This paper proposes a temporal graph neural network model for forecasting of graph-structured irregularly observed time series. Our TGNN4I model is designed to handle both irregular time steps and partial observations of the graph. This is achieved by introducing a time-continuous latent state in each node, following a linear Ordinary Differential Equation (ODE) defined by the output of a Gated Recurrent Unit (GRU). The ODE has an explicit solution as a combination of exponential decay and periodic dynamics. Observations in the graph neighborhood are taken into account by integrating graph neural network layers in both the GRU state update and predictive model. The time-continuous dynamics additionally enable the model to make predictions at arbitrary time steps. We propose a loss function that leverages this and allows for training the model for forecasting over different time horizons. Experiments on simulated data and real-world data from traffic and climate modeling validate the usefulness of both the graph structure and time-continuous dynamics in settings with irregular observations. 

Enabling resilient autonomous motion planning requires robust predictions of surrounding road users’ future behavior. In response to this need and the associated challenges, we introduce our model titled MTP-GO. The model encodes the scene using temporal graph neural networks to produce the inputs to an underlying motion model. The motion model is implemented using neural ordinary differential equations where the state-transition functions are learned with the rest of the model. Multimodal probabilistic predictions are obtained by combining the concept of mixture density networks and Kalman filtering. The results illustrate the predictive capabilities of the proposed model across various data sets, outperforming several state-of-the-art methods on a number of metrics.

Machine learning methods on graphs have proven useful in many applications due to their ability to handle generally structured data. The framework of Gaussian Markov Random Fields (GMRFs) provides a principled way to define Gaussian models on graphs by utilizing their sparsity structure. We propose a flexible GMRF model for general graphs built on the multi-layer structure of Deep GMRFs, originally proposed for lattice graphs only. By designing a new type of layer we enable the model to scale to large graphs. The layer is constructed to allow for efficient training using variational inference and existing software frameworks for Graph Neural Networks. For a Gaussian likelihood, close to exact Bayesian inference is available for the latent field. This allows for making predictions with accompanying uncertainty estimates. The usefulness of the proposed model is verified by experiments on a number of synthetic and real world datasets, where it compares favorably to other both Bayesian and deep learning methods.

In recent years, machine learning has established itself as a powerful tool forhigh-resolution weather forecasting. While most current machine learning modelsfocus on deterministic forecasts, accurately capturing the uncertainty in thechaotic weather system calls for probabilistic modeling. We propose a probabilisticweather forecasting model called Graph-EFM, combining a flexible latent-variableformulation with the successful graph-based forecasting framework. The use of ahierarchical graph construction allows for efficient sampling of spatially coherentforecasts. Requiring only a single forward pass per time step, Graph-EFM allowsfor fast generation of arbitrarily large ensembles. We experiment with the modelon both global and limited area forecasting. Ensemble forecasts from Graph-EFMachieve equivalent or lower errors than comparable deterministic models, with theadded benefit of accurately capturing forecast uncertainty.

Machine learning is revolutionizing global weather forecasting, with models that efficiently produce highly accurate forecasts. Apart from global forecasting there is also a large value in high-resolution regional weather forecasts, focusing on accurate simulations of the atmosphere for a limited area. Initial attempts have been made to use machine learning for such limited area scenarios, but these experiments do not consider realistic forecasting settings and do not investigate the many design choices involved. We present a framework for building kilometer-scale machine learning limited area models with boundary conditions imposed through a flexible boundary forcing method. This enables boundary conditions defined either from reanalysis or operational forecast data. Our approach employs specialized graph constructions with rectangular and triangular meshes, along with multi-step rollout training strategies to improve temporal consistency. We perform systematic evaluation of different design choices, including the boundary width, graph construction and boundary forcing integration. Models are evaluated across both a Danish and a Swiss domain, two regions that exhibit different orographical characteristics. Verification is performed against both gridded analysis data and in-situ observations, including a case study for the storm Ciara in February 2020. Both models achieve skillful predictions across a wide range of variables, with our Swiss model outperforming the numerical weather prediction baseline for key surface variables. With their substantially lower computational cost, our findings demonstrate great potential for machine learning limited area models in the future of regional weather forecasting.