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.

Versatile Inverse Reinforcement Learning via Cumulative Rewards

Inverse Reinforcement Learning infers a reward function from expert demonstrations, aiming to encode the behavior and intentions of the expert. Current approaches usually do this with generative and uni-modal models, meaning that they encode a single behavior. In the common setting, where there are various solutions to a problem and the experts show versatile behavior this severely limits the generalization capabilities of these methods. We propose a novel method for Inverse Reinforcement Learning that overcomes these problems by formulating the recovered reward as a sum of iteratively trained discriminators. We show on simulated tasks that our approach is able to recover general, high-quality reward functions and produces policies of the same quality as behavioral cloning approaches designed for versatile behavior.

Bimodal Speech Emotion Recognition Using Pre-Trained Language Models

Speech emotion recognition is a challenging task and an important step towards more natural human-machine interaction. We show that pre-trained language models can be fine-tuned for text emotion recognition, achieving an accuracy of 69.5% on Task 4A of SemEval 2017, improving upon the previous state of the art by over 3% absolute. We combine these language models with speech emotion recognition, achieving results of 73.5% accuracy when using provided transcriptions and speech data on a subset of four classes of the IEMOCAP dataset. The use of noise-induced transcriptions and speech data results in an accuracy of 71.4%. For our experiments, we created IEmoNet, a modular and adaptable bimodal framework for speech emotion recognition based on pre-trained language models. Lastly, we discuss the idea of using an emotional classifier as a reward for reinforcement learning as a step towards more successful and convenient human-machine interaction.