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Genetic Programming and Domain Knowledge: Beyond the Limitations of GrammarGuided Machine Discovery
 Parallel Problem Solving from Nature  PPSN VI 6th International Conference
, 2000
"... . Application of Genetic Programming to the discovery of empirical laws is often impaired by the huge size of the domains involved. In physical applications, dimensional analysis is a powerful way to trim out the size of these spaces This paper presents a way of enforcing dimensional constraints ..."
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Cited by 18 (3 self)
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. Application of Genetic Programming to the discovery of empirical laws is often impaired by the huge size of the domains involved. In physical applications, dimensional analysis is a powerful way to trim out the size of these spaces This paper presents a way of enforcing dimensional constraints through formal grammars in the GP framework. As one major limitation for grammarguided GP comes from the initialization procedure (how to find admissible and sufficiently diverse trees with a limited depth), an initialization procedure based on dynamic grammar pruning is proposed. The approach is validated on the problem of identification of a materials response to a mechanical test. 1 Introduction This paper investigates the use of Genetic Programming [Koz92] for Machine Discovery (MD), the automatic discovery of empirical laws. In the classical Machine Learning framework introduced in the seminal work of Langley [LSB83], MD systems are based on inductive heuristics combined with s...
Theory Revision in Equation Discovery
, 2001
"... State of the art equation discovery systems start the discovery process from scratch, rather than from an initial hypothesis in the space of equations. On the other hand, theory revision systems start from a given theory as an initial hypothesis and use new examples to improve its quality. Two quali ..."
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Cited by 8 (0 self)
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State of the art equation discovery systems start the discovery process from scratch, rather than from an initial hypothesis in the space of equations. On the other hand, theory revision systems start from a given theory as an initial hypothesis and use new examples to improve its quality. Two quality criteria are usually used in theory revision systems.
Discovering the Structure of Partial Differential Equations from Example Behavior
 In Proceedings of the Seventeenth International Conference on Machine Learning
, 2000
"... One of the most powerful and widely accepted analytical formalisms for modeling biological and physical systems is that of the partial differential equation (PDE). Establishing an acceptable PDE model for a dynamic system occupies a major portion of the work of the mathematical modeler. There are tw ..."
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Cited by 8 (2 self)
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One of the most powerful and widely accepted analytical formalisms for modeling biological and physical systems is that of the partial differential equation (PDE). Establishing an acceptable PDE model for a dynamic system occupies a major portion of the work of the mathematical modeler. There are two main aspects to this activity. First, an appropriate structure has to be determined for the equations involved (the model identification problem). Second, acceptably accurate values for parameters are to be determined (the parameter estimation problem). Of these, the first is more challenging, and is the focus of this paper. We propose a method for discovering the structure of PDE models from example behavior. For simple PDE models, we illustrate that a straightforward adaptation of existing equation discovery methods is sufficient. However, complex PDE models require a more sophisticated approach: a twostage method is proposed in the paper. The efficacy of the approach is d...
Using Domain Knowledge on Population Dynamics Modeling for Equation Discovery
, 2001
"... State of the art equation discovery systems are concerned with the empirical approach to modeling of physical systems, where none or a very limited portion of the expert knowledge about the observed system is used in the modeling process. In this paper, we propose a formalism for integration of the ..."
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Cited by 8 (1 self)
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State of the art equation discovery systems are concerned with the empirical approach to modeling of physical systems, where none or a very limited portion of the expert knowledge about the observed system is used in the modeling process. In this paper, we propose a formalism for integration of the population dynamics modeling knowledge into the process of equation discovery. The formalism allows the encoding of a highlevel domain knowledge accessible to human experts. The encoded knowledge can be automatically transformed into the operational form of context dependent grammars. We present an extended version of the equation discovery system Lagramge that can use these context free grammars. Experimental evaluation shows that the integration of domain knowledge in the process of equation discovery considerably improves the eciency and noise robustness of Lagramge.
Enhancing the Plausibility of Law Equation Discovery
, 2000
"... After the pioneering work of the BACON system, the study in the field of scientific discovery has been directed to the discovery of more plausible law equations to represent the first principles underlying objective systems. The state of the art has only succeeded in a weak sense that the soun ..."
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Cited by 7 (0 self)
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After the pioneering work of the BACON system, the study in the field of scientific discovery has been directed to the discovery of more plausible law equations to represent the first principles underlying objective systems. The state of the art has only succeeded in a weak sense that the soundness, the reproducibility and the mathematical admissibility of the candidates hold within the experimental measurements. The plausibility should be checked for various objects and/or measurements sharing the common first principles, and only the equations having sufficient generality should be retained. In this paper, anovel principle and an algorithm are proposed to predict some mathematically admissible and consistent equation formulae for a newly given set of quantities from the candidate law equations obtained for another set of quantities in advance. The soundness and the reproducibility of the predicted equations are confirmed through the measurements. The law equatio...
Inducing polynomial equations for regression
 In
, 2004
"... Both equation discovery and regression methods aim at inducing models of numerical data. While the equation discovery methods are usually evaluated in terms of comprehensibility of the induced model, the emphasis of the regression methods evaluation is on their predictive accuracy. In this paper, we ..."
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Cited by 7 (2 self)
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Both equation discovery and regression methods aim at inducing models of numerical data. While the equation discovery methods are usually evaluated in terms of comprehensibility of the induced model, the emphasis of the regression methods evaluation is on their predictive accuracy. In this paper, we present Ciper, an efficient method for discovery of polynomial equations and empirically evaluate its predictive performance on standard regression tasks. The evaluation shows that polynomials compare favorably to linear and piecewise regression models, induced by the existing stateoftheart regression methods, in terms of degree of fit and complexity. 1
Discovering Admissible Model Equations from Observed Data Based on ScaleTypes and Identity Constraints
 Proc. of IJCAI'99: Sixteenth International Joint Conference on Artificial Intelligence, Vol.2
, 1999
"... Most conventional law equation discovery systems suchasBACON require experimental environments to acquire their necessary data. The mathematical techniques such as linear system identification and neural network fitting presume the classes of equations to model given observed data sets. The st ..."
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Cited by 6 (4 self)
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Most conventional law equation discovery systems suchasBACON require experimental environments to acquire their necessary data. The mathematical techniques such as linear system identification and neural network fitting presume the classes of equations to model given observed data sets. The study reported in this paper proposes a novel method to discover an admissible model equation from a given set of observed data, while the equation is ensured to reflect first principles governing the objective system. The power of the proposed method comes from the use of the scaletypes of the observed quantities, a mathematical property of identity and quasibivariate fitting to the given data set. Its principles and algorithm are described with moderately complex examples, and its practicality is demonstrated through a real application to psychological and sociological law equation discovery. 1 Introduction The most well known pioneering system to discover scientific law eq...
Revising Engineering Models: Combining Computational Discovery with Knowledge
 Proceedings of the Thirteenth European Conference on Machine Learning
, 2002
"... Developing mathematical models that represent physical devices is a difficult and time consuming task. In this paper, we present a hybrid approach to modeling that combines machine learning methods with knowledge from a human domain expert. Specifically, we propose a system for automatically revisin ..."
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Cited by 5 (1 self)
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Developing mathematical models that represent physical devices is a difficult and time consuming task. In this paper, we present a hybrid approach to modeling that combines machine learning methods with knowledge from a human domain expert. Specifically, we propose a system for automatically revising an initial model provided by an expert with an equation discovery program that is tightly constrained by domain knowledge. We apply our system to learning an improved model of a battery on the International Space Station from telemetry data. Our results suggest that this hybrid approach can reduce model development time and improve model quality.
Opening Pandora's box, bottom side up: Automated extraction of comprehensible multivariate power functions from real data
, 2002
"... In this thesis, we will present a method for automated extraction of multivariate, multiterm power functions from large, real data sets. We propose several modifications for the hybrid rule extraction/equation discovery system RF5 to make it applicable for large problems, and present a pruning algo ..."
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Cited by 2 (2 self)
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In this thesis, we will present a method for automated extraction of multivariate, multiterm power functions from large, real data sets. We propose several modifications for the hybrid rule extraction/equation discovery system RF5 to make it applicable for large problems, and present a pruning algorithm to strongly increase the comprehensibility of the found formulas.