In recent years, machine learning has established itself as a powerful tool for high-resolution weather forecasting.

We study a path planning problem where the possible move actions are represented as a finite set of motion primitives aligned with the grid representation of the environment. That is, each primitive corresponds to a short kinodynamically-feasible motion of an agent and is represented as a sequence of the swept cells of a grid. Typically heuristic search, i.e. A*, is conducted over the lattice induced by these primitives (lattice-based planning) to find a path. However due to the large branching factor such search may be inefficient in practice. To this end we suggest a novel technique rooted in the idea of searching over the grid cells (as in vanilla A*) simultaneously fitting the possible sequences of the motion primitives into these cells. The resultant algorithm, MeshA*, provably preserves the guarantees on completeness and optimality, on the one hand, and is shown to notably outperform conventional lattice-based planning (x1.5 decrease in the runtime), on the other hand. Moreover, we suggest an additional pruning technique that additionally decreases the search space of MeshA*. The resultant planner is combined with the regular A* to retain completeness and is shown to further increase the search performance at the cost of negligible decrease of the solution quality.

Traditional simulation of complex mechanical systems relies on numerical solvers of Partial Differential Equations (PDEs), e.g., using the Finite Element Method (FEM). The FEM solvers frequently suffer from intensive computation cost and high running time. Recent graph neural network (GNN)-based simulation models can improve running time meanwhile with acceptable accuracy. Unfortunately, they are hard to tailor GNNs for complex mechanical systems, including such disadvantages as ineffective representation and inefficient message propagation (MP). To tackle these issues, in this paper, with the proposed Up-sampling-only and Adaptive MP techniques, we develop a novel hierarchical Mesh Graph Network, namely UA-MGN, for efficient and effective mechanical simulation. Evaluation on two synthetic and one real datasets demonstrates the superiority of the UA-MGN. For example, on the Beam dataset, compared to the state-of-the-art MS-MGN, UA-MGN leads to 40.99% lower errors but using only 43.48% fewer network parameters and 4.49% fewer floating point operations (FLOPs).

Complex mechanic systems simulation is important in many real-world applications. The de-facto numeric solver using Finite Element Method (FEM) suffers from computationally intensive overhead. Though with many progress on the reduction of computational time and acceptable accuracy, the recent CNN or GNN-based simulation models still struggle to effectively represent complex mechanic simulation caused by the long-range spatial dependency of distance mesh nodes and independently learning local and global representation. In this paper, we propose a novel two-level mesh graph network. The key of the network is to interweave the developed Graph Block and Attention Block to better learn mechanic interactions even for long-rang spatial dependency. Evaluation on three synthetic and one real datasets demonstrates the superiority of our work. For example, on the Beam dataset, our work leads to 54.3\% lower prediction errors and 9.87\% fewer learnable network parameters.

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