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This paper introduces a low-boom aircraft optimization design method guided by equivalent area distribution, which effectively improves the intuitiveness and refinement of inverse design. A gradient optimization method based on discrete adjoint equations is proposed to achieve the fast solution of the gradient information of target equivalent area distribution relative to design variables and to drive the aerodynamic shape update to the optimal solution. An optimization experiment is carried out based on a self-developed supersonic civil aircraft configuration with engines. The results show that the equivalent area distribution adjoint equation can accurately solve the gradient information. After optimization, the sonic boom level of the aircraft was reduced by 13.2 PLdB, and the drag coefficient was reduced by 60.75 counts. Moreover, the equivalent area distribution adjoint optimization method has outstanding advantages, such as high sensitivity and fast convergence speed, and can take both the low sonic boom and the low drag force of the aircraft into account, providing a powerful tool for the comprehensive optimization design of supersonic civil aircraft by considering sonic boom and aerodynamic force. [ABSTRACT FROM AUTHOR]

This paper derives necessary optimality conditions for a certain class of optimal control problems without linearity or convexity assumptions. The optimal control problem has a general objective function of integral type and a finite number of isoperimetric type constraints. For proving the main result derived in this paper, the Lagrange function and the control Hamiltonian are introduced and an adjoint differential equation is stated. In addition, we formulate some examples where the derived necessary optimality conditions are applied. [ABSTRACT FROM AUTHOR]

Featured Application: This work could be readily used in modeling contaminant transportation in homogeneous porous media with constant mean transport velocity, first-order decay and linear equilibrium sorption, e.g., the spread of a solute in water. In particular, the proposed method recovers the time-dependent pollution source strength from point measurements in a(n) (un)bounded domain. In this paper, we suggest a method for recovering the unknown time-dependent strength of a contaminant concentration source from measurements of the concentration inside an unbounded domain. This problem is formulated as a Cauchy parabolic inverse problem. For its efficient numerical processing, the problem is solved by reduction of the Cauchy problem to a Dirichet one on a bounded domain using the method of the fundamental (potential) solutions in combination with an adjoint equation technique. A numerical solution to this approach is explained. Next, by choosing the source strength in the form of a finite series of shape functions with unknown constant coefficients and using a linear-square method, the term concentration source is estimated. Computational simulations using model examples from water pollution are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the non-zero-sum differential game problem based on the delayed backward doubly stochastic differential equation. We discuss the case where the controlled system contains time-delayed variables, and the time-delayed variables are different. We construct a new kind of adjoint equation consisting of a doubly stochastic differential equation and three simple differential equations. Under appropriate premises for such equations, we deduce a stochastic maximum principle as a necessary condition and a verification theorem for the Nash equilibrium point by using the duality method and convex variation technique. As an application, we apply our result to a linear delayed backward doubly stochastic non-zero-sum game problem to verify the effectiveness of our results. [ABSTRACT FROM AUTHOR]

The connection between numerical methods for solving differential equations and machine learning has been revealed recently. Differential equations have been proposed as continuous analogues of deep neural networks, and then used in handling certain tasks, such as image recognition, where the training of a model includes learning the parameters of systems of ODEs from certain points along their trajectories. Treating this inverse problem of determining the parameters of a dynamical system that minimize the difference between data and trajectory by a gradient-based optimization method presents the solution of the adjoint equation as the continuous analogue of backpropagation that yields the appropriate gradients. The paper explores an abstract approach that can be used to construct a family of loss functions with the aim of fitting the solution of an initial value problem to a set of discrete or continuous measurements. It is shown, that an extension of the adjoint equation can be used to derive the gradient of the loss function as a continuous analogue of backpropagation in machine learning. Numerical evidence is presented that under reasonably controlled circumstances the gradients obtained this way can be used in a gradient descent to fit the solution of an initial value problem to a set of continuous noisy measurements, and a set of discrete noisy measurements that are recorded at uncertain times. [ABSTRACT FROM AUTHOR]

Large-scale inverse problems that require high-performance computing arise in various fields, including regional air quality studies. The paper focuses on parallel solutions of an emission source identification problem for a 2D advection–diffusion–reaction model where the sources are identified by heterogeneous measurement data. In the inverse modeling approach we use, a source identification problem is transformed to a quasi-linear operator equation with a sensitivity operator, which allows working in a unified way with heterogeneous measurement data and provides natural parallelization of numeric algorithms by concurrent calculation of the rows of a sensitivity operator matrix. The parallel version of the algorithm implemented with a message passing interface (MPI) has shown a 40× speedup on four Intel Xeon Gold 6248R nodes in an inverse modeling scenario for the Lake Baikal region. [ABSTRACT FROM AUTHOR]

In this paper, considering the effect of environmental factors such as climate change, temperature and drought on the growth of forests and beetles as well as the pine forests death and economic loss caused by outbreaks of mountain pine beetles, we first develop a stochastic mountain pine beetle model with pesticide application, and then consider its near‐optimal control (NOC) problem. The problem NOC is formulated by decreasing the mountain pine beetles while keeping the cost of pesticide application to a minimum. By Pontryagin stochastic maximum principle, we establish some sufficient and necessary conditions of the near‐optimality. Some numerical simulations are carried out to illustrate the theoretical results, which indicate that the pesticide application could effectively control the number of beetles and relieve the pressure from the attacking of beetles on the pines. To some extent, this control strategy could protect the pine forests and reduce economic losses caused by the mountain pine beetles. [ABSTRACT FROM AUTHOR]

Pine wood nematode disease has become nowadays a major threat to forest ecosystems and caused huge economic and environmental losses to many countries and regions. Considering the influence of environmental factors such as temperature, drought, and humidity, as well as possible prevention strategies, including trunk injection, cutting infected pines, and insecticide application, in this paper, we develop a stochastic pine wilt disease model with prevention strategies, aiming to obtain the conditions for its near‐optimal control. The near‐optimality problem is constructed by decreasing the infected pine forests and beetle population while minimizing the costs of prevention strategies. We first verify that, under certain convexity conditions, the near‐minimum condition of the Hamiltonian function is sufficient for the near‐optimal control. Then, by utilizing the spike variational technique, we derive the necessary conditions of the near‐optimal control. Finally, we present an example to illustrate the validity of the main theoretical results, which indicates that reasonable prevention strategies could effectively reduce pine wilt infection, and therefore, to some extent, could protect the pine forests from pine wilt disease and reduce economic losses caused by this disease. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Euler-Bernoulli beam theory for bending boundary value problem into mechanically coupled system. We follow the inverse approach to find the exerted force on two beams separated by elastic material. The theory was utilized in two ways: in the first approach, we calculate the force exerted on the beams using known values for the stiffness constant and measured values for the beam deflections. In the second method, we calculate the stiffness constant using a single known force and measured deflections. These problems are typically illposed problems whose solution does not depend continuously on the boundary data. To minimize the variational functional, we develop an iterative algorithm based on the system of three equations: the direct, adjoint, and control equations. Then, we present numerical examples to obtain the solutions. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the problem of discrete-time stochastic control with multiplicative noise, where the control domains may not be convex. We propose a novel approach inspired by the classical spike variation in continuous-time cases, but adapted to the discrete-time setting by perturbing in a random scale instead of time scale. Our approach allows us to obtain the maximum principle recursively without the need for variation equations or adjoint equations, which are typically required in previous methods. Moreover, we provide two maximum principles, one for the general case and the other when feedback forms exist. Our approach covers the previous results when the control domains are convex. Finally, we demonstrate the effectiveness of our new results through an example. [ABSTRACT FROM AUTHOR]

This paper introduces a low-boom aircraft optimization design method guided by equivalent area distribution, which effectively improves the intuitiveness and refinement of inverse design. A gradient optimization method based on discrete adjoint equations is proposed to achieve the fast solution of the gradient information of target equivalent area distribution relative to design variables and to drive the aerodynamic shape update to the optimal solution. An optimization experiment is carried out based on a self-developed supersonic civil aircraft configuration with engines. The results show that the equivalent area distribution adjoint equation can accurately solve the gradient information. After optimization, the sonic boom level of the aircraft was reduced by 13.2 PLdB, and the drag coefficient was reduced by 60.75 counts. Moreover, the equivalent area distribution adjoint optimization method has outstanding advantages, such as high sensitivity and fast convergence speed, and can take both the low sonic boom and the low drag force of the aircraft into account, providing a powerful tool for the comprehensive optimization design of supersonic civil aircraft by considering sonic boom and aerodynamic force.

We present an analysis and numerical study of an optimal control problem for the Landau--de Gennes (LdG) model of nematic liquid crystals (LCs), which is a crucial component in modern technology. They exhibit long range orientational order in their nematic phase, which is represented by a tensor-valued (spatial) order parameter Q=Q(x). Equilibrium LC states correspond to Q functions that (locally) minimize an LdG energy functional. Thus, we consider an L2-gradient flow of the LdG energy that allows for finding local minimizers and leads to a semilinear parabolic PDE, for which we develop an optimal control framework. We then derive several a priori estimates for the forward problem, including continuity in space-time, that allow us to prove existence of optimal boundary and external "force" controls and to derive optimality conditions through the use of an adjoint equation. Next, we present a simple finite element scheme for the LdG model and a straightforward optimization algorithm. We illustrate optimization of LC states through numerical experiments in two and three dimensions that seek to place LC defects (where Q(x) = 0) in desired locations, which is desirable in applications. [ABSTRACT FROM AUTHOR]

Bayesian inference coupled with computational fluid dynamics (CFD) has been widely used in the source term estimation (STE). At present, most scholars have studied the pollution source released in the time-invariant flow field and the turn-on time of the source is often regarded as a known parameter which requires no estimation. Nevertheless, it is of greater practical significance to estimate the source parameters by considering the time-varying characteristics of flow field. Besides, estimating the turn-on time is very important as it provides the critical information for post-disaster rescue and accident cause analysis. In this paper, the predicted concentrations are calculated by the adjoint equation in the time-varying flow field, and the turn-on time, taken as an unknown parameter, is estimated together with the source location and the release rate. Accurate estimated results are thereby obtained. Then, how the sensors' sampling time intervals and the measured data in different dispersion stages influence the estimated results is investigated. It is found that reducing the sampling time interval can decrease the uncertainties of the estimations. In addition, in order to estimate the turn-on time accurately, the measured information in the developing stage of dispersion is indispensable. However, only using the measured information in the stable stage of dispersion cannot predict the turn-on time. Finally, the earliest time when the source parameters can be estimated with accuracy is also explored. The results show that the method of the STE proposed can obtain accurate source information at the early stage of dispersion. • The source parameters are estimated in the time-varying flow field. • The turn-on time treated as an unknown parameter is estimated. • The predicted concentrations are obtained by adjoint equation in time-varying flow. • The impacts of key factors of measured data on the estimated results are studied. • The source parameters can be estimated accurately at early stage of dispersion. [ABSTRACT FROM AUTHOR]

This paper presents an adjoint method for locating potential leakage in a single-phase fluid pipeline based on the analytic solution of inversion modeling. By studying the mechanism of pipeline leakage pressure, the adjoint equation based on the governing equation of transient flow is established in the single-liquid phase aspect using inverse adjoint theory and sensitivity analysis method. The inverse transient adjoint equation is primarily derived from the single linear fluid pipeline in the semi-infinite domain. The Laplace method is then used to obtain an analytical solution that determines the location of pipeline leakage. The experimental results indicate that the analytic solution can quickly and accurately judge the leakage location of the pipeline. Furthermore, it presents a new approach to engineering applications, such as gas-liquid two-phase flow complex pipe networks, etc.

In this paper, we obtain the stochastic maximum principle for progressive optimal control of the model driven by Brownian motions and Markov chain. The maximum principle in progressive structure is essentially different from that in the classical case. Our maximum principle has two parts, including continuous part and jump part, which are used to characterize the characteristics of control at continuous time and jump time respectively. This shows that the progressive structure can better describe the optimal control of stochastic system with jumps. Moreover, we give an LQ example to show that the cost functional can indeed get a smaller value in progressive structure. • Necessary and sufficient maximum principle in progressive structure. • Two maximum principle includes continuous part and jump part. • Progressive structure is essentially different from predictable structure. • Progressive structure accurately describes the feature of control for system with jump. • Progressive structure can find better control than predictable structure. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a method for recovering the unknown time-dependent strength of a contaminant concentration source from measurements of the concentration inside an unbounded domain. This problem is formulated as a Cauchy parabolic inverse problem. For its efficient numerical processing, the problem is solved by reduction of the Cauchy problem to a Dirichet one on a bounded domain using the method of the fundamental (potential) solutions in combination with an adjoint equation technique. A numerical solution to this approach is explained. Next, by choosing the source strength in the form of a finite series of shape functions with unknown constant coefficients and using a linear-square method, the term concentration source is estimated. Computational simulations using model examples from water pollution are discussed.

Large-scale inverse problems that require high-performance computing arise in various fields, including regional air quality studies. The paper focuses on parallel solutions of an emission source identification problem for a 2D advection–diffusion–reaction model where the sources are identified by heterogeneous measurement data. In the inverse modeling approach we use, a source identification problem is transformed to a quasi-linear operator equation with a sensitivity operator, which allows working in a unified way with heterogeneous measurement data and provides natural parallelization of numeric algorithms by concurrent calculation of the rows of a sensitivity operator matrix. The parallel version of the algorithm implemented with a message passing interface (MPI) has shown a 40× speedup on four Intel Xeon Gold 6248R nodes in an inverse modeling scenario for the Lake Baikal region.