Porous-DeepONet:Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media

Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varying porous structures and initial or boundary conditions.The deep operator network(DeepONet)has emerged as a popular deep learning framework for solving parametric partial differential equations.However,applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures.To address this issue,we propose the Porous-DeepONet,a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks(CNNs)to learn the solution operators of parametric reactive transport equations in porous media.By incorporating CNNs,we can effectively capture the intricate features of porous media,enabling accurate and efficient learning of the solution operators.We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions,multiple phases,and multiphysical fields through five examples.This approach offers significant computational savings,potentially reducing the computation time by 50–1000 times compared with the finite-element method.Our work may provide a robust alternative for solving parametric reactive transport equations in porous media,paving the way for exploring complex phenomena in porous media.

ON A CHARACTERIZATION OF THE S-ESSENTIAL SPECTRA OF THE SUM AND THE PRODUCT OF TWO OPERATORS AND APPLICATION TO A TRANSPORT OPERATOR

In this paper, we develop some operational calculus inspired from the Fredholm operator theory to investigate the S-essential spectra of the sum and the product of two operators acting on a Banach space. Furthermore, we apply the obtained results to determine the S-essential spectra of an integro-differential operator with abstract boundary conditions in L1（[-a,a]×[-1,1]）（a〉0）.

AVERAGE REGULARITY OF THE SOLUTION TO AN EQUATION WITH THE RELATIVISTIC-FREE TRANSPORT OPERATOR

Let u = u(t, x, p) satisfy the transport equation ?u/?t+p/p0 ?u/?x= f, where f =f(t, x, p) belongs to L~p((0, T) × R~3× R~3) for 1 < p < ∞ and ?/?t+p/p0 ?/?x is the relativisticfree transport operator from the relativistic Boltzmann equation. We show the regularity of ∫u(t, x, p)d p using the same method as given by Golse, Lions, Perthame and Sentis. This average regularity is considered in terms of fractional Sobolev spaces and it is very useful for the study of the existence of the solution to the Cauchy problem on the relativistic Boltzmann equation.

The Asymptotic Spectrum and Accumulation of Transport Operator in Slab Geometry

In this paper we investigate the asymptotic spectrum and accumulation of a transport operator A in slab geometry with continuous energy, anisotropic scattering and inhomogeneous medium. In L^p （1 ≤ p 〈 ＋∞） space we show a series of new results for the asymptotic point spectrum and accumulation of A.

ON THE ASYMPTOTIC SPECTRUM OF A TRANSPORT OPERATOR WITH ELASTIC AND INELASTIC COLLISION OPERATORS

In this article,we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1].Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators(when it exists).The last section of this work is devoted to the properties of the leading eigenvalue(when it exists).So,we discuss the irreducibility of the semigroups generated by these operators.We close this section by discussing the strict monotonicity of the leading eigenvalue with respect to the parameters of the operator.

Transport Operator of Accelerator Single-Freedom Nonlinear Components

For accelerator single-freedom nonlinear components,the general theory of nonlinear transportis developed,and the algorithm for the inverse transport operator is given,based on which an expert sys-tem can be built to automatically yield any order transport operator and its inverse transport operator forvarious accelerator single-freedom nonlinear components.

Linear Accelerator Beam Transport Operator

The accelerator beam transport operator presents the evolution of beam phasespace point with given transport elements and given initial point,while the inverse beamtransport operator presents the evolution of beam phase space configuration with giveninitial phase space geometry.Therefore,it is necessary to develop a general theory be-tween these two operators.Several concrete examples are worked out in detail to showthe practical applications of such a theory.This paper deals with the linear acceleratorbeam transport operator,and a theorem of finding the inverse linear beam transportoperator for both autonomous and nonautonomous accelerator dynamics is developed.

Optimization of Urban Rail Transportation in Emerging Countries Using Operational Research Techniques

Rail systems are gradually becoming the most desirable form of transit infrastructure around the world, partly because they are becoming more environmentally friendly compared with airplanes and automobiles. This paper examines the place of emerging countries in this move of implementing modern rail system that will eventually enhance the realization of a low-carbon society. Network model, transportation model and linear programming algorithms are used to model the present urban rail transport system in Nigeria, as an emerging country, in order to optimize it. Operational research methods, including simplex method and MODI, with the aids of computer software (excel solver and LIP solver) were adopted to solve the resulting models. The results showed that optimization of rail transport system will not only reduce carbon emission but also bring about economic development which is required for the eradication of prevalent poverty in these emerging countries.

Nonlinear Accelerator Beam Transport Operator

This paper deals with the theory of nonlinear accelerator beam transport op-erator.For nonautonomous accelerator dynamics,a theorem of finding the inversenonlinear beam transport operator is developed.Several concrete examples are workedout in detail to show the practical applications of this theory.

Expert System for the Transport Operator of Accelerator Single-Freedom Nonlinear Components

An expert system by Arity Prolog is developed for the transport operator of accelera-tor single-freedom nonlinear components. It automatically yields any order transport operatorand its inverse transport operator for various accelerator single-freedom nonlinear components.As an example, the fifth order inverse transport operator derived by the expert system is given.

Localisation Inverse Problem and Dirichlet-to-Neumann Operator for Absorbing Laplacian Transport

We study Laplacian transport by the Dirichlet-to-Neumann formalism in isotropic media (γ = I). Our main results concern the solution of the localisation inverse problem of absorbing domains and its relative Dirichlet-to-Neumann operator . In this paper, we define explicitly operator , and we show that Green-Ostrogradski theorem is adopted to this type of problem in three dimensional case.

Operator Splitting Method for Coupled Problems:Transport and Maxwell Equations

In this article a new approach is considered for implementing operator splitting methods for transport problems, influenced by electric fields. Our motivation came to model PE-CVD (plasma-enhanced chemical vapor deposition) processes, means the flow of species to a gas-phase, which are influenced by an electric field. Such a field we can model by wave equations. The main contributions are to improve the standard discretization schemes of each part of the coupling equation. So we discuss an improvement with implicit Runge- Kutta methods instead of the Yee’s algorithm. Further we balance the solver method between the Maxwell and Transport equation.

Operations Management Perspectives in the Air Transport Management

The area of operations management has had a substantial effect on the today’s air transportation management.Having moved with huge demand from management to obtain a competitive advantage in the market,the airlines are utilizing advanced optimization techniques to develop decision support systems for operations management and control.In order to provide a service with high quality and low cost,airlines spend a tremendous amount of resources and effort to generate profitable and cost-effective fare classes,flight schedules,fleet plans,aircraft routes,crew scheduling,gate assignment,etc.In this paper,the techniques and operations management applications that are used in the air transportation industry are reviewed including demand forecasting,fleet assignment,aircraft routing,crew scheduling,runway scheduling problem and gate assignment.

Study on multi-timescale operation of hydrogen-containing energy coupled with transportation system

With the widespread attention on hydrogen energy,the operation optimization of the coupling system of hydrogen energy and transportation has become a critical issue.Therefore,this study develops a hydrogen-containing energy transportation coupling system for the system collaborative operation framework,operation mode and equipment modelling of the system.Furthermore,a medium-to long-term operation optimization model and a short-term operation optimization model were constructed considering the differences in the operation of coupled systems at different timescales and operating costs as the objective function and power balance and system equipment as constraints.In the medium-and long-term operation optimization model,the planning scenario reduction method is used to reduce the wind power generation scenario.In the short-term operation optimization model,a multivariate uncertainty model is constructed to represent the uncertainty in the coupling system.Subsequently,the solution method of the model is proposed.Finally,a coupled system is simulated to verify the effectiveness of the model.(i)When the initial scene set is 600,the typical scene reduction method using Latin hypercube sampling and the Wasserstein distance can reduce operating costs by 7.60%and 9.49%compared with K-means reduction and K-media reduction methods.(ii)The sensitivity coefficients of hydrogen sales price,electricity sales price and maintenance rate to operating costs are-0.031%,-1.009%and 0.0105%,respectively.(iii)Considering multiple uncertainties can help make optimal decisions based on the overall consideration of disadvantage scenarios,thereby reducing system operating costs.

Study on Operation of Arctic Offshore Complex by Means of Multicomponent Process-Based Simulation

We developed a detailed simulation model of the Arctic marine transport system(MTS) for oil platform Prirazlomnaya. The model has a multidisciplinary nature and involves: sub-models of various transport and technological processes; stochastic weather generator to obtain time series of 15 environmental parameters; and contextual planning algorithm to build voyage plan considering several types of ships and cargoes. We used a significant amount of real operational data to identify model parameters and to prove its statistical reliability. Our main scientific task is to investigate the interaction of various processes of a different nature, while the practical aim is to find a set of measures to increase the efficiency of MTS. The results of the study reveal many examples of the mutual interaction of various processes that need to be considered at the design stage to avoid technical mistakes.The study formed a basis for making managerial decisions at the top level of Gazprom Neft Shelf Company.

Analysis on EAST LHCD Operation Space by Using Simple Core-SOL-Divertor Model

A simple core-SOL-divertor model （CSD model） was developed to investigate qual- itatively the overall features of the operational space for the integrated core and edge plasma. In the CSD model, the core plasma model of ITER physics guidelines and the two-point SOL-divertor model are applied, This CSD model is validated by the two dimensional divertor transport code （B2-EIRINE） and by the JT-60U divertor recycling database, and this model is applicable to the low- and high-recycling state of the divertor plasma. The CSD model is applied to the study of the EAST operational space with lower hybrid current drive under various kinds of trade-off for the basic plasma parameters, and the relationship between the operational space and the plasma discharge duration is also discussed.

ON THE TRANSPORT EQUATION WITH INTEGRAL BOUNDARY CONDITIONS AND ITS CONSERVAIVE LAW

The well-posedness for the time-dependent neutron transport equationwith integral boundary conditions is established in L^1 space. Some spectral propertiesof the transport operator are discussed, the dominant eigenvalue is proved existing,and furthermore, the conservative law of migrating particle numbers is established.

NONLINEAR SEMIGROUP APPROACH TOTRANSPORT EQUATIONS WITH DELAYED NEUTRONS

This paper deal with a nonlinear transport equation with delayed neutron andgeneral boundary conditions. We establish, via the nonlinear semigroups approach, the exis-tence and uniqueness of the mild solution, weak solution, strong solution and local solutionon LP-spaces （1 ≤ p 〈 ＋∞）. Local and non local evolution problems are discussed.

TheAnalysisofTransportNetworkStructureandFeatures

改革开放30年来，我国交通运输业取得了长足进步。如何准确地定位交通运输业务，发挥各种运输方式的竞争优势，形成分工协作、有机结合、布局合理、联结贯通的综合运输业务网络，促使我国的交通运输业向规范化、规模化、多元化的方向发展成为我国的交通运输业面临新的发展课题。在这种背景下，分析和研究交通运输业务网络结构和特征可以为我国的交通运输业和各运输企业的发展提供一些启示。

Localisation Inverse Problem of Absorbing Laplacian Transport

We study the localisation inverse problem corresponding to Laplacian transport of absorbing cell. Our main goal is to find sufficient Dirichelet-to-Neumann conditions insuring that this inverse problem is uniquely soluble. In this paper, we show that the conformal mapping technique is adopted to this type of problem in the two dimensional case.