Time Stepping

Goal

Provide a reliable workflow for choosing, ramping, and monitoring time steps plus output/checkpoint cadence.

Requirements

• Python 3.10+
• No external dependencies (uses stdlib)

Inputs to Gather

Input	Description	Example
Stability limits	CFL/Fourier/reaction limits	dt_max = 1e-4
Target dt	Desired time step	1e-5
Total run time	Simulation duration	10 s
Output interval	Time between outputs	0.1 s
Checkpoint cost	Time to write checkpoint	120 s

Decision Guidance

Time Step Selection

Is stability limit known?
├── YES → Use min(dt_target, dt_limit × safety)
└── NO → Start conservative, increase adaptively

Need ramping for startup?
├── YES → Start at dt_init, ramp to dt_target over N steps
└── NO → Use dt_target from start

Ramping Strategy

Problem Type	Ramp Steps	Initial dt
Smooth IC	None needed	Full dt
Sharp gradients	5-10	0.1 × dt
Phase change	10-20	0.01 × dt
Cold start	10-50	0.001 × dt

Script Outputs (JSON Fields)

Script	Key Outputs
scripts/timestep_planner.py	dt_limit, dt_recommended, ramp_schedule, notes
scripts/output_schedule.py	output_times, interval, count
scripts/checkpoint_planner.py	checkpoint_interval, checkpoints, overhead_fraction, warnings

output_schedule.py count is endpoint-inclusive: it includes both t_start and t_end, so count = number_of_intervals + 1 (e.g. t=0..5 at 0.05 spacing yields 101 frames for 100 intervals).

Workflow

1. Get stability limits - Use numerical-stability skill
2. Plan time stepping - Run scripts/timestep_planner.py
3. Schedule outputs - Run scripts/output_schedule.py
4. Plan checkpoints - Run scripts/checkpoint_planner.py
5. Monitor during run - Adjust dt if limits change

Conversational Workflow Example

User: I'm running a 10-hour phase-field simulation. How often should I checkpoint?

Agent workflow:

1. Plan checkpoints based on acceptable lost work:

   python3 scripts/checkpoint_planner.py --run-time 36000 --checkpoint-cost 120 --max-lost-time 1800 --json
   

2. Interpret: Checkpoint every 30 minutes, overhead ~6.7% (Acceptable per the interpretation table), max 30 min lost work on crash.

Pre-Run Checklist

• Confirm dt limits from stability analysis
• Define ramping strategy for transient startup
• Choose output interval consistent with physics time scales
• Plan checkpoints based on restart risk
• Re-evaluate dt after parameter changes

CLI Examples

# Plan time stepping with ramping
python3 scripts/timestep_planner.py --dt-target 1e-4 --dt-limit 2e-4 --safety 0.8 --ramp-steps 10 --json

# Schedule output times
python3 scripts/output_schedule.py --t-start 0 --t-end 10 --interval 0.1 --json

# Plan checkpoints for long run
python3 scripts/checkpoint_planner.py --run-time 36000 --checkpoint-cost 120 --max-lost-time 1800 --json

Error Handling

Error	Cause	Resolution
dt-target must be positive	Invalid time step	Use positive value
t-end must be > t-start	Invalid time range	Check time bounds
checkpoint-cost must be < run-time	Checkpoint too expensive	Reduce checkpoint size

Interpretation Guidance

dt Behavior

Observation	Meaning	Action
dt stable at target	Good	Continue
dt shrinking	Stability issue	Check CFL, reduce target
dt oscillating	Borderline stability	Add safety factor

Checkpoint Overhead

Overhead	Acceptability
< 1%	Excellent
1-5%	Good
5-10%	Acceptable
> 10%	Too frequent, increase interval

Verification checklist

• Recorded dt_recommended and dt_limit from timestep_planner.py and confirmed dt_recommended <= dt_limit with no "Recommended dt exceeds stability limit" note in the notes field.
• Captured the actual dt_limit value from the stability analysis (numerical-stability skill: CFL/Fourier/reaction limit) that was fed to --dt-limit, rather than guessing — and re-ran the planner after any parameter change.
• Confirmed safety <= 1.0 was applied (a margin below the limit), and logged the notes array (e.g. "Recommended dt reduced by stability limit", min/max clamps) so the binding constraint is known.
• Recorded the output_schedule.py count and verified it is endpoint-inclusive (count = intervals + 1, both t_start and t_end present), so frame counts and post-processing indices are not off-by-one.
• Recorded the checkpoint interval, method (daly vs cap), and overhead_fraction from checkpoint_planner.py, and confirmed overhead_fraction <= 0.10 (no warnings entry) against the overhead acceptability table.
• Confirmed every script exited 0 (not exit 2 / stderr ValueError) and that quoted dt/interval/checkpoint values come from the JSON results, not from a run that printed a validation error.

Common pitfalls & rationalizations

Tempting shortcut	Why it's wrong / what to do
"Implicit scheme, so any dt is fine — skip --dt-limit."	Unconditional stability is not accuracy; a large dt still ruins temporal error and resolves no transient. Still pass a physics-based dt-target and re-check the recommended dt against time scales.
"Set --safety above 1.0 to take bigger steps."	safety is a margin at or below the limit; safety > 1.0 would return a dt above the stability limit, so the planner rejects it (exit 2). Lower dt-limit expectations or use a finer mesh instead.
"It ran without crashing, so the dt is valid."	Run completion is not correctness. Verify dt_recommended <= dt_limit, read the notes array, and re-plan whenever v_max, D, dx, or the scheme changes — the limit moves with them.
"The output count looks one too many — drop the last frame."	count is endpoint-inclusive by design (intervals + 1); both t_start and t_end are real outputs. Trimming it silently loses the final state.
"Checkpoint every step to never lose work."	That drives overhead_fraction past 10% (the planner emits a warnings entry) and dominates runtime. Use --max-lost-time (cap) or --mtbf (Daly) so overhead stays in the Acceptable band.
"Reuse last week's dt/checkpoint plan; the model is basically the same."	Stability and optimal checkpoint interval depend on current dx, velocity/diffusivity, checkpoint-cost, and MTBF. Re-run the three scripts with current values rather than copying stale numbers.

Security

Input Validation

• All numeric parameters (dt-target, dt-limit, safety, t-start, t-end, interval, run-time, checkpoint-cost, max-lost-time) are validated as finite positive numbers (non-finite values such as inf/nan are rejected)
• safety is bounded to <= 1.0 (a safety factor is a stability margin at or below the limit; values above 1.0 are rejected)
• ramp-steps and preview-steps are validated as non-negative integers with an upper bound of 1,000,000; only the previewed slice of the ramp is materialized to bound memory use
• Time range consistency is enforced (t-end must exceed t-start; checkpoint-cost must be less than run-time)

File Access

• Scripts read no external files; all inputs are provided via CLI arguments
• Scripts write only to stdout (JSON output); no files are created unless the agent explicitly uses the Write tool

Tool Restrictions

• Read: Used to inspect script source, references, and user configuration files
• Bash: Used to execute the three Python planning scripts (timestep_planner.py, output_schedule.py, checkpoint_planner.py) with explicit argument lists
• Write: Used to save generated time-step plans or checkpoint schedules; writes are scoped to the user's working directory
• Grep/Glob: Used to locate relevant files and search references

Safety Measures

• No eval(), exec(), or dynamic code generation
• All subprocess calls use explicit argument lists (no shell=True)
• Scripts use only Python standard library; no pickle loading or deserialization of untrusted data
• All output is deterministic JSON with no shell-interpretable content

Limitations

• Not adaptive control: Plans static schedules, not runtime adaptation
• Assumes constant physics: If parameters change, re-plan

References

• references/cfl_coupling.md - Combining multiple stability limits
• references/ramping_strategies.md - Startup policies
• references/output_checkpoint_guidelines.md - Cadence rules

Version History

• v1.2.2 (2026-06-24): Added Verification checklist and Common pitfalls & rationalizations sections grounded in the three planning scripts' actual outputs
• v1.2.0 (2026-06-23): Corrected overhead/frame-count docs and evals, removed output-time float drift, hardened input validation (checkpoint-cost < run-time, safety <= 1.0, bounded ramp/preview steps, finite checks)
• v1.1.0 (2024-12-24): Enhanced documentation, decision guidance, examples
• v1.0.0: Initial release with 3 planning scripts