We propose the first reduced model simulation framework for deformable solid dynamics using autoencoder neural networks. We provide a data‐driven approach to generating nonlinear reduced spaces for deformation dynamics. In contrast to previous methods using machine learning which accelerate simulation by approximating the time‐stepping function, we solve the true equations of motion in the latent‐space using a variational formulation of implicit integration. Our approach produces drastically smaller reduced spaces than conventional linear model reduction, improving performance and robustness. Furthermore, our method works well with existing force‐approximation cubature methods.

EMU is an efficient and scalable model to simulate bulk musculoskeletal motion with heterogenous materials. First, EMU requires no model reductions, or geometric coarsening, thereby producing results visually accurate when compared to an FEM simulation. Second, EMU is efficient and scales much better than state‐of‐the‐art FEM with the number of elements in the mesh, and is more easily parallelizable. Third, EMU can handle heterogeneously stiff meshes with an arbitrary constitutive model, thus allowing it to simulate soft muscles, stiff tendons and even stiffer bones all within one unified system. These three key characteristics of EMU enable us to efficiently orchestrate muscle activated skeletal movements. We demonstrate the efficacy of our approach via a number of examples with tendons, muscles, bones and joints.

By starting with the assumption that motion is fundamentally a decision making problem, we use the world‐line concept from Special Relativity as the inspiration for a novel multi‐agent path planning method. We have identified a particular set of problems that have so far been overlooked by previous works. We present our solution for the global path planning problem for each agent and ensure smooth local collision avoidance for each pair of agents in the scene. We accomplish this by modelling the collision‐free trajectories of the agents through 2D space and time as rods in 3D. We obtain smooth trajectories by solving a non‐linear optimization problem with a quasi‐Newton interior point solver, initializing the solver with a non‐intersecting configuration from a modified Dijkstra's algorithm. This space–time formulation allows us to simulate previously ignored phenomena such as highly heterogeneous interactions in very constrained environments. It also provides a solution for scenes with unnaturally symmetric agent alignments without the need for jittering agent positions or velocities.

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