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# Implicit MPM

Newton's implicit Material Point Method (MPM) solver models particle materials
such as sand, snow, and other granular media. Isaac Lab integrates it as a
Newton solver configuration, a particle asset type, and an optional coupling
with rigid-body solvers. MPM support and rigid--MPM coupling are experimental.

This page explains how the integration works. For runnable scenes, see
`Examples and tasks`\_. For resolution, convergence, and material studies, and
the nearly rigid MPM limit, see [MPM Solver](/source/how-to/solver_tuning_mpm).

## How MPM fits into the Newton backend

Selecting `~isaaclab_newton.physics.MPMSolverCfg` as the `solver_cfg` of
`~isaaclab_newton.physics.NewtonCfg` installs
`~isaaclab_newton.physics.NewtonMPMManager`, a specialization of the
Newton manager that constructs Newton's `SolverImplicitMPM`. The solver
represents material as particles and solves its rheology implicitly on a
background voxel grid. The MPM manager configures the Newton manager as
follows:

* It advances particles in place on a single Newton state rather than double
  buffering state.
* It resolves collider contact inside the implicit solve. It does not use
  Newton's collision pipeline.
* It treats rigid geometry as colliders. It is not a rigid-body or
  articulation dynamics solver, and it does not accept external rigid-body
  forces. Kinematic bodies are given zero mass before the model is finalized,
  and convex meshes are passed to the solver as triangle meshes.

## Coupling with rigid bodies

On its own, the MPM solver advances only particles. Rigid bodies act as
colliders whose motion comes from elsewhere, such as kinematic pose writes, and
the material does not push back on them.

Two-way interaction uses the experimental coupler in
`isaaclab_contrib.coupling`. A
`~isaaclab_contrib.coupling.CouplerProxyCfg` partitions one Newton model
into named entries:

* a rigid entry, for example MJWarp, that owns the robot or object bodies;
* an MPM entry that owns the particles and must set `in_place=True`; and
* a proxy mapping that exposes selected rigid bodies as colliders in the MPM
  entry and feeds the resulting impulses back to the rigid entry.

The `mpm-two-way-coupling` example, the `snowball-smash` demo, and the
Franka Pour task all use this pattern. See [Coupled Solvers](/source/concepts/coupled_solvers) for
proxy and ADMM coupling, exchange modes, and tuning.

## Data model

### Configuration and USD

An MPM material is a scene asset. `~isaaclab_newton.assets.MPMObjectCfg`
extends the deformable-object configuration and takes a particle spawner:

* `~isaaclab_newton.sim.spawners.mpm.MPMGridCfg` fills an axis-aligned local box with
  a particle lattice whose resolution follows `voxel_size` and
  `particles_per_cell`.
* `~isaaclab_newton.sim.spawners.mpm.MPMPointsCfg` places particles at explicit
  local positions, with optional velocities, masses, and radii.

Both spawners author schema-valid `UsdGeom.Points` simulation geometry. Grid
configurations still generate the lattice in Isaac Lab before authoring
explicit points, widths, velocities, and masses. Per-particle material values
come from `~isaaclab_newton.sim.spawners.mpm.MPMParticleMaterialCfg` and are authored
with `NewtonMPMMaterialAPI`. Damping \[s] is authored as
`damping * young_modulus` \[Pa·s]. Solver-wide settings, including
`critical_fraction`, live on `MPMSolverCfg`; the schema-representable ones
are authored with `NewtonMPMSceneAPI` on the physics scene prim.

MPM objects are cloned through Newton replication. Grid jitter is generated
once in asset-local coordinates with a fixed seed, so USD clones share the same
local particle distribution. Use reset events or domain randomization when each
environment needs an independent distribution.

Use the same voxel size for the solver grid and particle generator. Add the
generated object to an `~isaaclab.scene.InteractiveSceneCfg` like any
other declarative asset:

```python
import isaaclab.sim as sim_utils
from isaaclab_newton.assets import MPMObjectCfg
from isaaclab_newton.physics import MPMSolverCfg, NewtonCfg
from isaaclab_newton.sim.spawners.mpm import MPMGridCfg

voxel_size = 0.02

sim_cfg = sim_utils.SimulationCfg(
    dt=1.0 / 100.0,
    physics=NewtonCfg(
        solver_cfg=MPMSolverCfg(
            voxel_size=voxel_size,
            max_iterations=100,
            tolerance=1.0e-4,
        ),
        num_substeps=2,
    ),
)

media = MPMObjectCfg(
    prim_path="{ENV_REGEX_NS}/Media",
    spawn=MPMGridCfg(
        lower=(-0.1, -0.1, 0.0),
        upper=(0.1, 0.1, 0.2),
        voxel_size=voxel_size,
        particles_per_cell=2.0,
        particle_placement="cell_center",
    ),
)
```

### Runtime asset

`~isaaclab_newton.assets.MPMObject` implements Isaac Lab's
deformable-object interface, so scene reset, update, and state workflows treat
it like other deformables. Each environment instance holds the same number of
particles, reported by `particles_per_object`.
`~isaaclab_newton.assets.MPMObjectData` exposes particle positions,
velocities, and combined state in the simulation world frame through
`particle_pos_w`, `particle_vel_w`, and `particle_state_w`. The
deformable `nodal_*` properties are aliases of these. `root_pos_w` and
`root_vel_w` are per-instance means over the particles. Position, velocity,
and state writers apply immediately. Deformable kinematic targets are not
supported.

## Configuration reference

The generated `~isaaclab_newton.physics.MPMSolverCfg` reference is the
source of truth for fields and defaults. The fields group as follows:

| Group                   | Fields                                                                                                     | Effect                                                                                                           |
| ----------------------- | ---------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------- |
| Resolution              | `voxel_size`, and `particles_per_cell` on the spawner                                                      | Background-grid and particle resolution, which set accuracy, active cells, and memory use.                       |
| Grid storage            | `grid_type`, `grid_padding`, `max_active_cell_count`, the `max_*_node_count` limits, and `separate_worlds` | Sparse, dense, or fixed grid allocation, reserved capacity, and whether each world uses its own local grid.      |
| Rheology solve          | `max_iterations`, `tolerance`, `solver`, and `warmstart_mode`                                              | Iteration cap, convergence tolerance, the solver or warm-start sequence, and warm-start source.                  |
| Discretization          | `transfer_scheme`, `integration_scheme`, `velocity_basis`, `strain_basis`, and `collider_basis`            | Particle-grid transfer, shape-function support, and the basis functions for each field.                          |
| Material and background | `critical_fraction` and `air_drag`                                                                         | Solver-global yield-surface collapse and numerical drag for empty space.                                         |
| Colliders               | `collider_velocity_mode`, `collider_normal_from_sdf_gradient`, and `project_outside_colliders`             | Collider velocity and normal computation, and an optional post-substep projection of particles out of colliders. |

The implicit solve already resolves collider contact. `project_outside_colliders`
adds a hard post-step correction for particles that remain inside colliders;
use it only when that geometric correction is intentional, and not as a
substitute for valid initial states, collision geometry, or a stable timestep.

### CUDA graph capture

CUDA graph capture of the MPM step is available only when the grid has
capture-stable storage:

* a `"fixed"` grid with a positive `max_active_cell_count`; or
* a `"sparse"` grid with a positive `max_active_cell_count`,
  `grid_padding=0`, and the `"Q1"` velocity basis. The strain basis must
  start with `"pic"` or be one of `"P0"`, `"P1d"`, `"Q1d"`, or
  `"Q1"`. The collider basis must start with `"pic"` or be one of
  `"Q1"`, `"S2"`, or `"S3"`.

Dense grids and unbounded grids run without capture.

### Resets

With the MPM solver alone, automatic asset resets leave solver history
untouched, because worlds that share one grid cannot have their history reset
individually. Under a coupler, automatic resets go through the coupled
solver's reset, which passes the per-world reset mask to every entry, including
the MPM entry. Tasks that need an exact history reset, such as Franka Pour, use
independent MPM worlds (`separate_worlds=True`) and call
`~isaaclab_newton.physics.NewtonMPMManager.reset_solver_state` after
writing their complete state. In a coupled run, this also resets the coupled
solver's history.

Try the [interactive MPM demo](https://isaac-sim.github.io/IsaacLab/release/3.0.0/source/setup/interactive_demos.html) to compare material
references and adjust stiffness, cohesion, friction, and hardening on a
repeatable particle drop.

## Rendering a particle surface

MPM simulation state remains a set of particles. Surface reconstruction is an
optional visualization pass: it does not change particle motion, collisions, or
material behavior. Run the teapot demo to compare the available modes:

```bash
# Reconstructed surface
uv run isaaclab demo teapot-fill \
  --visualizer newton_gl --fluid_render_mode surface
# Surface and source particles together
uv run isaaclab demo teapot-fill \
  --visualizer newton_gl --fluid_render_mode both
# Path-traced translucent surface
uv run --extra ovrtx isaaclab demo teapot-fill \
  --visualizer newton_rtx --fluid_render_mode surface
```

The teapot demo defaults to the reconstructed surface. Select `particles` or
`both` to inspect the source MPM state in Newton GL or Newton RTX.

Surface rendering is available in the Newton GL and Newton RTX visualizers.
The Kit visualizer continues to render the MPM particles directly.

[Watch the embedded video](https://download.isaacsim.omniverse.nvidia.com/isaaclab/videos/mpm_surface_reconstruction.mp4)
This recording demonstrates rendering appearance, not a different
constitutive model.

The teapot demo configures `newton.geometry.ParticleSurface` after
`sim.reset()` and updates the mesh before `sim.render()`. Its renderer
captures extraction on CUDA when enabled and stages the dynamic mesh inside
the viewer's frame lifecycle.

Tune reconstruction independently from the simulation:

* `voxel_size` controls surface detail and memory use. It can be smaller than
  the MPM solver voxel size.
* `kernel_radius` controls how far each particle contributes to the surface.
  Start near three times the particle spacing.
* `max_grid_cells` provides fixed-capacity storage for CUDA graph capture.
  Increase it if the reconstructed domain outgrows the reserved grid.
* Anisotropic kernels preserve sheets and stretched fluid features better, but
  cost more than isotropic kernels.

To render a surface in your own scene, pass the configured
`newton.geometry.ParticleSurface` to `ParticleSurfaceRenderer` after
`sim.reset()`. Call `update()` before `sim.render()` to extract and stage
the current mesh. The renderer handles CUDA graph capture, empty surfaces,
inactive particles, and dynamic topology:

```python
class ParticleSurfaceRenderer:
    """Extract one particle surface and stage its latest mesh for Newton viewers.

    Configure a Newton `ParticleSurface` and construct this renderer after
    resetting the simulation. Call `update` before rendering each frame
    to reconstruct the surface from the current particle state.
    """

    def __init__(
        self,
        visualizers: Iterable[BaseVisualizer],
        surface: ParticleSurface,
        *,
        path: str,
        color: tuple[float, float, float],
        opacity: float,
        roughness: float = 0.1,
        use_cuda_graph: bool = True,
    ) -> None:
        """Allocate reusable extraction storage and optionally capture its CUDA graph.

        Args:
            visualizers: Active visualizers; non-Newton viewers are ignored.
            surface: Configured Newton surface extractor.
            path: Viewer mesh path.
            color: Surface RGB color in [0, 1].
            opacity: Surface opacity in [0, 1].
            roughness: Surface roughness in [0, 1].
            use_cuda_graph: Capture extraction on CUDA when enabled.

        Raises:
            RuntimeError: If no Newton GL or RTX visualizer is active.
        """
        self._visualizers = tuple(
            visualizer
            for visualizer in visualizers
            if isinstance(visualizer, (NewtonGLVisualizer, NewtonRTXVisualizer))
        )
        if not self._visualizers:
            raise RuntimeError("Particle surface rendering requires a Newton GL or RTX visualizer.")

        self._model = NewtonManager.get_model()
        self._state = NewtonManager.get_state_0()
        self._surface = surface
        self._path = path
        self._color = color
        self._opacity = opacity
        self._roughness = roughness
        self._empty_points = wp.empty(0, dtype=wp.vec3, device=self._model.device)
        self._empty_indices = wp.empty(0, dtype=wp.int32, device=self._model.device)
        self._empty_normals = wp.empty(0, dtype=wp.vec3, device=self._model.device)
        self._surface_mesh = None
        self._surface_graph = None
        if use_cuda_graph and self._model.device.is_cuda:
            self._surface_mesh = self._extract_surface()
            with wp.ScopedCapture(device=self._model.device) as capture:
                self._surface_mesh = self._extract_surface()
            self._surface_graph = capture.graph

    def update(self) -> int:
        """Stage the latest surface mesh and return its triangle count."""
        if self._surface_graph is None:
            self._surface_mesh = self._extract_surface()
        else:
            wp.capture_launch(self._surface_graph)

        vertices, indices, normals = self._surface_mesh.to_arrays()
        hidden = vertices is None
        triangle_count = 0 if hidden else indices.shape[0] // 3
        if hidden:
            vertices = self._empty_points
            indices = self._empty_indices
            normals = self._empty_normals

        for visualizer in self._visualizers:
            visualizer.log_mesh(
                self._path,
                vertices,
                indices,
                normals=normals,
                hidden=hidden,
                backface_culling=False,
                color=self._color,
                roughness=self._roughness,
                metallic=0.0,
                dynamic=True,
                opacity=self._opacity,
            )
        return triangle_count

    def _extract_surface(self):
        """Extract the surface from the current Newton particle state."""
        return self._surface.extract(
            self._state.particle_q,
            self._model.particle_radius,
            particle_flags=self._model.particle_flags,
            particle_world=self._model.particle_world if self._surface.world_count > 1 else None,
        )
```

## Examples and tasks

These examples and demos introduce MPM construction and interaction. They
default to Newton GL for interactive viewing. The launcher uses `cuda:0` by
default. Pass `--device cuda:N` to select a different GPU.

[Watch the embedded video](https://download.isaacsim.omniverse.nvidia.com/isaaclab/videos/mpm_granular.mp4)

```bash
uv run isaaclab example mpm-granular
```

[Watch the embedded video](https://download.isaacsim.omniverse.nvidia.com/isaaclab/videos/mpm_two_way.mp4)

```bash
uv run isaaclab example mpm-two-way-coupling
```

[Watch the embedded video](https://download.isaacsim.omniverse.nvidia.com/isaaclab/videos/mpm_snowball.mp4)

```bash
uv run isaaclab demo snowball-smash
```

[Watch the embedded video](https://download.isaacsim.omniverse.nvidia.com/isaaclab/videos/mpm_teapot_particles.mp4)

```bash
uv run isaaclab demo teapot-fill --fluid_render_mode particles
```

### Franka Pour

The `IsaacContrib-Franka-Pour` task restores episodes from a reset artifact
containing the connected 14-phase reset distribution. The canonical 20,000-row
artifact downloads from the standard Isaac Lab asset root on first use, so
training needs no artifact setup:

```bash
uv run isaaclab train --rl_library rsl_rl --task IsaacContrib-Franka-Pour \
  --num_envs 2048
```

The checked-in generator remains the executable reference for reproducing or
customizing the distribution. It takes about two minutes on an L40S-class GPU
and writes a local artifact that can be selected explicitly:

```bash
uv run python scripts/tools/generate_franka_pour_reset_dataset.py
uv run isaaclab train --rl_library rsl_rl --task IsaacContrib-Franka-Pour \
  --num_envs 2048 \
  env.reset_dataset_path=datasets/franka_pour/reset_dataset.pt
```

The task validates the payload's stored content digest automatically. Setting
`ISAACSIM_ASSET_ROOT` redirects the canonical artifact to a compatible local
or self-hosted asset tree. Digest pinning remains available for custom
reproducible experiments.

The source uses a non-colliding analytic fill volume whose height is controlled
by `env.source_fill_level` in `(0, 1]`. The default `0.70` fills roughly
70% of the cup height; the particle count follows the requested fill level
while voxel size and particle spacing stay fixed.
`env.pour_target_frac` independently controls the fraction of that live
payload that must reach the receiver.

Play a checkpoint in Kit with the canonical task configuration; no external
callback or particle override is required:

```bash
uv run --extra isaacsim isaaclab play --rl_library rsl_rl --task IsaacContrib-Franka-Pour \
  --checkpoint /path/to/model.pt --num_envs 1 --visualizer kit
```

## Limitations

* Coupled MPM entries must step in place and do not support
  `project_outside_colliders`.