1. Borrett et al. 2006 Computational Discovery of Process Models for Aquatic Ecosystems August 2006 Ecological Society of America, Memphis, TN Natasa Atanasova Civil and Geodetic Engineering, University of Ljubljana, Slovenia Acknowledgements Saso Dzeroski, Lupco Todorovski, Borris Kompare, Kevin Arrigo NSF # IIS-0326059 Computational Learning Laboratory, CSLI, Stanford University, USA Stuart R. Borrett, Will Bridewell and Pat Langley

2. Borrett et al. 2006 Inductive Process Modeling (2) Background Knowledge (1) Data (time-series) Entities variables & parameters Given Search for Models that Explain the Data Task Two Spaces (1) Structures Beam search (2) Parameters Gradient decent Langley et al. in press; Asgharbeygi et al. 2006; Todorovski et al. 2005 Processes hierarchical functional forms parameters

3. Borrett et al. 2006 Lotka-Volterra Processes Growth Predation Death Library of Generic Processes

4. Borrett et al. 2006 Bled Lake Atanasova et al. 2006

5. Task Find models to explain phytoplankton dynamics for 1997–2002

6. Borrett et al. 2006 Data: Lake Bled 1997 day Light Temperature PO 4 NO 3 SilicaDaphnia

7. Borrett et al. 2006 Background Knowledge: Entities Phytoplankton Zooplankton Nutrients –PO 4 –NO 3 –Si Environment Phytoplankton Entity (pe) Variables conc (sum) growth_rate (prod) decay_rate (prod) Parameters max_growth_rate (0.05, 2) max_decay_rate (0.001, 0.2) sinking_rate (0.001, 0.9)

8. Borrett et al. 2006 Background Knowledge: Process Hierarchy

9. Borrett et al. 2006 Background Knowledge: Process Hierarchy

10. Borrett et al. 2006 Background Knowledge: Process Hierarchy

11. Borrett et al. 2006 Phytoplankton Simulations

12. Borrett et al. 2006 “Best” Models 1999 2000 Ranked by SSE

13. Borrett et al. 2006 Model Generalization

14. Borrett et al. 2006 Summary and Conclusions Inductive Process Modeling Represent knowledge as Entities and Processes Search for models that Explain the data Lake Bled Discovered yearly models that explain phytoplankton observations System organization appears to vary interannually

15. Borrett et al. 2006 Future Work Bled Lake Model diatoms separately from other phytoplankton Search for 2+ equation models Inductive Process Modeling Hierarchical entities Process-based sensitivity analysis Model selection criteria

16. Borrett et al. 2006

17. Model Rank: SSE Candidate Models = 947 Candidate Models = 991Candidate Models = 1011 Candidate Models = 938Candidate Models = 805Candidate Models = 992

18. Borrett et al. 2006 Background Knowledge: Generic Entities and Processes Phytoplankton Entity (pe) Variables conc (sum) growth_rate (prod) decay_rate (prod) Parameters max_growth_rate (0.05, 2) max_decay_rate (0.001, 0.2) sinking_rate (0.001, 0.9) Grazing Process Subprocesses Grazing Rate Roles Z (ze), P (pe), E (ee) Parameters none Equations Z.conc :: Z.assim * Z. grazing_rate * Z.conc P.conc :: -1 * Z. grazing_rate * Z.conc

19. Borrett et al. 2006 Related Work LaGramge

20. Borrett et al. 2006 Phytoplankton: 1997 – 2002