system dynamics for complex adapve systems · system dynamics • strengths: – easy model...
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System Dynamics for Complex Adap6ve Systems
Kiyan Ahmadizadeh, Maarika Teose, Carla Gomes,
Yrjo Grohn, Steve Ellner, Eoin O’Mahony, Becky Smith,
Zhao Lu, Becky Mitchell
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Outline
• Complex Adap6ve Systems • Modeling paradigms – System Dynamics
• Popula6on Growth • Epidemiology
– Agent‐based Modeling – Strengths/weaknesses of each
• Embedded (Hybrid) Models
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Complex Adap6ve Systems
“The whole is not only more than but very different than the sum of its parts.” (Anderson, Phil W. 1972. “More is Different.” Science 177: 393‐96)
• Dynamic network of many agents (e.g. cells, species, individuals, firms, na6ons) ac6ng in parallel, constantly ac6ng and reac6ng to what the other agents are doing
• Control of CAS is dispersed, decentralized • Emergent behaviors (e.g. equilibria, pa`erns) arise from
compe66on and coopera6on among agents
System behavior is unpredictable and the result of decisions made every moment by many individual agents
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ornl.gov
ecosystems.noaa.gov
Complex Adap6ve Systems
• Examples: – Energy grids – Ecosystems – Social diffusion – Disease dynamics – Poli6cs – Supply chain networks – Etc.
Computa<onal Sustainability seeks to model the CAS of our world in the hopes of guiding them toward long‐
term, sustainable outcomes
caida.org
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Modeling CAS
• Two basic approaches: – Top‐down: System Dynamics
• ODEs, Stock and Flow Diagrams
– Bo`om‐up: Agent‐based Modeling • Cellular Automata, Intelligent Agents
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System Dynamics
Stocks: State Variables Flows: Rates of Change Feedback Loops: Nonlinear Interac6ons
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• Flows can be of three types: – Genera6ve (Fgen) – Stock‐to‐Stock (Fin, Fout) – Destruc6ve (Fdes)
System Dynamics
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System Dynamics
• Discrete systems: – Stocks: homogenous groups of well‐mixed agents
– Flows: movement of agents between groups – Feedback Loops: nonlinear interac6ons and effects
• r2 = f(X,Y)
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• Example 1: Popula6on Growth
– Exponen6al growth when popula6on is small – Exponen6al decay when popula6on above K
System Dynamics
• P – popula6on size at 6me t
• r – growth rate • K – habitat carrying
capacity
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Popula6on Growth
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Popula6on Growth
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Popula6on Growth: Delayed Maturity
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Popula6on Growth: Delayed Maturity and Consump6on
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• Example 2: Infec6ous Disease
System Dynamics
• S – Suscep6ble popula6on • I – Infec6ous popula6on • R – Recovered popula6on
• β – Transmission rate • γ – Recovery rate
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Infec6ous Disease
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Infec6ous Disease
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System Dynamics
• Simula6on – For most systems of ODEs, analy6cal solu6ons do not exist
– Con6nuous stock (e.g. money in savings): use numerical methods to approximate solu6on
– Discrete stock (e.g. people): use stochas6c simula6on methods
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Stochas6c Simula6on of ODEs
• Assump6on: Future state of system depends only on present state, independent of history
Con6nuous Time Markov Chain! – Time between events Exponen6ally distributed – Event occurrences in [t, t+Δt) Poisson distributed
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Stochas6c Simula6on of ODEs
• ODEs as CTMCs – Flows are interpreted as transi6on probabili6es per unit 6me
– Events: • {X X+1} ~ Pois(r1Δt) • {(X,Y) (X‐1,Y+1)} ~ Pois(r2Δt)
• {Y Y‐1} ~ Pois(r3Δt)
– For Δt small, probability of more than one event per 6me step is o(Δt2), negligible
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Stochas6c Simula6on of ODEs
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System Dynamics
• Strengths: – Easy model construc6on and valida6on with available data – Simula6on methods computa6onally efficient
• Weaknesses: – Assumes homogenous and well‐mixed popula6on – Captures only average behavior – Assumes mathema6cal equa6ons capture all feedback structure in system
– Assumes macro‐level behavior is independent of micro‐level behavior
– Difficult to model certain interven6ons (ac6ons by outsiders) that influence flows in the model
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Agent‐Based Modeling
• System modeled as popula6on of heterogeneous agents with evolving state space (e.g. Schelling Segrega6on Model)
• Agent interac6ons can cause complex emergent behavior to arise
• Object‐oriented programming well‐suited for represen6ng interac6ng agents
www.marginalrevolu6on.com
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Agent‐Based Modeling
• Example: EpiSims – Highly detailed – Virtual laboratory
www.sciam.com www.sciam.com
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Agent‐Based Modeling
• Strengths: – Allows sophis6cated interac6ons between agents with heterogeneous state space (e.g. contact network)
– Yields greater and more intui6ve informa6on that can be used by researchers and policymakers
– More “lifelike” than system dynamics models • Weaknesses:
– larger state space means poor computa6onal efficiency – Model construc6on is difficult: hard to link observed behavior to local interac6ons, capture all cri6cal feedback loops
– Model calibra6on, valida6on, and sensi6vity analysis require large amounts of data and 6me
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Embedded (Hybrid) Models
• A complete agent‐based model need not be fi`ed, but individual‐level granularity in the model is maintained and heterogeneity in agents can be exploited
• Allows for simula6on of novel, complex interven6on strategies at the level of agents that might otherwise be difficult or impossible to express succinctly in system dynamics terminology