Family Selection API

silva_networks.families is the high-level factory surface for choosing a SILVA, DEQ, scientific operator, flow, diffusion, or optimization family by name. Use it when a notebook, experiment config, or teaching example should select the model family without importing every concrete class directly.

The named choices connect to DEQ [4], MDEQ [5], Neural ODEs [7], differentiable optimization [8] [9], and optical-flow equilibria [22] [23]. Scientific operator families connect to FNO [31] and neural operators [32]. Recent SILVA families also connect to Fourier equilibria [43], physics-guided graph equilibria [44], homotopy continuation [46], and distributional equilibria [45]. The registry also exposes a learned equilibrium solver [87] and a quantum-circuit equilibrium [90]. JFB [88] and SHINE [89] remain solver-level backward choices that can be paired with compatible families.

The factory normalizes hyphenated names and compatibility aliases before dispatching to the package-native constructors. It does not choose dataset splits, optimizer schedules, checkpoint recipes, or paper-specific metric claims.

Every equilibrium family still defines

\[ z^\star=f_\theta(z^\star,x), \]

but the state may be a matrix, image field, multiscale tuple, flow pair, diffusion trajectory, sampled physical field, or constrained optimization variable. It may also be a continuous-flow endpoint or an empirical measure represented by variable-size particles.

Canonical Families

Family	Constructor target
silva_layer	generalized SILVA layer
silva_graph	stacked graph SILVA network
silva_graph_preset	reference graph SILVA preset
silva_cortex	single cortex-style equilibrium point
silva_cortex_network	linked SILVA points with independent internal architectures
silva_image_cortex	convolutional retina plus linked cortex points
compact_deq	affine-tanh DEQ reduction
message_passing_deq	message-passing DEQ reduction
mdeq	compact multiscale DEQ bridge block
multiscale_vision_deq	full multiresolution MDEQ-style vision core
sequence_deq	sequence DEQ with relative attention
implicit_graph	IGNN-style graph equilibrium
implicit_neural_representation	coordinate-based implicit representation
diffusion_equilibrium	joint DDIM trajectory equilibrium
scientific_operator	selectable source-to-field SILVA operator
fourier_operator_equilibrium	Fourier neural operator inside a SILVA equilibrium
implicit_time_step	backward-Euler ODE or PDE step
silva_deq_flow	SILVA-named optical-flow equilibrium
raft_deq_flow	coupled RAFT/DEQ-Flow architecture
quadratic_optimization	unconstrained quadratic optimization layer
silva_projected_qp	projected quadratic-program layer
silva_fno_deq	input-injected Fourier block inside a SILVA equilibrium
silva_physics_graph_deq	SILVA graph equilibrium with reaction, diffusion, and directed transport
silva_homotopy_equilibrium	conditioned SILVA residual flow with a fixed-point stationary state
silva_distributional_deq	empirical-measure SILVA equilibrium using discrepancy descent
silva_monotone_graph_equilibrium	monotone forward-backward graph equilibrium
silva_generative_equilibrium_transformer	one-time-injected token equilibrium
silva_poisson_mirror_equilibrium	positive Poisson mirror-descent equilibrium
silva_physics_informed_equilibrium	physics-informed ODE solution equilibrium
silva_implicit_dae_step	implicit Runge-Kutta DAE root layer
silva_consistency_deq	trajectory-consistency refiner for few-step equilibrium inference
silva_psi_gnn	mixed-boundary Poisson graph equilibrium
silva_ifno	tied implicit Fourier material-response operator
silva_snarf	differentiable multi-start forward-skinning roots
silva_mesh_inference	typed distributed mesh relaxation
silva_physics_guided_diffusion_pde	reverse diffusion with PDE-energy guidance and boundary projection
silva_therino	thermodynamically informed physical-state equilibrium
silva_fixed_point_diffusion	timestep-conditioned fixed-point denoiser
silva_monotone_operator_equilibrium	strongly monotone equilibrium with selectable operator splitting
silva_positive_concave_equilibrium	positive-concave dense or convolutional equilibrium
silva_non_euclidean_equilibrium	weighted-infinity well-posed equilibrium
silva_efficient_infinite_graph	spectral or iterative infinite-depth graph equilibrium
silva_multiscale_graph_implicit	graph-power equilibria with nodewise scale attention
silva_delta_equilibrium	thresholded cached equilibrium updates
silva_hyper_deq	learned initializer and Anderson controller for a replaceable transition
silva_quantum_deq	measured quantum-circuit equilibrium with direct and implicit routes

Minimal Use

from silva_networks import SolverConfig, silva_equilibrium_model

model = silva_equilibrium_model(
    "silva_graph_preset",
    in_dim=16,
    hidden_dim=32,
    out_dim=3,
    num_layers=2,
    task="graph",
    solver_configs=SolverConfig(solver="anderson", max_iter=20),
)

Use return_result=True when the selected family supports structured results, then inspect the state shape, solver residual, convergence flag, and gradient mode before comparing task metrics. Constructor signatures remain family specific; silva_family_description(name) summarizes the intended state and use before dispatch.

Full reductions and source links are in Selecting Model Families.

canonical_silva_family resolves aliases without constructing a model. build_scaled_silva then adds scalable numerical defaults while leaving all task dimensions and modules explicit. See Full-Scale SILVA for the all-family data, benchmark, and extension matrix.

For heterogeneous SILVA equilibrium points:

model = silva_equilibrium_model(
    "silva_cortex_network",
    layers=[spatial_point, vector_point],
    links=[spatial_to_vector],
    head=classification_head,
)

API

Factory helpers for selecting SILVA and DEQ-style model families.

available_silva_families

available_silva_families()

Return supported family names for silva_equilibrium_model.

Source code in src/silva_networks/families.py

def available_silva_families() -> tuple[str, ...]:
    """Return supported family names for `silva_equilibrium_model`."""

    return tuple(_FAMILY_DESCRIPTIONS)

canonical_silva_family

canonical_silva_family(family)

Resolve a family name or documented alias to its canonical SILVA key.

Source code in src/silva_networks/families.py

def canonical_silva_family(family: str) -> str:
    """Resolve a family name or documented alias to its canonical SILVA key."""

    key = _normalize_family(family)
    if key not in _FAMILY_DESCRIPTIONS:
        raise KeyError(_unknown_family_message(family))
    return key

silva_equilibrium_model

silva_equilibrium_model(family, **kwargs)

Create a SILVA, DEQ, optimization, or flow model by family name.

Parameters:

Name	Type	Description	Default
family	SILVAFamily | str	One of available_silva_families().	required
kwargs	Any	Keyword arguments forwarded to the selected constructor.	{}

Returns:

Type	Description
Any	A PyTorch module from the requested family.

Source code in src/silva_networks/families.py

def silva_equilibrium_model(family: SILVAFamily | str, **kwargs: Any) -> Any:
    """Create a SILVA, DEQ, optimization, or flow model by family name.

    Args:
        family: One of `available_silva_families()`.
        kwargs: Keyword arguments forwarded to the selected constructor.

    Returns:
        A PyTorch module from the requested family.
    """

    return silva_family_constructor(family)(**kwargs)

silva_family_constructor

silva_family_constructor(family)

Return the public constructor behind a canonical family or alias.

Source code in src/silva_networks/families.py

def silva_family_constructor(family: str) -> Callable[..., Any]:
    """Return the public constructor behind a canonical family or alias."""

    return _FAMILY_CONSTRUCTORS[canonical_silva_family(family)]

silva_family_description

silva_family_description(family)

Return a short description for a selectable model family.

Source code in src/silva_networks/families.py

def silva_family_description(family: str) -> str:
    """Return a short description for a selectable model family."""

    key = _normalize_family(family)
    try:
        return _FAMILY_DESCRIPTIONS[key]
    except KeyError as exc:
        raise KeyError(_unknown_family_message(family)) from exc

silva_family_signature

silva_family_signature(family)

Return the complete inspectable constructor signature for a family.

Source code in src/silva_networks/families.py

def silva_family_signature(family: str) -> Signature:
    """Return the complete inspectable constructor signature for a family."""

    return signature(silva_family_constructor(family))

Where to Go Next

Question	Page
How should I choose among these families?	Selecting Model Families
Which classes implement ODE, PDE, and learned operators?	Scientific Operators API
Which classes implement the recent operator, graph, flow, and measure families?	Recent Equilibrium API
Which classes implement monotone, transformer, mirror, physics, and DAE mechanisms?	Advanced Equilibria API