Transformer Meets Boundary Value Inverse Problems

A Transformer-based deep direct sampling method is proposed for a class of boundary value inverse problems. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and the reconstructed images. An effort is made to give a specific example to a fundamental question: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural networks? Specifically, inspired by direct sampling methods for inverse problems, the 1D boundary data in different frequencies are preprocessed by a partial differential equation-based feature map to yield 2D harmonic extensions as different input channels. Then, by introducing learnable non-local kernels, the direct sampling is recast to a modified attention mechanism. The proposed method is then applied to electrical impedance tomography, a well-known severely ill-posed nonlinear inverse problem. The new method achieves superior accuracy over its predecessors and contemporary operator learners, as well as shows robustness with respect to noise. This research shall strengthen the insights that the attention mechanism, despite being invented for natural language processing tasks, offers great flexibility to be modified in conformity with the a priori mathematical knowledge, which ultimately leads to the design of more physics-compatible neural architectures

TransNFV: Integrating Transactional Semantics for Efficient State Management in Virtual Network Functions

Managing shared mutable states in high concurrency state access operations is a persistent challenge in Network Functions Virtualization (NFV). This is particularly true when striving to meet chain output equivalence (COE) requirements. This paper presents TransNFV, an innovative NFV framework that incorporates transactional semantics to optimize NFV state management. The TransNFV integrates VNF state access operations as transactions, resolves transaction dependencies, schedules transactions dynamically, and executes transactions efficiently. Initial findings suggest that TransNFV maintains shared VNF state consistency, meets COE requirements, and skillfully handles complex cross-flow states in dynamic network conditions. TransNFV thus provides a promising solution to enhance state management and overall performance in future NFV platforms

Convergence and optimality of an adaptive modified weak Galerkin finite element method

An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is studied in this paper, in addition to its convergence and optimality. The weak Galerkin bilinear form is simplified without the need of the skeletal variable, and the approximation space is chosen as the discontinuous polynomial space as in the discontinuous Galerkin method. Upon a reliable residual-based a posteriori error estimator, an adaptive algorithm is proposed together with its convergence and quasi-optimality proved for the lowest order case. The major tool is to bridge the connection between weak Galerkin method and the Crouzeix-Raviart nonconforming finite element. Unlike the traditional convergence analysis for methods with a discontinuous polynomial approximation space, the convergence of AmWG is penalty parameter free

Optimal Operation of an Integrated Electricity-heat Energy System Considering Flexible Resources Dispatch for Renewable Integration

Large fluctuations may occur on the energy supply and the load sides when large-scale renewable energies are integrated, leading to great challenges in power systems. The renewable power curtailment is especially numerous in the integrated electricity-heat energy system (IEHES) on account of electricity-heat coupling. The flexible resources (FRs) on both the energy supply and load sides are introduced into the optimal dispatch of the IEHES and further modeled to alleviate the renewable fluctuations in this paper. On the energy supply side, three kinds of FRs based on electricity-heat coordination are modeled and discussed. On the load side, the shiftable electricity demand resource is characterized. On this basis, the solution for FRs participating in IEHES dispatch is given, with goals of maximizing the renewable penetration ratio and lowering operation costs. Two scenarios are performed, and the results indicate that the proposed optimal dispatch strategy can effectively reduce the renewable energy curtailment and improve the flexibility of the IEHES. The contribution degrees of different FRs for renewable integration are also explored