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Tao Hao

Publications and source records attributed to Tao Hao.

10 recordsLinked to original sources

XiChen: A global weather observation-to-forecast machine learning system via four-dimensional variational gradient-guided flexible assimilation

Machine Learning (ML) has shown great promise in revolutionizing weather forecasting, yet most ML systems still rely on initial conditions generated by Numerical Weather Prediction (NWP) systems. End-to-end ML models aim to eliminate this dependency, but they often rely on observation-specific encoders and require redesign or retraining when observation sources change, thereby limiting their operational robustness. Here, we introduce XiChen, a global weather observation-to-forecast ML system via four-dimensional variational (4DVar) gradient-guided flexible assimilation. We demonstrate that the gradient of the 4DVar cost function serves as a physically grounded interface that maps heterogeneous observations into a common state space. This novel formulation enables XiChen to flexibly assimilate diverse conventional and raw satellite observations while preserving physical consistency. Experiments show that the system achieves forecasting metrics competitive with operational NWP systems. This work provides a practical and physically consistent route toward operational ML-based global weather forecasting systems with heterogeneous and evolving observations.

cs.LG

Mean-field backward stochastic Volterra integral equations: well-posedness and related particle system

This paper studies the mean-field backward stochastic Volterra integral equations (mean-field BSVIEs) and associated particle systems. We establish the existence and uniqueness of solutions to mean-field BSVIEs when the generator $g$ is of linear growth or quadratic growth with respect to $Z$, respectively. Moreover, the propagation of chaos is analyzed for the corresponding particle systems under two conditions. When $g$ is of linear growth in $Z$, the convergence rate is proven to be of order $\mathscr{Q}(N)$. When $g$ is of quadratic growth in $Z$ and is independent of the law of $Z$, we not only establish the convergence of the particle systems but also derive a convergence rate of order $\mathscr{O}(N^{-\frac{1}{2λ}})$, where $λ>1$.

math.PR

Maximum Principle of Stochastic Optimal Control Problems with Model Uncertainty

This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching. Firstly, the $ L^β$-solutions of forward-backward stochastic differential equations with regime switching are given. Secondly, we obtain the variational inequality by making use of the continuity of solutions to variational equations with respect to the uncertainty parameter $θ$. Thirdly, utilizing the linearization and weak convergence techniques, we prove the necessary stochastic maximum principle and provide sufficient conditions for the stochastic optimal control. Finally, as an application, a risk-minimizing portfolio selection problem is studied.

math.OC

Mean-field backward stochastic differential equations and nonlocal PDEs with quadratic growth

In this paper, we study general mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. First, the existence and uniqueness of local and global solutions are proved with some new ideas for a one-dimensional mean-field BSDE when the generator $g\big(t, Y, Z, \mathbb{P}_{Y}, \mathbb{P}_{Z}\big)$ has a quadratic growth in $Z$ and the terminal value is bounded. Second, a comparison theorem for the general mean-field BSDEs is obtained with the Girsanov transform. Third, we prove the convergence of the particle systems to the mean-field BSDEs with quadratic growth, and the convergence rate is also given. Finally, in this framework, we use the mean-field BSDE to provide a probabilistic representation for the viscosity solution of a nonlocal partial differential equation (PDE, for short) as an extended nonlinear Feynman-Kac formula, which yields the existence and uniqueness of the solution to the PDE.

math.PR

A local maximum principle for robust optimal control problems of quadratic BSDEs

The paper concerns the necessary maximum principle for robust optimal control problems of quadratic BSDEs. The coefficient of the systems depends on the parameter $θ$, and the generator of BSDEs is of quadratic growth in $z$. Since the model is uncertain, the variational inequality is proved by weak convergence technique. In addition, due to the generator being quadratic with respect to $z$, the forward adjoint equations are SDEs with unbounded coefficient involving mean oscillation martingales. Using reverse Hölder inequality and John-Nirenberg inequality, we show that its solutions are continuous with respect to the parameter $θ$. The necessary and sufficient conditions for robust optimal control are proved by linearization method.

math.OC

A Global Maximum Principle for Controlled Conditional Mean-field FBSDEs with Regime Switching

This paper is devoted to a global stochastic maximum principle for conditional mean-field forward-backward stochastic differential equations (FBSDEs, for short) with regime switching. The control domain is unnecessarily convex and the driver of backward stochastic differential equations (BSDEs, for short) could depend on $Z$. Different from the case of non-recursive utility, the first-order and second-order adjoint equations are both high-dimensional linear BSDEs. Based on the adjoint equations, we reveal the relations among the terms of the first- and second-order Taylor's expansions. A general maximum principle is proved, which develops the work of Nguyen, Yin, and Nguyen [22] to recursive utility. As applications, the linear-quadratic problem is considered and a problem with state constraint is studied.

math.OC

Solvability of a class of mean-field BSDEs with quadratic growth

In this paper, we study the multi-dimensional mean-field backward stochastic differential equations (BSDEs, for short) with quadratic growth. Under small terminal value, the existence and uniqueness are proved for the multi-dimensional situation when the generator f(t,Y,E[Y],Z,E[Z]) is of quadratic growth with respect to the last four items, using some new methods. Besides, a kind of comparison theorem is obtained.

math.PR

A global maximum principle for optimal control of general mean-field forward-backward stochastic systems with jumps

In this paper we prove a necessary condition of the optimal control problem for a class of general mean-field forward-backward stochastic systems with jumps in the case where the diffusion coefficients depend on control, the control set does not need to be convex, the coefficients of jump terms are independent of control as well as the coefficients of mean-field backward stochastic differential equations depend on the joint law of $(X(t),Y(t))$. Two new adjoint equations are brought in as well as several new generic estimates of their solutions are investigated for analysing the higher terms, especially, those involving the expectation which come from the derivatives of the coefficients with respect to the measure. Utilizing these subtle estimates, the second-order expansion of the cost functional, which is the key point to analyse the necessary condition, is obtained, and whereafter the stochastic maximum principle.

math.OC

Global maximum principle for mean-field forward-backward stochastic systems with delay and application to finance

The purpose of this paper is to explore the necessary conditions for optimality of mean-field forward-backward delay control systems. A new estimate is proved, which is a powerfultool to deal with the optimal control problems of mean-field type with delay. Different from the classical situation, in our case the first-order adjoint system is an anticipated mean-field backward stochastic differential equation, and the second-order adjoint system is a system of matrix-valued process, not mean-field type.With the help of two adjoint systems, the second-order expansion of the variation of the state $Y$ is proved, and therewith the Peng's stochastic maximum principle. As an illustrative example, we apply our result to the mean-field game in Finance. Although we just investigate the case of one pointwise delay for convenience, but our method is adequate for analysing the case of pointwise delay.

math.OC