Creating Polytope Representations of Design Spaces for Visual Exploration Using Consistency Techniques

Devanathan, Srikanth; Ramani, Karthik

doi:10.1115/1.4001528

Cited by 10 publications

(8 citation statements)

References 22 publications

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“…where the estimated labelŷ = arg max y P θ (y|x x x) is the most probable label (in our case, valid/invalid) at x x x under the model θ. Initially, the model θ is trained with a seed set of labeled samples X L 0 = {x x x (1) , x x x (2) , ..., x x x (n 0 ) }. Uncertainty sampling will query an instance closest to the decision boundary (e.g., Point 1 or 3 in Fig.…”

Section: Sequential Sampling and Active Learningmentioning

confidence: 99%

“…Our airfoil samples are from the UIUC Airfoil Coordinates Database, which provides the Cartesian coordinates for nearly 1,600 airfoils. 2 We use PCA to learn a two-way mapping between the original design space X ∈ R 200 and the subspace (embedding space) F ∈ R 2 .…”

Section: Example: Airfoilmentioning

confidence: 99%

“…Identifying the feasible design space is important in design research. For example, design space exploration visualizes a design space and tries to generate feasible designs [1,2,3]. Also, reliability-based design optimization (RBDO) requires an accurate boundary of feasible regions in the space [4,5].…”

Section: Introductionmentioning

confidence: 99%

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

Chen

Fuge

2017

Journal of Mechanical Design

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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.

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Section: Sequential Sampling and Active Learningmentioning

confidence: 99%

Section: Example: Airfoilmentioning

confidence: 99%

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

Chen

Fuge

2017

Journal of Mechanical Design

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“…In applications like design space exploration (e.g. Yannou et al, 2005;Devanathan and Ramani, 2010;Larson and Mattson, 2012) and reliability analysis (e.g. Lee and Jung, 2008;Zhuang and Pan, 2012), people need to find feasible domains within which solutions are valid.…”

Section: Introductionmentioning

confidence: 99%

Active expansion sampling for learning feasible domains in an unbounded input space

Chen

Fuge

2018

Struct Multidisc Optim

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Many engineering problems require identifying feasible domains under implicit constraints. One example is finding acceptable car body styling designs based on constraints like aesthetics and functionality. Current active-learning based methods learn feasible domains for bounded input spaces. However, we usually lack prior knowledge about how to set those input variable bounds. Bounds that are too small will fail to cover all feasible domains; while bounds that are too large will waste query budget. To avoid this problem, we introduce Active Expansion Sampling (AES), a method that identifies (possibly disconnected) feasible domains over an unbounded input space. AES progressively expands our knowledge of the input space, and uses successive exploitation and exploration stages to switch between learning the decision boundary and searching for new feasible domains. We show that AES has a misclassification loss guarantee within the explored region, independent of the number of iterations or labeled samples. Thus it can be used for real-time prediction of samples' feasibility within the explored region. We evaluate AES on three test examples and compare AES with two adaptive sampling methods -the Neighborhood-Voronoi algorithm and the straddle heuristic -that operate over fixed input variable bounds.

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“…The solution of a CSP is a set of feasible values for the design variables that satisfy all of the design constraints. With its concise and formal representation, the CSP formulation has been applied in floor plan design [1,2], geometric modeling [3], conceptual design [4,5], embodiment design [6], collaborative design [7][8][9], design space searching [10][11][12], and other design problems. The CSP formulation can help engineers to explore the design space and find feasible solutions that satisfy the given constraints.…”

Section: Introductionmentioning

confidence: 99%

Searching Feasible Design Space by Solving Quantified Constraint Satisfaction Problems

Aminzadeh

Wang

2013

Journal of Mechanical Design

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In complex systems design, multidisciplinary constraints are imposed by stakeholders. Engineers need to search feasible design space for a given problem before searching for the optimum design solution. Searching feasible design space can be modeled as a constraint satisfaction problem (CSP). By introducing logical quantifiers, CSP is extended to quantified constraint satisfaction problem (QCSP) so that more semantics and design intent can be captured. This paper presents a new approach to formulate searching design problems as QCSPs in a continuous design space based on generalized interval, and to numerically solve them for feasible solution sets, where the lower and upper bounds of design variables are specified. The approach includes two major components. One is a semantic analysis which evaluates the logic relationship of variables in generalized interval constraints based on Kaucher arithmetic, and the other is a branch-and-prune algorithm that takes advantage of the logic interpretation. The new approach is generic and can be applied to the case when variables occur multiple times, which is not available in other QCSP solving methods. A hybrid stratified Monte Carlo method that combines interval arithmetic with Monte Carlo sampling is also developed to verify the correctness of the QCSP solution sets obtained by the branch-and-prune algorithm.

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Creating Polytope Representations of Design Spaces for Visual Exploration Using Consistency Techniques

Abstract: Understanding the limits of a design is an important

Cited by 10 publications

References 22 publications

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

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

Active expansion sampling for learning feasible domains in an unbounded input space

Searching Feasible Design Space by Solving Quantified Constraint Satisfaction Problems

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