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Description
Problem
gds-sim only supports discrete-time simulation (timestep-based). Many dynamical systems — differential games, optimal control, continuous-time control theory — require continuous-time ODE solvers with adaptive step control.
Proposed Solution
Add a ContinuousModel to gds-sim wrapping scipy.solve_ivp:
- ODE right-hand side function specification
- Adaptive RK45/RK23 integration with configurable tolerances
- Backward-time integration support (for reachable sets, adjoint equations)
- Compatible with
gds-psuu(Metric extraction from continuous results)
Motivation
The Homicidal Chauffeur notebook demonstrates a pursuit-evasion differential game that requires solve_ivp at rtol=1e-10. This class of problem cannot be approximated well with discrete timesteps.
Scope
ContinuousModelclass withrhsfunction and time span- Integration backend using SciPy
ContinuousResultscompatible with existingResultscolumnar storage- Backward integration via time reversal
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enhancementNew feature or requestNew feature or request