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

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`

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

0.05

spacing yields 101 frames for 100 intervals).

Workflow

Get stability limits - Use numerical-stability skill
Plan time stepping - Run
```
scripts/timestep_planner.py
```
Schedule outputs - Run
```
scripts/output_schedule.py
```
Plan checkpoints - Run
```
scripts/checkpoint_planner.py
```
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:

Plan checkpoints based on acceptable lost work:

bash

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

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

bash

# 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

time-stepping

NPX Install

Tags

SKILL.md Content