Intelligent Computing Based Formulas to Predict the Settlement of Shallow Foundations on Cohesionless Soils

Tarawneh, Bashar; Bodour, Wassel Al; Ajmi, Khaled Al

doi:10.2174/1874149501913010001

Cited by 6 publications

(3 citation statements)

References 26 publications

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“…Recent applications of SR for physical models can be found in civil engineering [32] and material science [33]. Although successfully proven, the earlier proposed SR was based on a heuristic search that could terminate the optimization in local minima solutions, potentially producing less suitable models than possible.…”

Section: Introductionmentioning

confidence: 99%

A new formulation for symbolic regression to identify physico-chemical laws from experimental data

Neumann

Cao

Russo

et al. 2020

Chemical Engineering Journal

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A modification to the mixed-integer nonlinear programming (MINLP) formulation for symbolic regression was proposed with the aim of identification of physical models from noisy experimental data. In the proposed formulation, a binary tree in which equations are represented as directed, acyclic graphs, is fully constructed for a pre-defined number of layers. The introduced modification results in the reduction in the number of required binary variables and removal of redundancy due to possible symmetry of the tree formulation. The formulation was tested using numerical models and was found to be more efficient than the previous literature example with respect to the numbers of predictor variables and training data points. The globally optimal search was extended to identify physical models and to cope with noise in the experimental data predictor variable. The methodology was proven to be successful in identifying the correct physical models describing the relationship between shear stress and shear rate for both Newtonian and non-Newtonian fluids, and simple kinetic laws of chemical reactions. Future work will focus on addressing the limitations of the present formulation and solver to enable extension of target problems to larger, more complex physical models.

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Section: Introductionmentioning

confidence: 99%

A new formulation for symbolic regression to identify physico-chemical laws from experimental data

Neumann

Cao

Russo

et al. 2020

Chemical Engineering Journal

View full text Add to dashboard Cite

show abstract

“…Recent application of SR for physical models can be found in civil engineering [23] and material science [24]. Although successfully proven, the proposed SR was based on a heuristic search that could terminate the optimization in local minima solutions, producing potentially less suitable models than possible.…”

Section: Introductionmentioning

confidence: 99%

Identifying Physico-Chemical Laws from the Robotically Collected Data

Cao¹,

Russo²,

Vs³

et al. 2019

Preprint

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A mixed-integer nonlinear programming (MINLP) formulation for symbolic regression was proposed to identify physical models from noisy experimental data. The formulation was tested using numerical models and was found to be more efficient than the previous literature example with respect to the number of predictor variables and training data points. The globally optimal search was extended to identify physical models and to cope with noise in the experimental data predictor variable. The methodology was coupled with the collection of experimental data in an automated fashion, and was proven to be successful in identifying the correct physical models describing the relationship between the shear stress and shear rate for both Newtonian and non-Newtonian fluids, and simple kinetic laws of reactions. Future work will focus on addressing the limitations of the formulation presented in this work, by extending it to be able to address larger complex physical models.

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“…We note that other loss functions involving general norms are also possible and that, in general, problem (1.1) is an infinite-dimensional optimization problems. Various applications of symbolic regression have been presented in different fields including materials science [21], fluid systems [7], physics [16,19,20], and civil engineering [17]. Symbolic regression is especially useful when we do not know the precise functional form that relates the independent variables x to the dependent variables z or when we wish to exploit the freedom of optimally choosing the functional form.…”

mentioning

confidence: 99%

Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

Kim,

Leyffer,

Balaprakash

2021

Preprint

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In this paper we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. The symbolic regression problem can be formulated as a nonconvex mixed-integer nonlinear program (MINLP), where binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program-based method and a neural-network-based method from the literature.

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Intelligent Computing Based Formulas to Predict the Settlement of Shallow Foundations on Cohesionless Soils

Cited by 6 publications

References 26 publications

A new formulation for symbolic regression to identify physico-chemical laws from experimental data

A new formulation for symbolic regression to identify physico-chemical laws from experimental data

Identifying Physico-Chemical Laws from the Robotically Collected Data

Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

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