Continuous States

[EwoutH]

Introduction

Agent-based models traditionally operate in discrete time steps, where agent states are updated at fixed intervals. However, many real-world phenomena involve continuous changes over time - energy depleting, resources growing, temperatures changing, etc. While Mesa has evolved to support discrete events and flexible timing through the DiscreteEventScheduler and DEVSimulator, it lacks first-class support for continuously changing states.

Current workarounds involve manually calculating state changes each time step or scheduling discrete update events, but these approaches have several limitations:

• Need to carefully balance update frequency with performance
• Difficult to accurately detect threshold crossings
• No standardized way to query current state values
• Complex to coordinate multiple changing states
• Inefficient when states are polled at varying frequencies
• Risk of missing critical state transitions

To address these limitations, I propose adding support for Continuous States.

The Continuous State

A Continuous State represents a value that changes smoothly over time according to defined rules. It automatically tracks elapsed time and updates its value only when queried, making it both precise and efficient. Key properties include:

• Rate of Change: The speed and direction of the state change (can be constant or time-varying)
• Last Update Time: Tracks when the state was last queried/updated
• Current Value: Calculated on demand based on elapsed time and rate
• Thresholds: Critical values that trigger events when crossed
• Update Method: Formula for calculating the state (linear, exponential, etc.)

I believe both devs and observables provide a solid foundation for such a feature in Mesa:

• support for discrete event scheduling #2066
• Add support for Observables to MESA #2291

Examples

Animal Energy Systems

Consider wolves in a predator-prey simulation. Their energy continuously depletes at a base metabolic rate, but running increases the depletion rate. When energy drops below certain thresholds, it triggers behaviors like hunting or resting. The continuous state system ensures precise energy tracking without needing frequent updates, while automatically triggering behaviors at exact threshold crossings.

Environmental Growth

Plant growth models often involve continuous resource changes - water levels decrease through evaporation, nutrients are gradually consumed, biomass increases through photosynthesis. These processes happen simultaneously and affect each other. Continuous states allow efficient tracking of multiple interrelated resources with different natural timescales.

Social Network Influence

In opinion dynamics models, agent beliefs might gradually shift based on social influence. Their conviction in certain ideas can strengthen or weaken continuously over time, with threshold effects triggering sudden belief changes or actions when certain confidence levels are reached.

Key Features to Consider

Efficient Polling

• States only update when queried
• Multiple entities can poll without synchronization issues
• Caching mechanisms for frequently accessed states

Event Generation

• Automatic event scheduling at threshold crossings
• Support for multiple thresholds per state
• Precise timing of threshold events

State Dependencies

• States that affect each other's rates of change
• Compound states derived from other states
• State change propagation rules

Future Considerations

Non-linear Changes

Support for more complex change patterns beyond linear rates:

• Exponential growth/decay
• Periodic functions
• State-dependent rates
• Environmental influences

Discussion Points

1. Implementation complexity: How can we keep this manageable while supporting key use cases?
2. Integration: How should this interact with Mesa's existing time management?
3. Use Cases: What are the most important scenarios this needs to support?
4. Performance: How do we balance accuracy with computational efficiency?
5. API Design: What's the most intuitive interface for modelers?