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  1. Physical systems ranging from elastic bodies to kinematic linkages are defined on high-dimensional configuration spaces, yet their typical low-energy configurations are concentrated on much lower-dimensional subspaces. This work addresses the challenge of identifying such subspaces automatically: given as input an energy function for a high-dimensional system, we produce a low-dimensional map whose image parameterizes a diverse yet low-energy submanifold of configurations. The only additional input needed is a single seed configuration for the system to initialize our procedure; no dataset of trajectories is required. We represent subspaces as neural networks that map a low-dimensional latent vector to the full configuration space, and propose a training scheme to fit network parameters to any system of interest. This formulation is effective across a very general range of physical systems; our experiments demonstrate not only nonlinear and very low-dimensional elastic body and cloth subspaces, but also more general systems like colliding rigid bodies and linkages. We briefly explore applications built on this formulation, including manipulation, latent interpolation, and sampling. 
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    Free, publicly-accessible full text available July 23, 2024
  2. Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of found solutions using ad hoc heuristics. We present an end-to-end method to learn the proximal operator of a family of training problems so that multiple local minima can be quickly obtained from initial guesses by iterating the learned operator, emulating the proximal-point algorithm that has fast convergence. The learned proximal operator can be further generalized to recover multiple optima for unseen problems at test time, enabling applications such as object detection. The key ingredient in our formulation is a proximal regularization term, which elevates the convexity of our training loss: by applying recent theoretical results, we show that for weakly-convex objectives with Lipschitz gradients, training of the proximal operator converges globally with a practical degree of over-parameterization. We further present an exhaustive benchmark for multi-solution optimization to demonstrate the effectiveness of our method. 
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  3. We introduce MechSense, 3D-printed rotary encoders that can be fabricated in one pass alongside rotational mechanisms, and report on their angular position, direction of rotation, and speed. MechSense encoders utilize capacitive sensing by integrating a floating capacitor into the rotating element and three capacitive sensor patches in the stationary part of the mechanism. Unlike existing rotary encoders, MechSense does not require manual assembly but can be seamlessly integrated during design and fabrication. Our MechSense editor allows users to integrate the encoder with a rotating mechanism and exports files for 3D-printing. We contribute a sensor topology and a computational model that can compensate for print deviations. Our technical evaluation shows that MechSense can detect the angular position (mean error: 1.4°) across multiple prints and rotations, different spacing between sensor patches, and different sizes of sensors. We demonstrate MechSense through three application examples on 3D-printed tools, tangible UIs, and gearboxes. 
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  4. Additive manufacturing has become one of the forefront technologies in fabrication, enabling products impossible to manufacture before. Although many materials exist for additive manufacturing, most suffer from performance trade-offs. Current materials are designed with inefficient human-driven intuition-based methods, leaving them short of optimal solutions. We propose a machine learning approach to accelerating the discovery of additive manufacturing materials with optimal trade-offs in mechanical performance. A multiobjective optimization algorithm automatically guides the experimental design by proposing how to mix primary formulations to create better performing materials. The algorithm is coupled with a semiautonomous fabrication platform to substantially reduce the number of performed experiments and overall time to solution. Without prior knowledge of the primary formulations, the proposed methodology autonomously uncovers 12 optimal formulations and enlarges the discovered performance space 288 times after only 30 experimental iterations. This methodology could be easily generalized to other material design systems and enable automated discovery. 
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  5. Manufactured parts are meticulously engineered to perform well with respect to several conflicting metrics, like weight, stress, and cost. The best achievable trade-offs reside on the Pareto front , which can be discovered via performance-driven optimization. The objectives that define this Pareto front often incorporate assumptions about the context in which a part will be used, including loading conditions, environmental influences, material properties, or regions that must be preserved to interface with a surrounding assembly. Existing multi-objective optimization tools are only equipped to study one context at a time, so engineers must run independent optimizations for each context of interest. However, engineered parts frequently appear in many contexts: wind turbines must perform well in many wind speeds, and a bracket might be optimized several times with its bolt-holes fixed in different locations on each run. In this paper, we formulate a framework for variable-context multi-objective optimization. We introduce the Pareto gamut , which captures Pareto fronts over a range of contexts. We develop a global/local optimization algorithm to discover the Pareto gamut directly, rather than discovering a single fixed-context "slice" at a time. To validate our method, we adapt existing multi-objective optimization benchmarks to contextual scenarios. We also demonstrate the practical utility of Pareto gamut exploration for several engineering design problems. 
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