Cycle Invariant Positional Encoding for Graph Representation Learning

Cycles are fundamental elements in graph-structured data and have demonstrated their effectiveness in enhancing graph learning models. To encode such information into a graph learning framework, prior works often extract a summary quantity, ranging from the number of cycles to the more sophisticated persistence diagram summaries. However, more detailed information, such as which edges are encoded in a cycle, has not yet been used in graph neural networks. In this paper, we make one step towards addressing this gap, and propose a structure encoding module, called CycleNet, that encodes cycle information via edge structure encoding in a permutation invariant manner. To efficiently encode the space of all cycles, we start with a cycle basis (i.e., a minimal set of cycles generating the cycle space) which we compute via the kernel of the 1-dimensional Hodge Laplacian of the input graph. To guarantee the encoding is invariant w.r.t. the choice of cycle basis, we encode the cycle information via the orthogonal projector of the cycle basis, which is inspired by BasisNet proposed by Lim et al. We also develop a more efficient variant which however requires that the input graph has a unique shortest cycle basis. To demonstrate the effectiveness of the proposed module, we provide some theoretical understandings of its expressive power. Moreover, we show via a range of experiments that networks enhanced by our CycleNet module perform better in various benchmarks compared to several existing SOTA models.Comment: Accepted as oral presentation in the Learning on Graphs Conference (LoG 2023

Receding‐horizon based optimal dispatch of virtual power plant considering stochastic dynamic of photovoltaic generation

Abstract The merits of a virtual power plant in integrating photovoltaic generation and flexible loads, such as a chilled water thermal storage air conditioning system and an electric vehicle, are well recognized. However, the optimal operation of a virtual power plant is challenged by the complexities of solar irradiance and the large size of a chilled water thermal storage air conditioning system and an electric vehicle. This paper proposes a new approach to the optimal dispatch problem of a virtual power plant. The stochastic dynamic of solar irradiance is modelled by a stochastic differential equation set. The binary decision for a chilled water thermal storage air conditioning system and an electric vehicle are characterized by a mixed logical dynamical model. The resulting optimal dispatch problem is solved by the receding horizon approach. The appeal of the proposed approach is in its capability to consider the stochastically dynamical impact of solar irradiance. Besides, the proposed approach can solve the optimization problem over a relatively small period of time, and thus has the potential for online applications. Finally, the feasibility and effectiveness of the proposed approach is demonstrated by numerical simulations

Cycle Representation Learning for Inductive Relation Prediction

In recent years, algebraic topology and its modern development, the theory of persistent homology, has shown great potential in graph representation learning. In this paper, based on the mathematics of algebraic topology, we propose a novel solution for inductive relation prediction, an important learning task for knowledge graph completion. To predict the relation between two entities, one can use the existence of rules, namely a sequence of relations. Previous works view rules as paths and primarily focus on the searching of paths between entities. The space of rules is huge, and one has to sacrifice either efficiency or accuracy. In this paper, we consider rules as cycles and show that the space of cycles has a unique structure based on the mathematics of algebraic topology. By exploring the linear structure of the cycle space, we can improve the searching efficiency of rules. We propose to collect cycle bases that span the space of cycles. We build a novel GNN framework on the collected cycles to learn the representations of cycles, and to predict the existence/non-existence of a relation. Our method achieves state-of-the-art performance on benchmarks.Comment: Accepted in ICML 202

Significance analysis of the factors influencing the strength of the frozen soil-structure interface and their interactions in different phase transition zones

The freezing strength of the contact interface between foundation soil and infrastructure has been a key and difficult problem in the study of frost jacking of piles in cold regions; previous studies have focused on the influence law of experimental factors on freezing strength, and there are few studies on the significance of the effects of factors and their interactions on the freezing strength in different phase transition zones. In this paper, based on the existing test data, the orthogonal experimental design method considering the interactions, the principles of range analysis and variance analysis were used to investigate the significance of the effects of factors influencing the freezing strength in different phase transition zones and their interactions. Finally, a new method for establishing the prediction model of freezing strength based on the multiple linear regression model was proposed. The research shows that there are significant differences in the effects of the experimental factors and their interactions on the freezing strength in different phase transition zones. The freezing strength prediction model established by the new method can better reflect the variation law of freezing strength with factors in different phase transition zones and the influence degree of the interactions between factors