Substeps vs iterations

25 · Convergence

The same 30 Hz frame is split into 2, 4, 8 or 16 steps, keeping 48 PGS sweeps per frame. Smaller steps make each contact's correction smaller and the problem easier to converge, so a tall stack of ten 8 cm boxes that topples at large steps stands at small ones.

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Cost

Time per 30 Hz frame, CUDA graph replay, median of 7 interleaved rounds on one NVIDIA RTX PRO 6000 Blackwell Server Edition; ratios are against the first row. Solver allocation is the GPU memory the solver allocates at construction, before warm-up and graph capture. Scene: the 8-box stack in each world; every option simulates the same 1/30 s frame.

Option	1 world	64 worlds	1024 worlds	solver allocation, 1024 worlds	result in this tutorial
2 x 24	3.62 ms	4.01 ms	5.25 ms	215 MB	10-box stack falls
4 x 12	4.23 ms 1.17×	5.18 ms 1.29×	7.22 ms 1.38×	215 MB	10-box stack falls
8 x 6	5.39 ms 1.49×	6.81 ms 1.70×	9.96 ms 1.90×	215 MB	stands, 8.7 mm sag
16 x 3	7.60 ms 2.10×	10.57 ms 2.64×	14.75 ms 2.81×	215 MB	stands, 3.8 mm sag

What to look at

2 and 4 substeps: the stack drifts and falls.
8 and 16 substeps: it stands, with less sag at 16.

Key parameter

dt

The step size you pass to solver.step. Substeps cost collision and setup per step; iterations cost only sweeps.

Try changing

Try 8 substeps × 12 iterations.
Set contact_warmstart=True at 4 substeps.

Concept

Substeps vs iterations

What it is

Halving the step halves each correction and the change per step, which helps convergence more than doubling sweeps at a fixed step. Substeps cost more, though: each step repeats collision, mass-matrix work and integration.

In this scene

At 48 sweeps per 30 Hz frame, the 10-box stack collapses at 2×24 and 4×12 and stands at 8×6 and 16×3.

Considerations

Cost: Per 1/30 s frame on the 8-box stack: 2×24 3.6 ms, 4×12 4.2, 8×6 5.4, 16×3 7.6 in one world; 5.3, 7.2, 10.0 and 14.8 ms in 1024 worlds.
Failure modes: Tall stacks of small boxes at large steps drift sideways until they topple.
Use it when: Substeps for tall stacks and fast contacts; iterations when per-frame cost matters, since they are cheaper per frame (see Cost).

The script

cd tutorials && python 25_substeps.py prints each variant's final metric; --record out.json also writes the replay. Every tutorial imports replay.py from the same folder.

25_substeps.py
replay.py

# SPDX-FileCopyrightText: Copyright (c) 2026 Skild AI and the Steel contributors
# SPDX-License-Identifier: Apache-2.0

"""Substeps vs iterations: split the same 30 Hz frame into more, cheaper solver steps."""

import newton
import warp as wp
from newton.solvers import SolverSteel

from replay import Recorder

FRAME_DT = 1.0 / 30.0
N, H = 10, 0.04


def build():
    builder = newton.ModelBuilder()
    builder.add_ground_plane(cfg=newton.ModelBuilder.ShapeConfig(mu=0.6))
    for i in range(N):
        box = builder.add_body(
            xform=wp.transform((0.0, 0.0, H + 2 * H * i + 0.0002 * i), wp.quat_identity())
        )
        builder.add_shape_box(box, hx=H, hy=H, hz=H, cfg=newton.ModelBuilder.ShapeConfig(mu=0.6))
    return builder.finalize()


def simulate(rec, substeps, iterations):
    model = build()
    solver = SolverSteel(model, iterations=iterations)
    pipeline = newton.CollisionPipeline(model)
    contacts = pipeline.contacts()
    state_0, state_1, control = model.state(), model.state(), model.control()
    dt = FRAME_DT / substeps

    run = rec.variant(f"{substeps} substeps x {iterations} iterations", model)
    for _ in range(rec.frames(4.0)):
        top = state_0.body_q.numpy()[N - 1, 2]
        run.frame(state_0, sag_mm=1000.0 * (H * (2 * N - 1) - top))
        for _ in range(substeps):
            pipeline.collide(state_0, contacts)
            solver.step(state_0, state_1, control, contacts, dt)
            state_0, state_1 = state_1, state_0
    run.check(solver)


if __name__ == "__main__":
    rec = Recorder()
    simulate(rec, 2, 24)  # 48 sweeps per frame
    simulate(rec, 4, 12)
    simulate(rec, 8, 6)
    simulate(rec, 16, 3)
    rec.save()

# SPDX-FileCopyrightText: Copyright (c) 2026 Skild AI and the Steel contributors
# SPDX-License-Identifier: Apache-2.0

"""Record Steel tutorial runs as replay JSON for the tutorials page, or print a summary.

Every tutorial imports this module. ``python NN_name.py`` runs the variants and prints
the final metric of each; ``--record out.json`` also writes body poses, shapes and metric
series that the page replays in 3D.
"""

import argparse
import base64
import json
import os
import subprocess
import sys
import time

import newton
import numpy as np
import warp as wp

from source_hash import source_sha256

_RENDERED_TYPES = {
    newton.GeoType.PLANE,
    newton.GeoType.SPHERE,
    newton.GeoType.CAPSULE,
    newton.GeoType.ELLIPSOID,
    newton.GeoType.CYLINDER,
    newton.GeoType.BOX,
    newton.GeoType.MESH,
    newton.GeoType.CONE,
    newton.GeoType.CONVEX_MESH,
}


class Recorder:
    """Collect the variants of one tutorial; ``fps`` is the replay frame rate."""

    def __init__(self, fps: int = 30):
        parser = argparse.ArgumentParser()
        parser.add_argument(
            "--record", metavar="OUT.json", help="write a replay file for the tutorials page"
        )
        parser.add_argument("--device", default=None, help="Warp device, for example cuda:0")
        self.args = parser.parse_args()
        if self.args.device:
            wp.set_device(self.args.device)
        self.fps = fps
        self.script = os.path.abspath(sys.argv[0])
        self.variants: list[Variant] = []

    def frames(self, seconds: float) -> int:
        """Number of replay frames in ``seconds``, including the first."""
        return int(round(seconds * self.fps)) + 1

    def variant(
        self,
        label: str,
        model: newton.Model,
        *,
        ghost: bool = False,
        slot: int | None = None,
        scene: str | None = None,
    ) -> "Variant":
        """Start one run; ``ghost`` overlays run ``slot``, ``scene`` groups runs for charts."""
        variant = Variant(label, model, self.fps, ghost, slot, scene)
        self.variants.append(variant)
        return variant

    def save(self) -> None:
        """Print a summary and, with ``--record``, write the replay file."""
        for variant in self.variants:
            last = variant.metrics[-1] if variant.metrics else {}
            flag = "  (rows dropped)" if variant.overflow else ""
            print(f"{variant.label:<48} {json.dumps(last)}  {variant.wall:.2f} s{flag}")
        if not self.args.record:
            return
        source_sha = source_sha256(self.script)
        doc = {
            "script": os.path.basename(self.script),
            "script_sha256": source_sha,
            "newton_commit": _newton_commit(),
            "newton_version": newton.__version__,
            "warp_version": wp.config.version,
            "gpu": wp.get_device().name,
            "fps": self.fps,
            "variants": [v.to_json() for v in self.variants],
        }
        with open(self.args.record, "w") as f:
            json.dump(doc, f, separators=(",", ":"))
        print(f"wrote {self.args.record}")


class Variant:
    """One recorded run: a pose per frame for every body, plus named metric values."""

    def __init__(self, label, model, fps, ghost, slot, scene):
        self.label, self.model, self.fps, self.ghost, self.slot = label, model, fps, ghost, slot
        self.scene = scene
        self.poses: list[np.ndarray] = []
        self.metrics: list[dict] = []
        self.awake: list[list[int]] = []
        self.particles: list[np.ndarray] = []
        self.overflow = False
        self.start = time.perf_counter()
        self.wall = 0.0

    def frame(self, state: newton.State, awake=None, particles=None, **metrics) -> None:
        """Record ``state.body_q``, optional awake flags, particle positions and metric values."""
        self.poses.append(state.body_q.numpy().astype(np.float32).copy())
        if particles is not None:
            self.particles.append(particles.numpy().astype(np.float32).copy())
        self.metrics.append({k: _round(v) for k, v in metrics.items()})
        if awake is not None:
            self.awake.append([int(x) for x in awake.numpy()])
        self.wall = time.perf_counter() - self.start

    def check(self, solver) -> None:
        """Note whether the solver dropped rows; call once after the run."""
        try:
            solver.check_constraint_capacity()
        except RuntimeError:
            self.overflow = True

    def to_json(self) -> dict:
        poses = (
            np.stack(self.poses)
            if self.poses
            else np.zeros((0, self.model.body_count, 7), np.float32)
        )
        return {
            "label": self.label,
            "fps": self.fps,
            "ghost": self.ghost,
            "slot": self.slot,
            "scene": self.scene,
            "bodies": int(self.model.body_count),
            "frames": int(poses.shape[0]),
            "poses": base64.b64encode(poses.astype(np.float32).tobytes()).decode(),
            "shapes": _shape_table(self.model),
            "metric": self.metrics,
            "awake": self.awake or None,
            "particles": self._particles_json(),
            "wall_s": round(self.wall, 3),
            "overflow": self.overflow,
        }

    def _particles_json(self):
        if not self.particles:
            return None
        frames = np.stack(self.particles)
        tris = self.model.tri_indices
        radius = self.model.particle_radius.numpy()
        return {
            "count": int(frames.shape[1]),
            "frames": base64.b64encode(frames.astype(np.float32).tobytes()).decode(),
            "radius": round(float(radius.mean()), 5) if radius.size else 0.0,
            "tris": [int(v) for v in tris.numpy().reshape(-1)]
            if tris is not None and tris.shape[0]
            else None,
        }


def _shape_table(model):
    types = model.shape_type.numpy()
    scales = model.shape_scale.numpy()
    xforms = model.shape_transform.numpy()
    bodies = model.shape_body.numpy()
    flags = model.shape_flags.numpy()
    shapes = []
    for i, t in enumerate(types):
        if int(t) not in _RENDERED_TYPES or not flags[i] & int(newton.ShapeFlags.VISIBLE):
            continue
        shape = {
            "b": int(bodies[i]),
            "t": int(t),
            "s": [round(float(v), 5) for v in scales[i]],
            "x": [round(float(v), 6) for v in xforms[i]],
        }
        if int(t) in (newton.GeoType.MESH, newton.GeoType.CONVEX_MESH):
            mesh = model.shape_source[i]
            shape["v"] = [round(float(v), 5) for v in np.asarray(mesh.vertices).reshape(-1)]
            shape["i"] = [int(v) for v in np.asarray(mesh.indices).reshape(-1)]
        shapes.append(shape)
    return shapes


def _round(value):
    value = float(value)
    return round(value, 5) if np.isfinite(value) else None


def _newton_commit():
    if os.environ.get("NEWTON_COMMIT"):
        return os.environ["NEWTON_COMMIT"]
    try:
        root = os.path.dirname(os.path.dirname(newton.__file__))
        return subprocess.check_output(["git", "-C", root, "rev-parse", "HEAD"], text=True).strip()
    except (OSError, subprocess.CalledProcessError):
        return None

Recorded with SolverSteel on Newton 1.9.0.dev0, Warp 1.19.0, NVIDIA RTX PRO 6000 Blackwell Server Edition. Replays read the state back every frame, so they are not a speed benchmark. Script · page text

Steel docs and tutorials are licensed under Apache-2.0. Third-party notices. "Skild", "Skild AI" and the Skild logo are trademarks of Skild AI and are not licensed under Apache-2.0.