Graph neural network-based surrogate modelling for real-time hydraulic prediction of urban drainage networks

Physics-based models are computationally time-consuming and infeasible for real-time scenarios of urban drainage networks, and a surrogate model is needed to accelerate the online predictive modelling. Fully-connected neural networks (NNs) are potential surrogate models, but may suffer from low interpretability and efficiency in fitting complex targets. Owing to the state-of-the-art modelling power of graph neural networks (GNNs) and their match with urban drainage networks in the graph structure, this work proposes a GNN-based surrogate of the flow routing model for the hydraulic prediction problem of drainage networks, which regards recent hydraulic states as initial conditions, and future runoff and control policy as boundary conditions. To incorporate hydraulic constraints and physical relationships into drainage modelling, physics-guided mechanisms are designed on top of the surrogate model to restrict the prediction variables with flow balance and flooding occurrence constraints. According to case results in a stormwater network, the GNN-based model is more cost-effective with better hydraulic prediction accuracy than the NN-based model after equal training epochs, and the designed mechanisms further limit prediction errors with interpretable domain knowledge. As the model structure adheres to the flow routing mechanisms and hydraulic constraints in urban drainage networks, it provides an interpretable and effective solution for data-driven surrogate modelling. Simultaneously, the surrogate model accelerates the predictive modelling of urban drainage networks for real-time use compared with the physics-based model.

Discounted Adaptive Online Prediction

Online learning is not always about memorizing everything. Since the future can be statistically very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we revisit the classical notion of discounted regret using recently developed techniques in adaptive online learning. Our main result is a new algorithm that adapts to the complexity of both the loss sequence and the comparator, improving the widespread non-adaptive algorithm - gradient descent with a constant learning rate. In particular, our theoretical guarantee does not require any structural assumption beyond convexity, and the algorithm is provably robust to suboptimal hyperparameter tuning. We further demonstrate such benefits through online conformal prediction, a downstream online learning task with set-membership decisions.

Understanding Adam Optimizer via Online Learning of Updates: Adam is FTRL in Disguise

Despite the success of the Adam optimizer in practice, the theoretical understanding of its algorithmic components still remains limited. In particular, most existing analyses of Adam show the convergence rate that can be simply achieved by non-adative algorithms like SGD. In this work, we provide a different perspective based on online learning that underscores the importance of Adam's algorithmic components. Inspired by Cutkosky et al. (2023), we consider the framework called online learning of updates, where we choose the updates of an optimizer based on an online learner. With this framework, the design of a good optimizer is reduced to the design of a good online learner. Our main observation is that Adam corresponds to a principled online learning framework called Follow-the-Regularized-Leader (FTRL). Building on this observation, we study the benefits of its algorithmic components from the online learning perspective.

Efficient Dynamic-NeRF Based Volumetric Video Coding with Rate Distortion Optimization

Volumetric videos, benefiting from immersive 3D realism and interactivity, hold vast potential for various applications, while the tremendous data volume poses significant challenges for compression. Recently, NeRF has demonstrated remarkable potential in volumetric video compression thanks to its simple representation and powerful 3D modeling capabilities, where a notable work is ReRF. However, ReRF separates the modeling from compression process, resulting in suboptimal compression efficiency. In contrast, in this paper, we propose a volumetric video compression method based on dynamic NeRF in a more compact manner. Specifically, we decompose the NeRF representation into the coefficient fields and the basis fields, incrementally updating the basis fields in the temporal domain to achieve dynamic modeling. Additionally, we perform end-to-end joint optimization on the modeling and compression process to further improve the compression efficiency. Extensive experiments demonstrate that our method achieves higher compression efficiency compared to ReRF on various datasets.

Improving Adaptive Online Learning Using Refined Discretization

We study unconstrained Online Linear Optimization with Lipschitz losses. The goal is to simultaneously achieve ($i$) second order gradient adaptivity; and ($ii$) comparator norm adaptivity also known as "parameter freeness" in the literature. Existing regret bounds (Cutkosky and Orabona, 2018; Mhammedi and Koolen, 2020; Jacobsen and Cutkosky, 2022) have the suboptimal $O(\sqrt{V_T\log V_T})$ dependence on the gradient variance $V_T$, while the present work improves it to the optimal rate $O(\sqrt{V_T})$ using a novel continuous-time-inspired algorithm, without any impractical doubling trick. This result can be extended to the setting with unknown Lipschitz constant, eliminating the range ratio problem from prior works (Mhammedi and Koolen, 2020). Concretely, we first show that the aimed simultaneous adaptivity can be achieved fairly easily in a continuous time analogue of the problem, where the environment is modeled by an arbitrary continuous semimartingale. Then, our key innovation is a new discretization argument that preserves such adaptivity in the discrete time adversarial setting. This refines a non-gradient-adaptive discretization argument from (Harvey et al., 2023), both algorithmically and analytically, which could be of independent interest.

Unconstrained Dynamic Regret via Sparse Coding

Motivated by time series forecasting, we study Online Linear Optimization (OLO) under the coupling of two problem structures: the domain is unbounded, and the performance of an algorithm is measured by its dynamic regret. Handling either of them requires the regret bound to depend on certain complexity measure of the comparator sequence -- specifically, the comparator norm in unconstrained OLO, and the path length in dynamic regret. In contrast to a recent work (Jacobsen & Cutkosky, 2022) that adapts to the combination of these two complexity measures, we propose an alternative complexity measure by recasting the problem into sparse coding. Adaptivity can be achieved by a simple modular framework, which naturally exploits more intricate prior knowledge of the environment. Along the way, we also present a new gradient adaptive algorithm for static unconstrained OLO, designed using novel continuous time machinery. This could be of independent interest.

Optimal Parameter-free Online Learning with Switching Cost

Parameter-freeness in online learning refers to the adaptivity of an algorithm with respect to the optimal decision in hindsight. In this paper, we design such algorithms in the presence of switching cost - the latter penalizes the optimistic updates required by parameter-freeness, leading to a delicate design trade-off. Based on a novel dual space scaling strategy, we propose a simple yet powerful algorithm for Online Linear Optimization (OLO) with switching cost, which improves the existing suboptimal regret bound [ZCP22a] to the optimal rate. The obtained benefit is extended to the expert setting, and the practicality of our algorithm is demonstrated through a sequential investment task.

Generative Compression for Face Video: A Hybrid Scheme

As the latest video coding standard, versatile video coding (VVC) has shown its ability in retaining pixel quality. To excavate more compression potential for video conference scenarios under ultra-low bitrate, this paper proposes a bitrate adjustable hybrid compression scheme for face video. This hybrid scheme combines the pixel-level precise recovery capability of traditional coding with the generation capability of deep learning based on abridged information, where Pixel wise Bi-Prediction, Low-Bitrate-FOM and Lossless Keypoint Encoder collaborate to achieve PSNR up to 36.23 dB at a low bitrate of 1.47 KB/s. Without introducing any additional bitrate, our method has a clear advantage over VVC under a completely fair comparative experiment, which proves the effectiveness of our proposed scheme. Moreover, our scheme can adapt to any existing encoder / configuration to deal with different encoding requirements, and the bitrate can be dynamically adjusted according to the network condition.