Designing physical artifacts that serve a purpose---such as tools and other functional structures---is central to engineering as well as everyday human behavior. Though automating design using machine learning has tremendous promise, existing methods are often limited by the task-dependent distributions they were exposed to during training.

Accurately simulating physics is crucial across scientific domains, with applications spanning from robotics to materials science. While traditional mesh-based simulations are precise, they are often computationally expensive and require knowledge of physical parameters, such as material properties. In contrast, data-driven approaches like Graph Network Simulators (GNSs) offer faster inference but suffer from two key limitations: Firstly, they must be retrained from scratch for even minor variations in physical parameters, and secondly they require labor-intensive data collection for each new parameter setting. This is inefficient, as simulations with varying parameters often share a common underlying latent structure. In this work, we address these challenges by learning this shared structure through meta-learning, enabling fast adaptation to new physical parameters without retraining. To this end, we propose a novel architecture that generates a latent representation by encoding graph trajectories using conditional neural processes (CNPs). To mitigate error accumulation over time, we combine CNPs with a novel neural operator architecture. We validate our approach, Meta Neural Graph Operator (MaNGO), on several dynamics prediction tasks with varying material properties, demonstrating superior performance over existing GNS methods. Notably, MaNGO achieves accuracy on unseen material properties close to that of an oracle model.

Designing physical artifacts that serve a purpose---such as tools and other functional structures---is central to engineering as well as everyday human behavior. Though automating design using machine learning has tremendous promise, existing methods are often limited by the task-dependent distributions they were exposed to during training. This constitutes a simple, fast, and reusable approach that solves high-dimensional problems with complex physical dynamics, including designing surfaces and tools to manipulate fluid flows and optimizing the shape of an airfoil to minimize drag. This framework produces high-quality designs by propagating gradients through trajectories of hundreds of steps, even when using models that were pre-trained for single-step predictions on data substantially different from the design tasks. In our fluid manipulation tasks, the resulting designs outperformed those found by sampling-based optimization techniques.

Designing physical artifacts that serve a purpose---such as tools and other functional structures---is central to engineering as well as everyday human behavior. Though automating design using machine learning has tremendous promise, existing methods are often limited by the task-dependent distributions they were exposed to during training. This constitutes a simple, fast, and reusable approach that solves high-dimensional problems with complex physical dynamics, including designing surfaces and tools to manipulate fluid flows and optimizing the shape of an airfoil to minimize drag. This framework produces high-quality designs by propagating gradients through trajectories of hundreds of steps, even when using models that were pre-trained for single-step predictions on data substantially different from the design tasks. In our fluid manipulation tasks, the resulting designs outperformed those found by sampling-based optimization techniques.

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.

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.

We develop a PyTorch-based Graph Network Simulator (GNS) that learns physics and predicts the flow behavior of particulate and fluid systems. GNS discretizes the domain with nodes representing a collection of material points and the links connecting the nodes representing the local interaction between particles or clusters of particles. The GNS learns the interaction laws through message passing on the graph. GNS has three components: (a) Encoder, which embeds particle information to a latent graph, the edges are learned functions; (b) Processor, which allows data propagation and computes the nodal interactions across steps; and (c) Decoder, which extracts the relevant dynamics (e.g., particle acceleration) from the graph. We introduce physics-inspired simple inductive biases, such as an inertial frame that allows learning algorithms to prioritize one solution (constant gravitational acceleration) over another, reducing learning time. The GNS implementation uses semi-implicit Euler integration to update the next state based on the predicted accelerations. GNS trained on trajectory data is generalizable to predict particle kinematics in complex boundary conditions not seen during training. The trained model accurately predicts within a 5\% error of its associated material point method (MPM) simulation. The predictions are 5,000x faster than traditional MPM simulations (2.5 hours for MPM simulations versus 20 s for GNS simulation of granular flow). GNS surrogates are popular for solving optimization, control, critical-region prediction for in situ viz, and inverse-type problems. The GNS code is available under the open-source MIT license at https://github.com/geoelements/gns.