arXiv subjects

Liu Hong

Publications and source records attributed to Liu Hong.

At least 19 recordsLinked to original sources

arXiv2026

Incorporating Continuous Dependence Qualifies Physics-Informed Neural Networks for Operator Learning

Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real applications are highly restricted by their poor generalization performance. Inspired by the rigorous mathematical statements on the well-posedness of PDEs, we develop a novel extension of PINNs by incorporating the additional information on the continuous dependence of PDE solutions with respect to parameters and initial/boundary values (abbreviated as cd-PINN). Extensive numerical experiments demonstrate that, with limited labeled data, cd-PINN achieves 1-3 orders of magnitude lower in test MSE than DeepONet and FNO. Therefore, incorporating the continuous dependence of PDE solutions provides a simple way for qualifying PINNs for operator learning.

math.DS↗

arXiv2026

A Comparative Investigation of Thermodynamic Structure-Informed Neural Networks

Physics-informed neural networks (PINNs) offer a unified framework for solving both forward and inverse problems of differential equations, yet their performance and physical consistency strongly depend on how governing laws are incorporated. In this work, we present a systematic comparison of different thermodynamic structure-informed neural networks by incorporating various thermodynamics formulations, including Newtonian, Lagrangian, and Hamiltonian mechanics for conservative systems, as well as the Onsager variational principle and extended irreversible thermodynamics for dissipative systems. Through comprehensive numerical experiments on representative ordinary and partial differential equations, we quantitatively evaluate the impact of these formulations on accuracy, physical consistency, noise robustness, and interpretability. The results show that Newtonian-residual-based PINNs can reconstruct system states but fail to reliably recover key physical and thermodynamic quantities, whereas structure-preserving formulation significantly enhances parameter identification, thermodynamic consistency, and robustness. These findings provide practical guidance for principled design of thermodynamics-consistency model, and lay the groundwork for integrating more general nonequilibrium thermodynamic structures into physics-informed machine learning.

cs.LG↗

arXiv2026

Four Levels of Thermodynamic Convergence of Singularly Perturbed Markov Semigroups

Assuming the dynamical convergence $P_t^\varepsilon\to\bar P_t$ for singular limits of time-homogeneous Markov diffusion semigroups, we develop a semigroup-level framework that upgrades this convergence into four levels of thermodynamic convergence (including non-reversible diffusions and multiplicative noise). Level~I yields convergence of the free energy, and under an $\varepsilon$-uniform curvature--dimension bound $CD(-\kappa,\infty)$, Level~II shows convergence of the non-adiabatic entropy production. By further assuming coefficient convergence, Level~III yields sharp $\liminf$ bounds for the adiabatic and total entropy productions. Moreover, Level~IV holds precisely when a locking condition holds, with no loss on entropy production arising from unresolved microscopic nonequilibrium forcing. We give two verifiable routes to the uniform $CD$ hypothesis (a Ricci-type criterion and an It\^{o}--Kunita derivative-flow method) and illustrate the theory on slow--fast averaging limits and stiff-potential regimes.

math.PR↗

arXiv2026

CoLA-Flow Policy: Temporally Coherent Imitation Learning via Continuous Latent Action Flow Matching for Robotic Manipulation

Learning long-horizon robotic manipulation requires jointly achieving expressive behavior modeling, real-time inference, and stable execution, which remains challenging for existing generative policies. Diffusion-based approaches offer strong modeling capacity but incur high inference latency, while flow matching enables fast, near-single-step generation yet often suffers from unstable execution when operating directly in the raw action space. We propose Continuous Latent Action Flow Policy (CoLA-Flow Policy), a trajectory-level imitation learning framework that performs flow matching in a continuous latent action space. By encoding action sequences into temporally coherent latent trajectories and learning an explicit latent-space flow, CoLA-Flow Policy decouples global motion structure from low-level control noise, enabling smooth and reliable long-horizon execution. The framework further integrates geometry-aware point cloud conditioning and execution-time multimodal modulation, using visual cues as a representative modality to enhance real-world robustness. Experiments in simulation and on real robots show that CoLA-Flow Policy achieves near-single-step inference, improves trajectory smoothness by up to 93.7% and task success by up to 25 percentage points over raw action-space flow baselines, while remaining significantly faster than diffusion-based policies.

cs.RO↗

arXiv2025

Kinetic and Thermodynamic Descriptions of Open Systems of Complex Chemical Reactions with Multiple Scales

The general theory of a complex system of nonlinear chemical reactions is a primary language of chemistry that includes chemical engineering and cellular biochemistry. Its significance as an analytical framework, however, has not been fully appreciated outside the community of physical chemists. In this review, we discuss the latest advances in the kinetics and Gibbsian thermodynamics of chemical reactions in a spatially homogeneous aqueous solution with a multiscale perspective on complex systems. From the microscopic level of single reaction events which are purely stochastic in continuous time, one at a time among a set of molecules, to the macroscopic chemical reaction systems in bulk in terms of deterministic rate equations, the mathematical descriptions of kinetic models for chemical reactions at different levels are presented in detail, with rigorous mathematical justifications presented. In parallel with the kinetics of chemical reactions, the irreversible thermodynamics of open systems and the stochastic thermodynamics along reactions trajectories are reviewed thoroughly. As a novel feature, the mathematical theory of large deviations is shown to play a pivotal role in the thermodynamics of chemical reactions in equilibrium and in irreversible processes. This review is expected to stimulate interests in and help defining multiscale phenomena and nonequilibrium thermodynamics in many research fields on population dynamics of interacting species using chemical reactions as an analytic paradigm.

physics.chem-ph↗

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↗

arXiv2025

Extracting Interaction Kernels for Many-Particle Systems by a Two-Phase Approach

This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation method, the first phase of our approach combines importance sampling with an adaptive threshold strategy to identify key terms in the kernel function, while the second phase uses the whole dataset to refine the coefficients. During the implementation of our method, the mean-field equation plays a key role in reformulating the task of extracting the interaction kernels into a learnable regression problem. We demonstrate the outstanding performance of our approach through extensive numerical examples, including interacting particle systems with a cubic potential, power-law repulsion-attraction potential, piecewise linear potential, as well as a two-dimensional radially symmetric potential.

physics.comp-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

Large Deviations Principle for the Fluctuating Boltzmann Equation

The Boltzmann equation is one of the most famous equations and has vast applications in modern science. In the current study, we take the randomness of binary collisions into consideration and generalize the classical Boltzmann equation into a stochastic framework. The corresponding Kolmogorov forward equations and Liouville equation in either discrete or continuous time and state space are derived respectively, whose characteristic line gives the Boltzmann equation as a consequence of the law of large numbers. Then the large deviations principle for these equations is established, which not only explains the probabilistic origin of the H-theorem in the Boltzmann equation, but also provides a natural way to incorporate the Boltzmann equation into a broader Hamiltonian structure. The so-called Hamilton-Boltzmann equation enjoys many significant merits, like time reversibility, the conservation laws of mass, momentum and energy, Maxwellian-Boltzmann distribution as the equilibrium solution, etc. We also present results under the diffusive limit in parallel. Finally, the macroscopic hydrodynamic models including 13 moments are derived with respect to our Hamilton-Boltzmann equation under the BGK approximation. We expect our study can inspire new insights into the classical Boltzmann equation from either the stochastic aspect or a Hamiltonian view.

cond-mat.stat-mech↗

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↗

arXiv2024

Optimal Strategy for Stabilizing Protein Folding Intermediates

To manipulate the protein population at certain functional state through chemical stabilizers is crucial for protein-related studies. It not only plays a key role in protein structure analysis and protein folding kinetics, but also affects protein functionality to a large extent and thus has wide applications in medicine, food industry, etc. However, due to concerns about side effects or financial costs of stabilizers, identifying optimal strategies for enhancing protein stability with a minimal amount of stabilizers is of great importance. Here we prove that either for the fixed terminal time (including both finite and infinite cases) or the free one, the optimal control strategy for stabilizing the folding intermediates with a linear strategy for stabilizer addition belongs to the class of Bang-Bang controls. The corresponding optimal switching time is derived analytically, whose phase diagram with respect to several key parameters is explored in detail. The Bang-Bang control will be broken when nonlinear strategies for stabilizer addition are adopted. Our current study on optimal strategies for protein stabilizers not only offers deep insights into the general picture of protein folding kinetics, but also provides valuable theoretical guidance on treatments for protein-related diseases in medicine.

q-bio.BM↗

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↗

arXiv2023

Entropy Structure Informed Learning for Inverse XDE Problems

Entropy, since its first discovery by Ludwig Boltzmann in 1877, has been widely applied in diverse disciplines, including thermodynamics, continuum mechanics, mathematical analysis, machine learning, etc. In this paper, we propose a new method for solving the inverse XDE (ODE, PDE, SDE) problems by utilizing the entropy balance equation instead of the original differential equations. This distinguishing feature constitutes a major difference between our current method and other previous classical methods (e.g. SINDy). Despite concerns about the potential information loss during the compression procedure from the original XDEs to single entropy balance equation, various examples from MM reactions, Schlogl model and chemical Lorenz equations in the form of ODEs to nonlinear porous medium equation and Fokker-Planck equation with a double-well potential in the PDE form all well confirm the accuracy, robustness and reliability of our method, as well as its comparable performance with respect to SINDy.

math.DS↗

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↗

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↗

arXiv2022

An in vitro living system for flow rectification

Small - but finite - fluid inertia can be leveraged to generate steady flows out of liquid vibrations around an immersed interface. In engineering, external high-frequency drivers (10$^2$-10$^5$ Hz) allow this inertial rectification phenomenon, known as viscous streaming, to be employed in micron-scale devices for precise flow control, particle manipulation and spatially controlled chemistry. However, beyond artificial settings, streaming may also be accessed by larger-scale biological systems pertaining to lower frequencies. Then, millimeter-size bacteria or larvae that oscillate cilia and appendages in the 1-10Hz range may be able to endogenously rectify surrounding flows, for feeding or locomotion, removing the need for external actuators, tethers or tubings. In support of this hypothesis, here we demonstrate an in vitro living system able to produce streaming flows, endogenously, autonomously and unassisted. Computationally informed, our biological device generates oscillatory flows through the cyclic contractions of an engineered muscle tissue, shaped in the form of a ring and suspended in fluid within a Micro-Particle Image Velocimetry setup, for analysis. Flow patterns consistent with streaming simulations are observed for low-frequency muscle contractions (2-4Hz), either spontaneous or light-induced, illustrating system autonomy and controllability, respectively. Thus, this work provides experimental evidence of biologically powered streaming in untethered millimeter-scale living systems, showcasing the utility of bio-hybrid technology for fundamental and applied fluid mechanics.

physics.flu-dyn↗

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↗