Interval prediction is crucial in decision-making processes across many domains. Although significant progress has been made in existing interval prediction methods, they still face several challenges, such as assumptions about data distribution, fixed interval widths, limitations of gradient-based optimization algorithm, crossing of upper and lower bounds, and insufficient consideration of multi-scale spatial-temporal patterns. To address these issues, we propose a Multi-Scale Deep Interval Prediction Network (MSDIPN). Specifically, a MultiScale Spatio-Temporal Self-Attention Mechanism is introduced to capture spatio-temporal dependencies across different spatial scales. Additionally, a Temporal Self-Attention Mechanism module is constructed to extract temporal dependencies of historical variables across varying lag phases. Then a Global Self-Attention Mechanism module is designed to address representation degradation using residual connections and self-attention mechanisms. To overcome limitations related to distributional assumptions, fixed interval widths, and crossing problems, an Improved LUBE module is developed as the output module for generating prediction intervals (PIs) of time series data. Furthermore, a gradientbased PIs loss function is designed to address the optimization issue of MSDIPN by integrating a smooth approximation function with a pinball loss function. We validate the effectiveness of the proposed algorithm using five real-world datasets, demonstrating its superiority over traditional models

Differentiable architecture search plays a prominent role in Neural Architecture Search (NAS) and exhibits preferable efficiency than traditional heuristic NAS methods, including those based on evolutionary algorithms (EA) and reinforcement learning (RL). However, differentiable NAS methods encounter challenges when dealing with non-differentiable objectives like energy efficiency, resource constraints, and other non-differentiable metrics, especially under multi-objective search scenarios. While the multi-objective NAS research addresses these challenges, the individual training required for each candidate architecture demands significant computational resources. To bridge this gap, this work combines the efficiency of the differentiable NAS with metrics compatibility in multi-objective NAS. The architectures are discretely sampled by the architecture parameter α within the differentiable NAS framework, and α are directly optimised by the policy gradient algorithm. This approach eliminates the need for a sampling controller to be learned and enables the encompassment of non-differentiable metrics. We provide an efficient NAS framework that can be readily customized to address real-world multi-objective NAS (MNAS) scenarios, encompassing factors such as resource limitations and platform specialization. Notably, compared with other multi-objective NAS methods, our NAS framework effectively decreases the computational burden (accounting for just 1/6 of the NSGA-Net). This search framework is also compatible with the other efficiency and performance improvement strategies under the differentiable NAS framework.