PreDiff: Precipitation Nowcasting with Latent Diffusion Models

Earth system forecasting has traditionally relied on complex physical models that are computationally expensive and require significant domain expertise. In the past decade, the unprecedented increase in spatiotemporal Earth observation data has enabled data-driven forecasting models using deep learning techniques. These models have shown promise for diverse Earth system forecasting tasks but either struggle with handling uncertainty or neglect domain-specific prior knowledge, resulting in averaging possible futures to blurred forecasts or generating physically implausible predictions. To address these limitations, we propose a two-stage pipeline for probabilistic spatiotemporal forecasting: 1) We develop PreDiff, a conditional latent diffusion model capable of probabilistic forecasts. 2) We incorporate an explicit knowledge control mechanism to align forecasts with domain-specific physical constraints. This is achieved by estimating the deviation from imposed constraints at each denoising step and adjusting the transition distribution accordingly. We conduct empirical studies on two datasets: N-body MNIST, a synthetic dataset with chaotic behavior, and SEVIR, a real-world precipitation nowcasting dataset. Specifically, we impose the law of conservation of energy in N-body MNIST and anticipated precipitation intensity in SEVIR. Experiments demonstrate the effectiveness of PreDiff in handling uncertainty, incorporating domain-specific prior knowledge, and generating forecasts that exhibit high operational utility.

GOPHER: Categorical probabilistic forecasting with graph structure via local continuous-time dynamics

We consider the problem of probabilistic forecasting over categories with graph structure, where the dynamics at a vertex depends on its local connectivity structure. We present GOPHER, a method that combines the inductive bias of graph neural networks with neural ODEs to capture the intrinsic local continuous-time dynamics of our probabilistic forecasts. We study the benefits of these two inductive biases by comparing against baseline models that help disentangle the benefits of each. We find that capturing the graph structure is crucial for accurate in-domain probabilistic predictions and more sample efficient models. Surprisingly, our experiments demonstrate that the continuous time evolution inductive bias brings little to no benefit despite reflecting the true probability dynamics.

Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting

Quantile regression is an effective technique to quantify uncertainty, fit challenging underlying distributions, and often provide full probabilistic predictions through joint learnings over multiple quantile levels. A common drawback of these joint quantile regressions, however, is \textit{quantile crossing}, which violates the desirable monotone property of the conditional quantile function. In this work, we propose the Incremental (Spline) Quantile Functions I(S)QF, a flexible and efficient distribution-free quantile estimation framework that resolves quantile crossing with a simple neural network layer. Moreover, I(S)QF inter/extrapolate to predict arbitrary quantile levels that differ from the underlying training ones. Equipped with the analytical evaluation of the continuous ranked probability score of I(S)QF representations, we apply our methods to NN-based times series forecasting cases, where the savings of the expensive re-training costs for non-trained quantile levels is particularly significant. We also provide a generalization error analysis of our proposed approaches under the sequence-to-sequence setting. Lastly, extensive experiments demonstrate the improvement of consistency and accuracy errors over other baselines.

Bridging Physics-based and Data-driven modeling for Learning Dynamical Systems

How can we learn a dynamical system to make forecasts, when some variables are unobserved? For instance, in COVID-19, we want to forecast the number of infected and death cases but we do not know the count of susceptible and exposed people. While mechanics compartment models are widely-used in epidemic modeling, data-driven models are emerging for disease forecasting. As a case study, we compare these two types of models for COVID-19 forecasting and notice that physics-based models significantly outperform deep learning models. We present a hybrid approach, AutoODE-COVID, which combines a novel compartmental model with automatic differentiation. Our method obtains a 57.4% reduction in mean absolute errors for 7-day ahead COVID-19 forecasting compared with the best deep learning competitor. To understand the inferior performance of deep learning, we investigate the generalization problem in forecasting. Through systematic experiments, we found that deep learning models fail to forecast under shifted distributions either in the data domain or the parameter domain. This calls attention to rethink generalization especially for learning dynamical systems.

Neural forecasting: Introduction and literature overview

Neural network based forecasting methods have become ubiquitous in large-scale industrial forecasting applications over the last years. As the prevalence of neural network based solutions among the best entries in the recent M4 competition shows, the recent popularity of neural forecasting methods is not limited to industry and has also reached academia. This article aims at providing an introduction and an overview of some of the advances that have permitted the resurgence of neural networks in machine learning. Building on these foundations, the article then gives an overview of the recent literature on neural networks for forecasting and applications.