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Register a new userAutomatic Calibration of Dynamic and Heterogeneous Parameters in Agent-based Model
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Dongjun Kim
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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While simulations have been utilized in diverse domains, such as urban growth modeling, market dynamics modeling, etc; some of these applications may require validations based upon some real-world observations modeled in the simulation, as well. This validation has been categorized into either qualitative face-validation or quantitative empirical validation, but as the importance and the accumulation of data grows, the importance of the quantitative validation has been highlighted in the recent studies, i.e. digital twin. The key component of quantitative validation is finding a calibrated set of parameters to regenerate the real-world observations with simulation models. While this parameter calibration has been fixed throughout a simulation execution, this paper expands the static parameter calibration in two dimensions: dynamic calibration and heterogeneous calibration. First, dynamic calibration changes the parameter values over the simulation period by reflecting the simulation output trend. Second, heterogeneous calibration changes the parameter values per simulated entity clusters by considering the similarities of entity states. We experimented the suggested calibrations on one hypothetical case and another real-world case. As a hypothetical scenario, we use the Wealth Distribution Model to illustrate how our calibration works. As a real-world scenario, we selected Real Estate Market Model because of three reasons. First, the models have heterogeneous entities as being agent-based models; second, they are economic models with real-world trends over time; and third, they are applicable to the real-world scenarios where we can gather validation data.
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This paper describes a formalization of agent-based models (ABMs) as random walks on regular graphs and relates the symmetry group of those graphs to a coarse-graining of the ABM that is still Markovian. An ABM in which $N$ agents can be in $delta$ different states leads to a Markov chain with $delta^N$ states. In ABMs with a sequential update scheme by which one agent is chosen to update its state at a time, transitions are only allowed between system configurations that differ with respect to a single agent. This characterizes ABMs as random walks on regular graphs. The non-trivial automorphisms of those graphs make visible the dynamical symmetries that an ABM gives rise to because sets of micro configurations can be interchanged without changing the probability structure of the random walk. This allows for a systematic loss-less reduction of the state space of the model.
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