arXiv subjects

Wenqiang Yang

Publications and source records attributed to Wenqiang Yang.

11 recordsLinked to original sources

arXiv2026

Melt-Quench Failures and Practical Solutions for Universal Machine-Learning Interatomic Potentials in Amorphous Structure Generation

Generating experimentally relevant amorphous structures via melt-quench molecular dynamics is prohibitively expensive at the first-principles level. Universal machine-learning interatomic potentials (uMLIPs) could accelerate such simulations, but their reliability under non-equilibrium conditions remains unclear. Here, we examine eight leading uMLIPs for generating amorphous IrO2, using this electrocatalytically relevant oxide as a diagnostic case. Under the conventional melt-quench protocol, all models yield unphysically expanded structures with densities of 1-4 g/cm3, far below the ab initio molecular dynamics (AIMD) reference value of 10.04 g/cm3. Comparisons against ab initio references show that accurate energies and forces alone do not ensure stable NPT dynamics; correct energy-volume responses and pressure predictions are also essential. We identify two practical remedies: pressure-targeted fine-tuning and a revised NVT-quench/NPT-equilibration protocol that avoids unphysical volume expansion without additional ab initio training data. Both recover IrO2 densities and local structures consistent with AIMD. Across 30 chemically diverse materials, the volume-expansion failure proves general, and the revised protocol substantially improves density predictions, reducing the AIMD-referenced MAE from 2.46 to 0.35 g/cm3. This work establishes practical validation criteria and simulation strategies for robust uMLIP-driven amorphous structure generation.

cond-mat.mtrl-sci↗

arXiv2026

A Dataset of Nonlinear Equations for Subdivision

In this paper, we report on the largest labelled dataset constructed so far for solving zero-dimensional square nonlinear systems with subdivision-based methods. A brief, non-exhaustive survey with emphasis on the literature from the past two decades is also provided to accompany with the dataset. The value of the dataset has been demonstrated through benchmarking several solvers as well as being used for learning to classify the real roots of nonlinear parametric systems.

cs.SC↗

arXiv2026

Double Coupling Architecture and Training Method for Optimization Problems of Differential Algebraic Equations with Parameters

Simulation and modeling are essential in product development, integrated into the design and manufacturing process to enhance efficiency and quality. They are typically represented as complex nonlinear differential algebraic equations. The growing diversity of product requirements demands multi-task optimization, a key challenge in simulation modeling research. A dual physics-informed neural network architecture has been proposed to decouple constraints and objective functions in parametric differential algebraic equation optimization problems. Theoretical analysis shows that introducing a relaxation variable with a global error bound ensures solution equivalence between the network and optimization problem. A genetic algorithm-enhanced training framework for physics-informed neural networks improves training precision and efficiency, avoiding redundant solving of differential algebraic equations. This approach enables generalization for multi-task objectives with a single, training maintaining real-time responsiveness to product requirements.

cs.LG↗

arXiv2024

Algorithmic reduction of polynomially nonlinear PDE systems to parametric ODE systems

Differential-elimination algorithms apply a finite number of differentiations and eliminations to systems of partial differential equations. For systems that are polynomially nonlinear with rational number coefficients, they guarantee the inclusion of missing integrability conditions and the statement of of existence and uniqueness theorems for local analytic solutions of such systems. Further, they are useful in obtaining systems in a form more amenable to exact and approximate solution methods. Maple's \maple{dsolve} and \maple{pdsolve} algorithms for solving PDE and ODE often automatically call such routines during applications. Indeed, even casual users of Maple's dsolve and pdsolve commands have probably unknowingly used Maple's differential-elimination algorithms. Suppose that a system of PDE has been reduced by differential-elimination to a system whose automatic existence and uniqueness algorithm has been determined to be finite-dimensional. We present an algorithm for rewriting the output as a system of parameterized ODE. Exact methods and numerical methods for solving ODE and DAE can be applied to this form.

cs.SC↗

arXiv2023

Physical Information Neural Networks for Solving High-index Differential-algebraic Equation Systems Based on Radau Methods

As is well known, differential algebraic equations (DAEs), which are able to describe dynamic changes and underlying constraints, have been widely applied in engineering fields such as fluid dynamics, multi-body dynamics, mechanical systems and control theory. In practical physical modeling within these domains, the systems often generate high-index DAEs. Classical implicit numerical methods typically result in varying order reduction of numerical accuracy when solving high-index systems.~Recently, the physics-informed neural network (PINN) has gained attention for solving DAE systems. However, it faces challenges like the inability to directly solve high-index systems, lower predictive accuracy, and weaker generalization capabilities. In this paper, we propose a PINN computational framework, combined Radau IIA numerical method with a neural network structure via the attention mechanisms, to directly solve high-index DAEs. Furthermore, we employ a domain decomposition strategy to enhance solution accuracy. We conduct numerical experiments with two classical high-index systems as illustrative examples, investigating how different orders of the Radau IIA method affect the accuracy of neural network solutions. The experimental results demonstrate that the PINN based on a 5th-order Radau IIA method achieves the highest level of system accuracy. Specifically, the absolute errors for all differential variables remains as low as $10^{-6}$, and the absolute errors for algebraic variables is maintained at $10^{-5}$, surpassing the results found in existing literature. Therefore, our method exhibits excellent computational accuracy and strong generalization capabilities, providing a feasible approach for the high-precision solution of larger-scale DAEs with higher indices or challenging high-dimensional partial differential algebraic equation systems.

math.NA↗

arXiv2023

Structural Analysis by Modified Signature Matrix for Integro-differential-algebraic Equations

Integro-differential-algebraic equations (IDAE)s are widely used in applications of engineering and analysis. When there are hidden constraints in an IDAE, structural analysis is necessary. But if derivatives of dependent variables appear in their integrals, the existing definition of the signature matrix for an IDAE cannot be satisfied. Moreover, if an IDAE has a singular Jacobian matrix after structural analysis by the Sigma-method, improved structural analysis methods are proposed to regularize it. However, the optimal value of an IDAE may be negative which can not ensure the termination of the regularization. Furthermore, overestimation of the signature matrix may also lead to failure of its structural analysis. In this paper, firstly, we redefine the signature matrix and introduce a definition of the degree of freedom for IDAEs. Thus, the termination of improved structural analysis methods can be guaranteed. Secondly, the detection method by points is proposed to deal with the problem of overestimation of signature matrix. Thirdly, the embedding method has proved to suitable for structural unamenable IDAEs, including those types that arise from symbolic cancellation and numerical degeneration. Finally, the global numerical method is applied to an example of two-stage drive system which can help to find all solutions for IDAEs by witness points. Hopefully, through the example of pendulum curtain, the approach for IDAEs proposed in this paper can be applied to integro-partial-differential-algebraic equations (IPDAE)s.

math.DS↗

arXiv2022

Index Reduction for Degenerated Differential-Algebraic Equations by Embedding

To find consistent initial data points for a system of differential-algebraic equations, requires the identification of its missing constraints. An efficient class of structural methods exploiting a dependency graph for this task was initiated by Pantiledes. More complete methods rely on differential-algebraic geometry but suffer from other issues (e.g. high complexity). In this paper we give a new class of efficient structural methods combined with new tools from numerical real algebraic geometry that has much improved completeness properties. Existing structural methods may fail for a system of differential-algebraic equations if its Jacobian matrix after differentiation is still singular due to symbolic cancellation or numerical degeneration. Existing structural methods can only handle degenerated cases caused by symbolic cancellation. However, if a system has parameters, then its parametric Jacobian matrix may be still singular after application of the structural method for certain values of the parameters. This case is called numerical degeneration. For polynomially nonlinear systems of differential-algebraic equations, numerical methods are given to solve both degenerated cases using numerical real algebraic geometry. First, we introduce a witness point method, which produces at least one witness point on every constraint component. This can help to ensure constant rank and detection of degeneration on all components of such systems. Secondly, we present a Constant Rank Embedding Lemma, and based on it propose an Index Reduction by Embedding (IRE) method which can construct an equivalent system with a full rank Jacobian matrix. Thirdly, IRE leads to a global structural differentiation method, to solve degenerated differential-algebraic equations on all components numerically. Application examples from circuits, mechanics, are used to demonstrate our method.

math.NA↗

arXiv2021

Embedding Method by Real Numerical Algebraic Geometry for Structurally Unamenable Differential-Algebraic Equations

Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for polynomial systems of differential-algebraic equations, numerical methods are given to solve such cases using numerical real algebraic geometry. First, we propose an embedding method that for a given real analytic system constructs an equivalent system with a full-rank Jacobian matrix. Secondly, we introduce a witness point method, which can help to detect degeneration on all components of constraints of such systems. Thirdly, the two methods above lead to a numerical global structural analysis method for structurally unamenable differential-algebraic equations on all components of constraints.

math.NA↗

arXiv2019

A Multiple Filter Based Neural Network Approach to the Extrapolation of Adsorption Energies on Metal Surfaces for Catalysis Applications

Computational catalyst discovery involves the development of microkinetic reactor models based on estimated parameters determined from density functional theory (DFT). For complex surface chemistries, the cost of calculating the adsorption energies by DFT for a large number of reaction intermediates can become prohibitive. Here, we have identified appropriate descriptors and machine learning models that can be used to predict part of these adsorption energies given data on the rest of them. Our investigations also included the case when the species data used to train the predictive model is of different size relative to the species the model tries to predict - an extrapolation in the data space which is typically difficult with regular machine learning models. We have developed a neural network based predictive model that combines an established model with the concepts of a convolutional neural network that, when extrapolating, achieves significant improvement over the previous models.

physics.chem-ph↗

arXiv2018

Optimal Solution of Linear Ordinary Differential Equations by Conjugate Gradient Method

Solving initial value problems and boundary value problems of Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions represented by points. However, few work about optimal solution to minimize the residual can be found in the literatures. In this paper, we first use Hermit cubic spline interpolation at mesh points to represent the solution, then we define the residual error as the square of the L2 norm of the residual obtained by substituting the interpolation solution back to ODEs. Thus, solving ODEs is reduced to an optimization problem in curtain solution space which can be solved by conjugate gradient method with taking advantages of sparsity of the corresponding matrix. The examples of IVP and BVP in the paper show that this method can find a solution with smaller global error without additional mesh points.

math.NA↗

arXiv2018

Error Estimation of Numerical Solvers for Linear Ordinary Differential Equations

Solving Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions. However, few work about global error estimation can be found in the literature. In this paper, we first give a definition of the residual, based on the piecewise Hermit interpolation, which is a kind of the backward-error of ODE solvers. It indicates the reliability and quality of numerical solution. Secondly, the global error between the exact solution and an approximate solution is the forward error and a bound of it can be given by using the backward-error. The examples in the paper show that our estimate works well for a large class of ODE models.

math.NA↗