We introduce a theory-driven mechanism for learning a neural network model that performs generative topology design in one shot given a problem setting, circumventing the conventional iterative process that computational design tasks usually entail. The proposed mechanism can lead to machines that quickly response to new design requirements based on its knowledge accumulated through past experiences of design generation. Achieving such a mechanism through supervised learning would require an impractically large amount of problem-solution pairs for training, due to the known limitation of deep neural networks in knowledge generalization. To this end, we introduce an interaction between a student (the neural network) and a teacher (the optimality conditions underlying topology optimization): The student learns from existing data and is tested on unseen problems. Deviation of the student's solutions from the optimality conditions is quantified, and used for choosing new data points to learn from. We call this learning mechanism "theory-driven", as it explicitly uses domain-specific theories to guide the learning, thus distinguishing itself from purely data-driven supervised learning. We show through a compliance minimization problem that the proposed learning mechanism leads to topology generation with near-optimal structural compliance, much improved from standard supervised learning under the same computational budget.
Lastly, the proposed learning method is aligned with the recent surge of machine learning techniques with integrated physics knowledge. Among this body of work, @cite_34 proposes to learn a neural network for predicting intrinsic physical properties of objects with the assistance of a physical simulator that computes object interactions based on the predicted properties. @cite_44 developed an encoder that computes object positions and velocities from images of objects, by enforcing these properties to be compliant with common sense. Similarly, @cite_16 proposed a physics-based regularization to learn object trajectories and human movements from videos. Instead of being taught physics, @cite_1 demonstrated a grounded way for machines to acquire an intuition of the physical world through reinforcement learning. Our paper is similar to those learning mechanisms with injected physics constraints, while employing adaptive sampling rather than batch-mode training to avoid expensive simulations. In addition, the use of theory-driven constraints for learning also aligns our method with Q learning, where values are learned to satisfy Bellman's equation.
@cite_44 @cite_34 @cite_1 @cite_16
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We propose position-velocity encoders (PVEs) which learn---without supervision---to encode images to positions and velocities of task-relevant objects. PVEs encode a single image into a low-dimensional position state and compute the velocity state from finite differences in position. In contrast to autoencoders, position-velocity encoders are not trained by image reconstruction, but by making the position-velocity representation consistent with priors about interacting with the physical world. We applied PVEs to several simulated control tasks from pixels and achieved promising preliminary results. When encountering novel objects, humans are able to infer a wide range of physical properties such as mass, friction and deformability by interacting with them in a goal driven way. This process of active interaction is in the same spirit as a scientist performing experiments to discover hidden facts. Recent advances in artificial intelligence have yielded machines that can achieve superhuman performance in Go, Atari, natural language processing, and complex control problems; however, it is not clear that these systems can rival the scientific intuition of even a young child. In this work we introduce a basic set of tasks that require agents to estimate properties such as mass and cohesion of objects in an interactive simulated environment where they can manipulate the objects and observe the consequences. We found that state of art deep reinforcement learning methods can learn to perform the experiments necessary to discover such hidden properties. By systematically manipulating the problem difficulty and the cost incurred by the agent for performing experiments, we found that agents learn different strategies that balance the cost of gathering information against the cost of making mistakes in different situations. In many machine learning applications, labeled data is scarce and obtaining more labels is expensive. We introduce a new approach to supervising neural networks by specifying constraints that should hold over the output space, rather than direct examples of input-output pairs. These constraints are derived from prior domain knowledge, e.g., from known laws of physics. We demonstrate the effectiveness of this approach on real world and simulated computer vision tasks. We are able to train a convolutional neural network to detect and track objects without any labeled examples. Our approach can significantly reduce the need for labeled training data, but introduces new challenges for encoding prior knowledge into appropriate loss functions.