Borrett et al 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 Computational Learning Laboratory, CSLI, Stanford University, USA Stuart R. Borrett, Will Bridewell and Pat Langley

Borrett et al 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 Processes hierarchical functional forms parameters

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

Borrett et al Bled Lake Atanasova et al. 2006

Task Find models to explain phytoplankton dynamics for 1997–2002

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

Borrett et al 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)

Borrett et al Background Knowledge: Process Hierarchy

Borrett et al Background Knowledge: Process Hierarchy

Borrett et al Background Knowledge: Process Hierarchy

Borrett et al Phytoplankton Simulations

Borrett et al “Best” Models Ranked by SSE

Borrett et al Model Generalization

Borrett et al 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

Borrett et al 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

Borrett et al. 2006

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

Borrett et al 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

Borrett et al Related Work LaGramge

Borrett et al Phytoplankton: 1997 – 2002