Scientific Discovery of Dynamic Models Based on Scale-type Constraints

This paper proposes a novel approach to discover dynamic laws and models represented by simultaneous time differential equations including hidden states from time series data measured in an objective process. This task has not been addressed in the past work though it is essentially important in scientific discovery since any behaviors of objective processes emerge in time evolution. The promising performance of the proposed approach is demonstrated through the analysis of synthetic data.

[1]  S. Haykin.  Kalman Filtering and Neural Networks , 2001 .

[2]  Takashi Washio,et al.  Discovering Admissible Simultaneous Equation Models from Observed Data , 2001, ECML.

[3]  Takashi Washio,et al.  Discovering Admissible Models of Complex Systems Based on Scale-Types and Idemtity Constraints , 1997, IJCAI.

[4]  Ryszard S. Michalski,et al.  Integrating Quantitative and Qualitative Discovery: The ABACUS System , 1990, Machine Learning.

[5]  Herbert A. Simon,et al.  Scientific discovery: compulalional explorations of the creative process , 1987 .

[6]  Saso Dzeroski,et al.  Inducing Process Models from Continuous Data , 2002, ICML.

[7]  Herbert A. Simon,et al.  Causality in Device Behavior , 1989, Artif. Intell..

[8]  Zoubin Ghahramani,et al.  Learning Nonlinear Dynamical Systems Using an EM Algorithm , 1998, NIPS.

[9]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[10]  室田 一雄.  Systems analysis by graphs and matroids : structural solvability and controllability , 1987 .

[11]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[12]  Pat Langley,et al.  An Integrated Approach to Empirical Discovery , 1989 .

[13]  B W Koehn,et al.  Experimenting and theorizing in theory formation , 1986, ISMIS '86.

[14]  Takashi Washio,et al.  Discovering Admissible Simultaneous Equations of Large Scale Systems , 1998, AAAI/IAAI.

[15]  M. Kokar.  Determining arguments of invariant functional descriptions , 2004, Machine Learning.

[16]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[17]  H. Motoda.  Discovery of First Principle Based on Data-driven Reasoning , 1997 .

[18]  S. Roweis,et al.  Learning Nonlinear Dynamical Systems Using the Expectation–Maximization Algorithm , 2001 .

[19]  Takashi Washio,et al.  Discovering Admissible Model Equations from Observed Data Based on Scale-Types and Identity Constrains , 1999, IJCAI.

[20]  Mieczyslaw M. Kokar,et al.  Determining Arguments of Invariant Functional Descriptions , 1986, Machine Learning.

[21]  Brian Falkenhainer,et al.  Integrating quantitative and qualitative discovery: The ABACUS system , 2004, Machine Learning.

[22]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[23]  Saso Dzeroski,et al.  Discovering dynamics: From inductive logic programming to machine discovery , 1993, Journal of Intelligent Information Systems.

[24]  H. Akaike.  Autoregressive model fitting for control , 1971 .

[25]  R. Shumway,et al.  AN APPROACH TO TIME SERIES SMOOTHING AND FORECASTING USING THE EM ALGORITHM , 1982 .

[26]  Ljup Co Todorovski.  Declarative Bias in Equation Discovery , 1997 .

[27]  Takashi Yanagawa,et al.  ESTIMATING THE EMBEDDING DIMENSION AND DELAY TIME FROM CHAOTIC TIME SERIES WITH DYNAMIC NOISE , 2001 .