Semantic and Qualitative Physics-Based Reasoning on Plain-English Flow Terms for Generating Function Model Alternatives

Author(s):  
Xiaoyang Mao ◽  
Chiradeep Sen

Abstract In graph-based function models, the function verbs and flow nouns are usually chosen from predefined vocabularies. The vocabulary class definitions, combined with function modeling grammars defined at various levels of formalism, enable function-based reasoning. However, the text written in plain English for the names of the functions and flows is presently not exploited for formal reasoning. This paper presents a formalism (representation and reasoning) to support semantic and physics-based reasoning on the information hidden in the plain-English flow terms, especially for automatically decomposing black box function models, and to generate multiple design alternatives. First, semantic reasoning infers the changes of flow types, flow attributes, and the direction of those changes between the input and output flows attached to the black box. Then, a representation of qualitative physics is used to determine the material and energy exchanges between the flows and the function features needed to achieve them. Finally, a topological reasoning is used to infer multiple options of composing those function features into topologies and to thus generate multiple alternative decompositions of the functional black box. The data representation formalizes flow phases, flow attributes, qualitative value scales for the attributes, and qualitative physics laws. An eight-step algorithm manipulates these data for reasoning. This paper shows four validation case studies to demonstrate the workings of this formalism.

Author(s):  
Xiaoyang Mao ◽  
Chiradeep Sen

In graph-based function models, the function verb and flow noun types are usually controlled by vocabularies of standard classes. The grammar is also controlled at different levels of formalism and contribute to reasoning. However, the text written in plain English for the names of the functions and flows is not used for formal reasoning to help with modeling or exploring the design space. This paper presents a formalism for semantic and physics-based reasoning on function model graphs, esp. to automatically decompose black box models and to generate design alternatives using those plain-English texts. A previously established formal language, which ensures that function models are consistent with physics laws, is used as a baseline. Semantic reasoning is added to use the unstructured information of the flow phrases to infer possible means of decomposing the model into a topology connecting appropriate subfunctions and to generate multiple alternative decompositions. A data structure of flow nouns, flow attributes, qualitative value scales, and qualitative physics laws is used as the data representation. An eight-step algorithm manipulates this data for reasoning. The paper shows two validation case studies to demonstrate the workings of the language.


2021 ◽  
Author(s):  
Bo Shen ◽  
Raghav Gnanasambandam ◽  
Rongxuan Wang ◽  
Zhenyu Kong

In many scientific and engineering applications, Bayesian optimization (BO) is a powerful tool for hyperparameter tuning of a machine learning model, materials design and discovery, etc. BO guides the choice of experiments in a sequential way to find a good combination of design points in as few experiments as possible. It can be formulated as a problem of optimizing a “black-box” function. Different from single-task Bayesian optimization, Multi-task Bayesian optimization is a general method to efficiently optimize multiple different but correlated “black-box” functions. The previous works in Multi-task Bayesian optimization algorithm queries a point to be evaluated for all tasks in each round of search, which is not efficient. For the case where different tasks are correlated, it is not necessary to evaluate all tasks for a given query point. Therefore, the objective of this work is to develop an algorithm for multi-task Bayesian optimization with automatic task selection so that only one task evaluation is needed per query round. Specifically, a new algorithm, namely, multi-task Gaussian process upper confidence bound (MT-GPUCB), is proposed to achieve this objective. The MT-GPUCB is a two-step algorithm, where the first step chooses which query point to evaluate, and the second step automatically selects the most informative task to evaluate. Under the bandit setting, a theoretical analysis is provided to show that our proposed MT-GPUCB is no-regret under some mild conditions. Our proposed algorithm is verified experimentally on a range of synthetic functions as well as real-world problems. The results clearly show the advantages of our query strategy for both design point and task.


2021 ◽  
Author(s):  
Bo Shen ◽  
Raghav Gnanasambandam ◽  
Rongxuan Wang ◽  
Zhenyu Kong

In many scientific and engineering applications, Bayesian optimization (BO) is a powerful tool for hyperparameter tuning of a machine learning model, materials design and discovery, etc. BO guides the choice of experiments in a sequential way to find a good combination of design points in as few experiments as possible. It can be formulated as a problem of optimizing a “black-box” function. Different from single-task Bayesian optimization, Multi-task Bayesian optimization is a general method to efficiently optimize multiple different but correlated “black-box” functions. The previous works in Multi-task Bayesian optimization algorithm queries a point to be evaluated for all tasks in each round of search, which is not efficient. For the case where different tasks are correlated, it is not necessary to evaluate all tasks for a given query point. Therefore, the objective of this work is to develop an algorithm for multi-task Bayesian optimization with automatic task selection so that only one task evaluation is needed per query round. Specifically, a new algorithm, namely, multi-task Gaussian process upper confidence bound (MT-GPUCB), is proposed to achieve this objective. The MT-GPUCB is a two-step algorithm, where the first step chooses which query point to evaluate, and the second step automatically selects the most informative task to evaluate. Under the bandit setting, a theoretical analysis is provided to show that our proposed MT-GPUCB is no-regret under some mild conditions. Our proposed algorithm is verified experimentally on a range of synthetic functions as well as real-world problems. The results clearly show the advantages of our query strategy for both design point and task.


Author(s):  
Cameron J. Turner ◽  
Richard H. Crawford

Metamodels are becoming increasingly popular for representing unknown black box functions. Several metamodel classes exist, including response surfaces and spline-based models, kriging and radial basis function models, and neural networks. For an inexperienced user, selecting an appropriate metamodel is difficult due to a limited understanding of the advantages and disadvantages of each metamodel type. This paper reviews several major metamodeling techniques with respect to their advantages and disadvantages and compares several significant metamodel types for use as a black box metamodeling tool. The results make a strong case for using Non-Uniform Rational B-spline (NURBs) HyPerModels as a generic metamodeling tool.


2005 ◽  
Vol 38 (7) ◽  
pp. 49
Author(s):  
DEEANNA FRANKLIN
Keyword(s):  

2005 ◽  
Vol 38 (9) ◽  
pp. 31
Author(s):  
BETSY BATES
Keyword(s):  

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