Beyond the Known: Detecting Novel Feasible Domains Over an Unbounded Design Space

Abstract

To solve a design problem, sometimes it is necessary to identify the feasible design space. For design spaces with implicit constraints, sampling methods are usually used. These methods typically bound the design space; that is, limit the range of design variables. But bounds that are too small will fail to cover all possible designs; while bounds that are too large will waste sampling budget. This paper tries to solve the problem of efficiently discovering (possibly disconnected) feasible domains in an unbounded design space. We propose a data-driven adaptive sampling technique-ε-margin sampling, which both learns the domain boundary of feasible designs, while also expanding our knowledge of the design space as available budget increases. This technique is dataefficient, in that it makes principled probabilistic trade-offs between refining existing domain boundaries versus expanding the design space.We demonstrate that this method can better identify feasible domains on standard test functions compared to both random and active sampling (via uncertainty sampling). However, a fundamental problem when applying adaptive sampling to real world designs is that designs often have high dimensionality and thus require (in the worst case) exponentially more samples per dimension. We show how coupling Design Manifolds with ε-margin * Corresponding author.sampling allows us to actively expand high-dimensional design spaces without incurring this exponential penalty.We demonstrate this on real-world examples of glassware and bottle design, where our method discovers designs that have different appearance and functionality from its initial design set.

Synthesizing Designs With Inter-Part Dependencies Using Hierarchical Generative Adversarial Networks

“…In other words, the generator is willing to take the minor loss incurred by this small region of the infeasible design space in order to avoid making the latent space representation more complicated. To solve this problem, we can perform adaptive sampling in the latent space to more accurately identify the feasible region(s) [2,5].…”

“…Despite the limitation of purely data-driven design methods, they can be used in the conceptual design stage for exploring a wide range of design alternatives and inspiring novel designs. We can also use validation based on simulation, experiment, or human annotation to exclude infeasible synthesized designs when performing latent space exploration [2,49], which could be an interesting avenue for future work.…”

“…Representing a high-dimensional design space with a lower-dimensional latent space makes it easier to explore, visualize, or optimize complex designs. This often means finding a latent representation, or a manifold, along which valid designs, such as geometries, lie [1,2].…”

“…However, finding individual part manifolds that both represent the design space well, while also satisfying part configuration, is non-trivial. Traditionally, to learn the inter-part dependency, one has to either define explicit constraints [3,4] or learn implicit constraints via adaptive sampling [2,5]. The former uses hard-coded (often applicationspecific) constraints and hence lacks flexibility; whereas the latter queries external sources by human annotation, experiment, or simulation, and thus is expensive.…”

An artificial intelligence based data-driven approach for design ideation

“…Recently, there has been a trend of learning new patterns by exploring large datasets [5]. Generating ideas in a data-driven way expands the design space to discover new feasible designs [6]. During an ideation process, potential stimuli such as analogies and bio-inspired knowledge can be provided by artificial intelligence based data-driven algorithms.…”