Learning Sub-Second Routing Optimization in Computer Networks requires Packet-Level Dynamics

Finding efficient routes for data packets is an essential task in computer networking. The optimal routes depend greatly on the current network topology, state and traffic demand, and they can change within milliseconds. Reinforcement Learning can help to learn network representations that provide routing decisions for possibly novel situations. So far, this has commonly been done using fluid network models. We investigate their suitability for millisecond-scale adaptations with a range of traffic mixes and find that packet-level network models are necessary to capture true dynamics, in particular in the presence of TCP traffic. To this end, we present $\textit{PackeRL}$, the first packet-level Reinforcement Learning environment for routing in generic network topologies. Our experiments confirm that learning-based strategies that have been trained in fluid environments do not generalize well to this more realistic, but more challenging setup. Hence, we also introduce two new algorithms for learning sub-second Routing Optimization. We present $\textit{M-Slim}$, a dynamic shortest-path algorithm that excels at high traffic volumes but is computationally hard to scale to large network topologies, and $\textit{FieldLines}$, a novel next-hop policy design that re-optimizes routing for any network topology within milliseconds without requiring any re-training. Both algorithms outperform current learning-based approaches as well as commonly used static baseline protocols in scenarios with high-traffic volumes. All findings are backed by extensive experiments in realistic network conditions in our fast and versatile training and evaluation framework.

KalMamba: Towards Efficient Probabilistic State Space Models for RL under Uncertainty

Probabilistic State Space Models (SSMs) are essential for Reinforcement Learning (RL) from high-dimensional, partial information as they provide concise representations for control. Yet, they lack the computational efficiency of their recent deterministic counterparts such as S4 or Mamba. We propose KalMamba, an efficient architecture to learn representations for RL that combines the strengths of probabilistic SSMs with the scalability of deterministic SSMs. KalMamba leverages Mamba to learn the dynamics parameters of a linear Gaussian SSM in a latent space. Inference in this latent space amounts to standard Kalman filtering and smoothing. We realize these operations using parallel associative scanning, similar to Mamba, to obtain a principled, highly efficient, and scalable probabilistic SSM. Our experiments show that KalMamba competes with state-of-the-art SSM approaches in RL while significantly improving computational efficiency, especially on longer interaction sequences.

Iterative Sizing Field Prediction for Adaptive Mesh Generation From Expert Demonstrations

Many engineering systems require accurate simulations of complex physical systems. Yet, analytical solutions are only available for simple problems, necessitating numerical approximations such as the Finite Element Method (FEM). The cost and accuracy of the FEM scale with the resolution of the underlying computational mesh. To balance computational speed and accuracy meshes with adaptive resolution are used, allocating more resources to critical parts of the geometry. Currently, practitioners often resort to hand-crafted meshes, which require extensive expert knowledge and are thus costly to obtain. Our approach, Adaptive Meshing By Expert Reconstruction (AMBER), views mesh generation as an imitation learning problem. AMBER combines a graph neural network with an online data acquisition scheme to predict the projected sizing field of an expert mesh on a given intermediate mesh, creating a more accurate subsequent mesh. This iterative process ensures efficient and accurate imitation of expert mesh resolutions on arbitrary new geometries during inference. We experimentally validate AMBER on heuristic 2D meshes and 3D meshes provided by a human expert, closely matching the provided demonstrations and outperforming a single-step CNN baseline.

Adaptive Swarm Mesh Refinement using Deep Reinforcement Learning with Local Rewards

Simulating physical systems is essential in engineering, but analytical solutions are limited to straightforward problems. Consequently, numerical methods like the Finite Element Method (FEM) are widely used. However, the FEM becomes computationally expensive as problem complexity and accuracy demands increase. Adaptive Mesh Refinement (AMR) improves the FEM by dynamically allocating mesh elements on the domain, balancing computational speed and accuracy. Classical AMR depends on heuristics or expensive error estimators, limiting its use in complex simulations. While learning-based AMR methods are promising, they currently only scale to simple problems. In this work, we formulate AMR as a system of collaborating, homogeneous agents that iteratively split into multiple new agents. This agent-wise perspective enables a spatial reward formulation focused on reducing the maximum mesh element error. Our approach, Adaptive Swarm Mesh Refinement (ASMR), offers efficient, stable optimization and generates highly adaptive meshes at user-defined resolution during inference. Extensive experiments, including volumetric meshes and Neumann boundary conditions, demonstrate that ASMR exceeds heuristic approaches and learned baselines, matching the performance of expensive error-based oracle AMR strategies. ASMR additionally generalizes to different domains during inference, and produces meshes that simulate up to 2 orders of magnitude faster than uniform refinements in more demanding settings.

Physics-informed MeshGraphNets (PI-MGNs): Neural finite element solvers for non-stationary and nonlinear simulations on arbitrary meshes

Engineering components must meet increasing technological demands in ever shorter development cycles. To face these challenges, a holistic approach is essential that allows for the concurrent development of part design, material system and manufacturing process. Current approaches employ numerical simulations, which however quickly becomes computation-intensive, especially for iterative optimization. Data-driven machine learning methods can be used to replace time- and resource-intensive numerical simulations. In particular, MeshGraphNets (MGNs) have shown promising results. They enable fast and accurate predictions on unseen mesh geometries while being fully differentiable for optimization. However, these models rely on large amounts of expensive training data, such as numerical simulations. Physics-informed neural networks (PINNs) offer an opportunity to train neural networks with partial differential equations instead of labeled data, but have not been extended yet to handle time-dependent simulations of arbitrary meshes. This work introduces PI-MGNs, a hybrid approach that combines PINNs and MGNs to quickly and accurately solve non-stationary and nonlinear partial differential equations (PDEs) on arbitrary meshes. The method is exemplified for thermal process simulations of unseen parts with inhomogeneous material distribution. Further results show that the model scales well to large and complex meshes, although it is trained on small generic meshes only.

Movement Primitive Diffusion: Learning Gentle Robotic Manipulation of Deformable Objects

Policy learning in robot-assisted surgery (RAS) lacks data efficient and versatile methods that exhibit the desired motion quality for delicate surgical interventions. To this end, we introduce Movement Primitive Diffusion (MPD), a novel method for imitation learning (IL) in RAS that focuses on gentle manipulation of deformable objects. The approach combines the versatility of diffusion-based imitation learning (DIL) with the high-quality motion generation capabilities of Probabilistic Dynamic Movement Primitives (ProDMPs). This combination enables MPD to achieve gentle manipulation of deformable objects, while maintaining data efficiency critical for RAS applications where demonstration data is scarce. We evaluate MPD across various simulated tasks and a real world robotic setup on both state and image observations. MPD outperforms state-of-the-art DIL methods in success rate, motion quality, and data efficiency.

Latent Task-Specific Graph Network Simulators

Simulating dynamic physical interactions is a critical challenge across multiple scientific domains, with applications ranging from robotics to material science. For mesh-based simulations, Graph Network Simulators (GNSs) pose an efficient alternative to traditional physics-based simulators. Their inherent differentiability and speed make them particularly well-suited for inverse design problems. Yet, adapting to new tasks from limited available data is an important aspect for real-world applications that current methods struggle with. We frame mesh-based simulation as a meta-learning problem and use a recent Bayesian meta-learning method to improve GNSs adaptability to new scenarios by leveraging context data and handling uncertainties. Our approach, latent task-specific graph network simulator, uses non-amortized task posterior approximations to sample latent descriptions of unknown system properties. Additionally, we leverage movement primitives for efficient full trajectory prediction, effectively addressing the issue of accumulating errors encountered by previous auto-regressive methods. We validate the effectiveness of our approach through various experiments, performing on par with or better than established baseline methods. Movement primitives further allow us to accommodate various types of context data, as demonstrated through the utilization of point clouds during inference. By combining GNSs with meta-learning, we bring them closer to real-world applicability, particularly in scenarios with smaller datasets.

Swarm Reinforcement Learning For Adaptive Mesh Refinement

Adaptive Mesh Refinement (AMR) is crucial for mesh-based simulations, as it allows for dynamically adjusting the resolution of a mesh to trade off computational cost with the simulation accuracy. Yet, existing methods for AMR either use task-dependent heuristics, expensive error estimators, or do not scale well to larger meshes or more complex problems. In this paper, we formalize AMR as a Swarm Reinforcement Learning problem, viewing each element of a mesh as part of a collaborative system of simple and homogeneous agents. We combine this problem formulation with a novel agent-wise reward function and Graph Neural Networks, allowing us to learn reliable and scalable refinement strategies on arbitrary systems of equations. We experimentally demonstrate the effectiveness of our approach in improving the accuracy and efficiency of complex simulations. Our results show that we outperform learned baselines and achieve a refinement quality that is on par with a traditional error-based AMR refinement strategy without requiring error indicators during inference.

Grounding Graph Network Simulators using Physical Sensor Observations

Physical simulations that accurately model reality are crucial for many engineering disciplines such as mechanical engineering and robotic motion planning. In recent years, learned Graph Network Simulators produced accurate mesh-based simulations while requiring only a fraction of the computational cost of traditional simulators. Yet, the resulting predictors are confined to learning from data generated by existing mesh-based simulators and thus cannot include real world sensory information such as point cloud data. As these predictors have to simulate complex physical systems from only an initial state, they exhibit a high error accumulation for long-term predictions. In this work, we integrate sensory information to ground Graph Network Simulators on real world observations. In particular, we predict the mesh state of deformable objects by utilizing point cloud data. The resulting model allows for accurate predictions over longer time horizons, even under uncertainties in the simulation, such as unknown material properties. Since point clouds are usually not available for every time step, especially in online settings, we employ an imputation-based model. The model can make use of such additional information only when provided, and resorts to a standard Graph Network Simulator, otherwise. We experimentally validate our approach on a suite of prediction tasks for mesh-based interactions between soft and rigid bodies. Our method results in utilization of additional point cloud information to accurately predict stable simulations where existing Graph Network Simulators fail.

Inferring Versatile Behavior from Demonstrations by Matching Geometric Descriptors

Humans intuitively solve tasks in versatile ways, varying their behavior in terms of trajectory-based planning and for individual steps. Thus, they can easily generalize and adapt to new and changing environments. Current Imitation Learning algorithms often only consider unimodal expert demonstrations and act in a state-action-based setting, making it difficult for them to imitate human behavior in case of versatile demonstrations. Instead, we combine a mixture of movement primitives with a distribution matching objective to learn versatile behaviors that match the expert's behavior and versatility. To facilitate generalization to novel task configurations, we do not directly match the agent's and expert's trajectory distributions but rather work with concise geometric descriptors which generalize well to unseen task configurations. We empirically validate our method on various robot tasks using versatile human demonstrations and compare to imitation learning algorithms in a state-action setting as well as a trajectory-based setting. We find that the geometric descriptors greatly help in generalizing to new task configurations and that combining them with our distribution-matching objective is crucial for representing and reproducing versatile behavior.