arXiv subjects

Jianzhong Wu

Publications and source records attributed to Jianzhong Wu.

16 recordsLinked to original sources

arXiv2026

Two Approximate Solutions of the Ornstein-Zernike (OZ) Integral Equation

This thesis explores the evolution of liquid-state theories based on the Ornstein-Zernike (OZ) equation, summarizing the foundational methods developed by Baxter, Lebowitz, Wertheim, and others. A unifying feature of these approaches is their shared analytical strategy: by introducing an intermediate function with specific mathematical properties, they effectively decouple the total correlation function and the direct correlation function. This allows the OZ equation to be solved within specific spatial intervals by exploiting regions where either the total or direct correlation function is known. Furthermore, this work presents a comprehensive derivation of analytical solutions to the OZ integral equation under the hard-sphere model. This includes applications of the Percus-Yevick (PY) approximation for both single- and multi-component systems, as well as the Mean Spherical Approximation (MSA) for systems of charged hard spheres. Building upon these analytical solutions, explicit expressions for macroscopic thermodynamic properties, such as the equation of state and activity coefficients, are rigorously derived. These derivations extensively employ advanced mathematical techniques, including Fourier transforms, complex analysis, and integral equation theory. Notably, many of the intermediate analytical steps and thermodynamic derivations presented herein offer a level of clarity and completeness previously absent from the existing literature.

math-ph↗

arXiv2026

A Process-Aware Demand Response Evaluation Framework for Hydrogen-Integrated Zero-Carbon Steel Plants Coupled with Methanol Production

High penetration of renewables (RES) and the retirement of thermal units aggravate flexibility scarcity in power systems. Hydrogen-based low-carbon steel production systems possess substantial demand response (DR) potential. This paper proposes a process-aware DR evaluation framework for hydrogen-integrated zero-carbon steel plants coupled with methanol production (H2-DRI-EAF-MeOH). First, a novel H2-DRI-EAF-MeOH architecture is introduced to eliminate residual emissions via methanol synthesis. Integrated energy-material flows are formulated to reflect coupling interactions governing DR potential. Second, to capture electric arc furnace (EAF) operational constraints while preserving tractability, an operating feasible region model is developed and validated using field data from a pure hydrogen direct reduced iron and EAF plant, yielding a 4.1% average relative error. Third, a process-aware DR potential evaluation model is formulated, incorporating a nonlinear asymmetric penalty and an adaptive rolling mechanism to reflect operators' aversion to process deviations and avoid myopic scheduling. Finally, dual-side evaluation metrics are established to quantify grid-side delivered DR capacity and ramping risks, making load-side unit-level regulation behaviors observable. Case studies show the proposed framework achieves an average effective delivered DR capacity of 178.3 MW, improves RES-load matching from 0.257 to 0.587, and reduces costs by 15.68% compared to the baseline. Furthermore, the exponential asymmetric penalty mitigates extreme tail risks of process deviations. Ultimately, this work provides a theoretical foundation for leveraging RES-steel-chemical synergies to mitigate flexibility scarcity.

eess.SY↗

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 $ρ(x)$, 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 $V_{ext} \mapsto ρ$ 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

Multiscale Modeling of Gas Adsorption and Surface Coverage in Thermocatalytic Systems

Conventional methods for modeling thermocatalytic systems are typically based on the Kohn-Sham density functional theory (KS-DFT), neglecting the inhomogeneous distributions of gas molecules in the reactive environment. However, industrial reactions often take place at high temperature and pressure, where the local densities of gas molecules near the catalyst surface can reach hundreds of times their bulk values. To assess the environmental impacts on surface composition and reaction kinetics, we integrate KS-DFT calculations for predicting surface bonding energy with classical DFT to evaluate gas distribution and the grand potential of the entire reactive system. This multiscale approach accounts for both bond formation and non-bonded interactions of gas molecules with the catalyst surface and reveals that the surface composition is determined not only by chemisorption but also by the accessibility of surface sites and their interactions with the surrounding molecules in the gas phase. This theoretical procedure was employed to establish the relationship between surface coverage, gas-phase composition, and bulk phase thermodynamic conditions with thermocatalytic hydrogenation of CO2 as a benchmark. The computational framework opens new avenues for studying adsorption and coverage on catalytic surfaces under industrially relevant conditions.

physics.chem-ph↗

arXiv2025

Solution-corrected Constant Potential Model for CO2 Electrocatalysis in Ionic Liquids

The selection of suitable ionic liquids (ILs) is critical for CO2 capture and electrocatalytic conversion into valuable chemical products. The screening process can be enhanced with theoretical simulations that reveal the property-performance relationship of ILs, accelerating the identification of optimal candidates. However, anhydrous ionic liquids exhibit low dielectric constants and high ion concentrations, challenging traditional first-principles calculations. Additionally, the spatial distribution of CO2 in the electric double layer (EDL) plays a crucial role in determining the electrocatalytic activity. This work proposes a solution-corrected constant potential model (CPM-sol) to account for the imbalance between the net charge and the number of electrons on the electrode surface through an implicit consideration of ion distributions. By incorporating solution-phase corrections into the conventional CPM model, we reveal the changes in the Fermi level and charge alongside the reaction process. Furthermore, we systematically investigate the impact of various IL properties on electrode surface charging and CO2 distribution. The theoretical results highlight the critical role of interactions between solution components, forming chain-like structures, in determining their distribution in confined environments and influencing the electrode surface charge. These findings provide insights for mechanism-guided electrolyte design.

physics.chem-ph↗

arXiv2025

A Mechanism-Guided Inverse Engineering Framework to Unlock Design Principles of H-Bonded Organic Frameworks for Gas Separation

The diverse combinations of novel building blocks offer a vast design space for hydrogen-boned frameworks (HOFs), rendering it a great promise for gas separation and purification. However, the underlying separation mechanism facilitated by their unique hydrogen-bond networks has not yet been fully understood. In this work, a comprehensive understanding of the separation mechanisms was achieved through an iterative data-driven inverse engineering approach established upon a hypothetical HOF database possessing nearly 110,000 structures created by a material genomics method. Leveraging a simple yet universal feature extracted from hydrogen bonding information with unambiguous physical meanings, the entire design space was exploited to rapidly identify the optimization route towards novel HOF structures with superior Xe/Kr separation performance (selectivity >103). This work not only provides the first large-scale HOF database, but also demonstrates the enhanced machine learning interpretability of our model-driven iterative inverse design framework, offering new insights into the rational design of nanoporous materials for gas separation.

physics.chem-ph↗

arXiv2024

A Two-Stage AI-Powered Motif Mining Method for Efficient Power System Topological Analysis

Graph motif, defined as the microstructure that appears repeatedly in a large graph, reveals important topological characteristics of the large graph and has gained increasing attention in power system analysis regarding reliability, vulnerability and resiliency. However, searching motifs within the large-scale power system is extremely computationally challenging and even infeasible, which undermines the value of motif analysis in practice. In this paper, we introduce a two-stage AI-powered motif mining method to enable efficient and wide-range motif analysis in power systems. In the first stage, a representation learning method with specially designed network structure and loss function is proposed to achieve ordered embedding for the power system topology, simplifying the subgraph isomorphic problem into a vector comparison problem. In the second stage, under the guidance of the ordered embedding space, a greedy-search-based motif growing algorithm is introduced to quickly obtain the motifs without traversal searching. A case study based on a power system database including 61 circuit models demonstrates the effectiveness of the proposed method.

eess.SY↗

arXiv2024

High-Dimensional Operator Learning for Molecular Density Functional Theory

Classical density functional theory (cDFT) provides a systematic approach to predict the structure and thermodynamic properties of chemical systems through the single-molecule density profiles. Whereas the statistical-mechanical framework is theoretically rigorous, its practical applications are often constrained by challenges in formulating a reliable free-energy functional and the complexity of solving multidimensional integro-differential equations. In this work, we established an optimized operator learning method that effectively separates the high-dimensional molecular density profile into two lower-dimensional components, thereby exponentially reducing the vast input space. The convoluted operator learning network demonstrates exceptional learning capabilities, accurately mapping the relationship between the density profile of a carbon dioxide system to its one-body direct correlation function using an atomistic polarizable model. The neural operator model can be generalized to more complex systems, offering high-precision cDFT calculations at low computational cost.

physics.chem-ph↗

arXiv2024

Reliable emulation of complex functionals by active learning with error control

A statistical emulator can be used as a surrogate of complex physics-based calculations to drastically reduce the computational cost. Its successful implementation hinges on an accurate representation of the nonlinear response surface with a high-dimensional input space. Conventional "space-filling" designs, including random sampling and Latin hypercube sampling, become inefficient as the dimensionality of the input variables increases, and the predictive accuracy of the emulator can degrade substantially for a test input distant from the training input set. To address this fundamental challenge, we develop a reliable emulator for predicting complex functionals by active learning with error control (ALEC). The algorithm is applicable to infinite-dimensional mapping with high-fidelity predictions and a controlled predictive error. The computational efficiency has been demonstrated by emulating the classical density functional theory (cDFT) calculations, a statistical-mechanical method widely used in modeling the equilibrium properties of complex molecular systems. We show that ALEC is much more accurate than conventional emulators based on the Gaussian processes with "space-filling" designs and alternative active learning methods. Besides, it is computationally more efficient than direct cDFT calculations. ALEC can be a reliable building block for emulating expensive functionals owing to its minimal computational cost, controllable predictive error, and fully automatic features.

physics.chem-ph↗

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↗

arXiv2022

Efficient force field and energy emulation through partition of permutationally equivalent atoms

Gaussian process (GP) emulator has been used as a surrogate model for predicting force field and molecular potential, to overcome the computational bottleneck of molecular dynamics simulation. Integrating both atomic force and energy in predictions was found to be more accurate than using energy alone, yet it requires $O((NM)^3)$ computational operations for computing the likelihood function and making predictions, where $N$ is the number of atoms and $M$ is the number of simulated configurations in the training sample, due to the inversion of a large covariance matrix. The large computational need limits its applications to emulating simulation of small molecules. The computational challenge of using both gradient information and function values in GPs was recently noticed in statistics and machine learning communities, where conventional approximation methods, such as the low rank decomposition or sparse approximation, may not work well. Here we introduce a new approach, the atomized force field (AFF) model, that integrates both force and energy in the emulator with many fewer computational operations. The drastic reduction on computation is achieved by utilizing the naturally sparse structure of the covariance satisfying the constraints of the energy conservation and permutation symmetry of atoms. The efficient machine learning algorithm extends the limits of its applications on larger molecules under the same computational budget, with nearly no loss of predictive accuracy. Furthermore, our approach contains uncertainty assessment of predictions of atomic forces and potentials, useful for developing a sequential design over the chemical input space, with almost no increase in computational cost.

physics.chem-ph↗

arXiv2022

Applications of blockchain and artificial intelligence technologies for enabling prosumers in smart grids: A review

Governments' net zero emission target aims at increasing the share of renewable energy sources as well as influencing the behaviours of consumers to support the cost-effective balancing of energy supply and demand. These will be achieved by the advanced information and control infrastructures of smart grids which allow the interoperability among various stakeholders. Under this circumstance, increasing number of consumers produce, store, and consume energy, giving them a new role of prosumers. The integration of prosumers and accommodation of incurred bidirectional flows of energy and information rely on two key factors: flexible structures of energy markets and intelligent operations of power systems. The blockchain and artificial intelligence (AI) are innovative technologies to fulfil these two factors, by which the blockchain provides decentralised trading platforms for energy markets and the AI supports the optimal operational control of power systems. This paper attempts to address how to incorporate the blockchain and AI in the smart grids for facilitating prosumers to participate in energy markets. To achieve this objective, first, this paper reviews how policy designs price carbon emissions caused by the fossil-fuel based generation so as to facilitate the integration of prosumers with renewable energy sources. Second, the potential structures of energy markets with the support of the blockchain technologies are discussed. Last, how to apply the AI for enhancing the state monitoring and decision making during the operations of power systems is introduced.

cs.IT↗

arXiv2021

Predicting Material Properties Using a 3D Graph Neural Network with Invariant Local Descriptors

Accurate prediction of physical properties is critical for discovering and designing novel materials. Machine learning technologies have attracted significant attention in the materials science community for their potential for large-scale screening. Graph Convolution Neural Network (GCNN) is one of the most successful machine learning methods because of its flexibility and effectiveness in describing 3D structural data. Most existing GCNN models focus on the topological structure but overly simplify the three-dimensional geometric structure. However, in materials science, the 3D-spatial distribution of atoms is crucial for determining the atomic states and interatomic forces. This paper proposes an adaptive GCNN with a novel convolution mechanism that simultaneously models atomic interactions among all neighbor atoms in three-dimensional space. We apply the proposed model to two distinctly challenging problems on predicting material properties. The first is Henry's constant for gas adsorption in Metal-Organic Frameworks (MOFs), which is notoriously difficult because of its high sensitivity to atomic configurations. The second is the ion conductivity in solid-state crystal materials, which is difficult because of few labeled data available for training. The new model outperforms existing graph-based models on both data sets, suggesting that the critical three-dimensional geometric information is indeed captured.

cond-mat.mtrl-sci↗

arXiv2020

On microscopic entropy production, heat and fluctuation theorem

We demonstrate that the Gibbs-Shannon entropy is applicable to non-equilibrium systems of any size and boundary conditions. The change in microscopic entropy can be attributed to the stochastic nature of dynamic processes and to the inherent uncertainties of thermodynamic systems. The latter predicts that entropy production is nonnegative on average and varies with different trajectories according to the fluctuation theorem. By contrast, heat is affiliated with stochastic processes underlying particle motions and the ensemble average over all possible trajectories leads to the Clausius inequality. The Jarzynski/Crooks equations can be readily derived by applying the fluctuation theorem to heat variation over different trajectories linking equilibrium states.

cond-mat.stat-mech↗

arXiv2020

Emulating the First Principles of Matter: A Probabilistic Roadmap

This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the electronic structure and diverse static properties of of many-particle systems useful for practical applications. Pedagogical examples are given to illustrate the basic concepts and simple applications of quantum Monte Carlo and density functional theory -- two representative methods commonly used in the literature of first principles modeling. In addition, this chapter highlights the practical needs for the integration of physics-based modeling and data-science approaches to reduce the computational cost and expand the scope of applicability. A special emphasis is placed on recent developments of statistical surrogate models to emulate first principles calculation from a probabilistic point of view. The probabilistic approach provides an internal assessment of the approximation accuracy of emulation that quantifies the uncertainty in predictions. Various recent advances toward this direction establish a new marriage between Gaussian processes and first principles calculation, with physical properties, such as translational, rotational, and permutation symmetry, naturally encoded in new kernel functions. Finally, it concludes with some prospects on future advances in the field toward faster yet more accurate computation leveraging a synergetic combination {of} novel theoretical concepts and efficient numerical algorithms.

cs.CE↗

arXiv2016

Potential of mean force and transient states in polyelectrolyte complexation

The association between polyelectrolytes (PEs) of the same size but opposite charge is systematically studied in terms of the potential of mean force (PMF) along their center-of-mass reaction coordinate via coarse-grained, implicit-solvent, explicit-salt computer simulations. The focus is set on the onset and the intermediate, transient stages of complexation. At conditions above the counterion-condensation threshold, the PE association process exhibits a distinct sliding-rod-like behavior where the polymer chains approach each other by first stretching out at a critical distance close to their contour length, then 'shaking hand' and sliding along each other in a parallel fashion, before eventually folding into a neutral complex. The essential part of the PMF for highly charged PEs can be very well described by a simple theory based on sliding charged `Debye--Hückel' rods with renormalized charges in addition to an explicit entropy contribution owing to the release of condensed counterions. Interestingly, at the onset of complex formation, the mean force between the PE chains is found to be discontinuous, reflecting a bimodal structural behavior that arises from the coexistence of interconnected-rod and isolated-coil states. These two microstates of the PE complex are balanced by subtle counterion release effects and separated by a free-energy barrier due to unfavorable stretching entropy.

cond-mat.soft↗