but also may apply to other infectious diseases.

q-bio.PE↗

arXiv2021

Recent Advances in Conservation-Dissipation Formalism for Irreversible Processes

The main purpose of this review is to summarize the recent advances of the Conservation-Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF's physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker-Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, \textit{etc.} Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.

math-ph↗

arXiv2020

Epidemic analysis of COVID-19 in China by dynamical modeling

The outbreak of novel coronavirus-caused pneumonia (COVID-19) in Wuhan has attracted worldwide attention. Here, we propose a generalized SEIR model to analyze this epidemic. Based on the public data of National Health Commission of China from Jan. 20th to Feb. 9th, 2020, we reliably estimate key epidemic parameters and make predictions on the inflection point and possible ending time for 5 different regions. According to optimistic estimation, the epidemics in Beijing and Shanghai will end soon within two weeks, while for most part of China, including the majority of cities in Hubei province, the success of anti-epidemic will be no later than the middle of March. The situation in Wuhan is still very severe, at least based on public data until Feb. 15th. We expect it will end up at the beginning of April. Moreover, by inverse inference, we find the outbreak of COVID-19 in Mainland, Hubei province and Wuhan all can be dated back to the end of December 2019, and the doubling time is around two days at the early stage.

q-bio.PE↗

arXiv2020

Identification of hydrodynamic instability by convolutional neural networks

The onset of hydrodynamic instabilities is of great importance in both industry and daily life, due to the dramatic mechanical and thermodynamic changes for different types of flow motions. In this paper, modern machine learning techniques, especially the convolutional neural networks (CNN), are applied to identify the transition between different flow motions raised by hydrodynamic instability, as well as critical non-dimensionalized parameters for characterizing this transit. CNN not only correctly predicts the critical transition values for both Taylor-Couette (TC) flow and Rayleigh- Bénard (RB) convection under various setups and conditions, but also shows an outstanding performance on robustness and noise-tolerance. In addition, key spatial features used for classifying different flow patterns are revealed by the principal component analysis.

physics.comp-ph↗

arXiv2020

When Machine Learning Meets Multiscale Modeling in Chemical Reactions

Due to the intrinsic complexity and nonlinearity of chemical reactions, direct applications of traditional machine learning algorithms may face with many difficulties. In this study, through two concrete examples with biological background, we illustrate how the key ideas of multiscale modeling can help to reduce the computational cost of machine learning a lot, as well as how machine learning algorithms perform model reduction automatically in a time-scale separated system. Our study highlights the necessity and effectiveness of an integration of machine learning algorithms and multiscale modeling during the study of chemical reactions.

q-bio.MN↗

arXiv2020

Thermodynamics of Markov Processes with Non-extensive Entropy and Free Energy

Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a ``thermodynamic'' theory can also be developed based on Tsallis' generalized entropy $S^{(q)}=\sum_{i=1}^N(p_i-p_i^q)/[q(q-1)]$ and Shiino's generalized free energy $F^{(q)}=[\sum_{i=1}^Np_i(p_i/π_i)^{q-1}-1]/[q(q-1)]$, where $π_i$ is the stationary distribution. $dF^{(q)}/dt=-f_d^{(q)}\le 0$ and it is zero iff the system is in its stationary state. $dS^{(q)}/dt-Q_{ex}^{(q)} = f_d^{(q)}$ where $Q_{ex}^{(q)}$ characterizes the heat exchange. For systems approaching equilibrium with detailed balance, $f_d^{(q)}$ is the product of Onsager's thermodynamic flux and force. However, it is discovered that the Onsager's force is non-local. This is a consequence of the particular transformation invariance for zero energy of Tsallis' statistics.

math-ph↗

arXiv2019

Conservation-Dissipation Formalism for Soft Matter Physics: I. Equivalence with Doi's Variational Approach

In this paper, we proved that by choosing the proper variational function and variables, the variational approach proposed by M. Doi in soft matter physics was equivalent to the Conservation-Dissipation Formalism. To illustrate the correspondence between these two theories, several novel examples in soft matter physics, including particle diffusion in dilute solutions, polymer phase separation dynamics and nematic liquid crystal flows, were carefully examined. Based on our work, a deep connection among the generalized Gibbs relation, the second law of thermodynamics and the variational principle in non-equilibrium thermodynamics was revealed.

cond-mat.stat-mech↗

arXiv2019

Conservation-Dissipation Formalism for Soft Matter Physics: II. Application to Non-isothermal Nematic Liquid Crystals

To most existing non-equilibrium theories, the modeling of non-isothermal processes was a hard task. Intrinsic difficulties involved the non-equilibrium temperature, the coexistence of conserved energy and dissipative entropy, etc. In this paper, by taking the non-isothermal flow of nematic liquid crystals as a typical example, we illustrated that thermodynamically consistent models in either vectorial or tensorial forms could be constructed within the framework of Conservation-Dissipation Formalism (CDF). And the classical isothermal Ericksen-Leslie model and Qian-Sheng model were shown to be special cases of our new vectorial and tensorial models in the isothermal, incompressible and stationary limit. Most importantly, from above examples, it was learnt that mathematical modeling based on CDF could easily solve the issues relating with non-isothermal situations in a systematic way. The first and second laws of thermodynamics were satisfied simultaneously. The non-equilibrium temperature was defined self-consistently through the partial derivative of entropy function. Relaxation-type constitutive relations were constructed, which gave rise to the classical linear constitutive relations, like Newton's law and Fourier's law, in stationary limits. Therefore, CDF was expected to have a broad scope of applications in soft matter physics, especially under the complicated situations, such as non-isothermal, compressible and nanoscale systems.

cond-mat.soft↗

arXiv2017

The Markov Process Admits a Consistent Steady-State Thermodynamic Formalism

The seek for a new universal formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that: 1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; 2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; 3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that, with respect to the steady state, general Markov processes admit a unified and self-consistent non-equilibrium thermodynamic formulation, regardless of underlying detailed models.

cond-mat.stat-mech↗