The Finite Element Method, an important technique in engineering, is aided by Adaptive Mesh Refinement (AMR), which dynamically refines mesh regions to allow for a favorable trade-off between computational speed and simulation accuracy. Classical methods for AMR depend on task-specific heuristics or expensive error estimators, hindering their use for complex simulations. Recent learned AMR methods tackle these problems, but so far scale only to simple toy examples. We formulate AMR as a novel Adaptive Swarm Markov Decision Process in which a mesh is modeled as a system of simple collaborating agents that may split into multiple new agents. This framework allows for a spatial reward formulation that simplifies the credit assignment problem, which we combine with Message Passing Networks to propagate information between neighboring mesh elements. We experimentally validate the effectiveness of our approach, Adaptive Swarm Mesh Refinement (ASMR), showing that it learns reliable, scalable, and efficient refinement strategies on a set of challenging problems. Our approach significantly speeds up computation, achieving up to 30-fold improvement compared to uniform refinements in complex simulations. Additionally, we outperform learned baselines and achieve a refinement quality that is on par with a traditional error-based AMR strategy without expensive oracle information about the error signal.

The Finite Element Method, an important technique in engineering, is aided by Adaptive Mesh Refinement (AMR), which dynamically refines mesh regions to allow for a favorable trade-off between computational speed and simulation accuracy. Classical methods for AMR depend on task-specific heuristics or expensive error estimators, hindering their use for complex simulations. Recent learned AMR methods tackle these problems, but so far scale only to simple toy examples. We formulate AMR as a novel Adaptive Swarm Markov Decision Process in which a mesh is modeled as a system of simple collaborating agents that may split into multiple new agents. This framework allows for a spatial reward formulation that simplifies the credit assignment problem, which we combine with Message Passing Networks to propagate information between neighboring mesh elements.

The ability to perform causal and counterfactual reasoning are central properties of human intelligence. Decision-making systems that can perform these types of reasoning have the potential to be more generalizable and interpretable. Simulations have helped advance the state-of-the-art in this domain, by providing the ability to systematically vary parameters (e.g., confounders) and generate examples of the outcomes in the case of counterfactual scenarios. However, simulating complex temporal causal events in multi-agent scenarios, such as those that exist in driving and vehicle navigation, is challenging. To help address this, we present a high-fidelity simulation environment that is designed for developing algorithms for causal discovery and counterfactual reasoning in the safety-critical context. A core component of our work is to introduce \textit{agency}, such that it is simple to define and create complex scenarios using high-level definitions. The vehicles then operate with agency to complete these objectives, meaning low-level behaviors need only be controlled if necessary. We perform experiments with three state-of-the-art methods to create baselines and highlight the affordances of this environment. Finally, we highlight challenges and opportunities for future work.