silva_ifno Reproduction Dossier

tied residual Fourier operator for material response. This dossier connects the source mechanism to its SILVA implementation, compact evidence, replaceable components, and source-scale route. Existing tests and notebooks remain the executable authority.

Evidence boundary

The mechanism is compact-verified in the package suite. The final source-scale stage remains planned until the cited data, complete optimization budget, checkpoints, and evaluation protocol have actually run.

Identity and Sources

Field	Value
Domain	scientific operators
Task contract	coordinate, material, loading, and boundary fields -> displacement or damage field
Source relation	paper-adaptation
References	[61]
Repositories	https://arxiv.org/abs/2203.08205
Editable scale plan	experiments/reproduction/configs/silva_ifno.json

Governing Equation

The domain-level state contract is

\[ u^\star=\sigma\!\left(S_\theta(a)+\mathcal K_\theta[u^\star]+\mathcal C(u^\star)\right). \]

The implementation registry specializes it operationally as

h_(l+1)=h_l+dt sigma(W h_l+F_inv(R_theta F(h_l))+c)

Define the root residual

\[ R_\theta(z;x)=z-T_\theta(z;x). \]

At a regular equilibrium, differentiating \(R_\theta(z^\star;x)=0\) gives

\[ \frac{\partial z^\star}{\partial x} = \left(I-\frac{\partial T_\theta}{\partial z}\right)^{-1} \frac{\partial T_\theta}{\partial x}. \]

This identity explains why the forward residual, the conditioning derivative, and the adjoint linear solve must be diagnosed separately from the task metric.

What Is Preserved

• layer-independent Fourier kernel, pointwise channel map, bias, and residual increment
• input lift and shallow projection for displacement or damage fields
• shared-depth nonlocal integration and optional zero-increment root solve

What Can Be Replaced

Each item below is an explicit control rather than an undocumented modification:

• replace lift, tied integral increment, boundary projector, or material readout
• switch between finite shared-depth integration and the zero-increment equilibrium
• grid resolution
• Fourier modes
• state width
• shared depth

Constructor and Shape Contract

silva_ifno(in_channels: 'int', state_channels: 'int', out_channels: 'int', *, depth: 'int' = 16, step_size: 'float' = 0.1, mode: 'IFNOMode' = 'unrolled', modes_height: 'int' = 8, modes_width: 'int' = 8, lift: 'nn.Module | None' = None, increment: 'nn.Module | None' = None, readout: 'nn.Module | None' = None, boundary_projector: 'Callable[[Tensor, Tensor], Tensor] | None' = None, config: 'SolverConfig | None' = None)

The transition must preserve the declared equilibrium-state shape even when the encoder, branch operators, constraints, solver, and readout are replaced. Test the transition by itself before testing the complete root solve.

Progressive Experiment Ladder

1. Equation and tensor contract

Objective: Make the state, conditioning variables, operator, and readout explicit.

Procedure:

• Write and evaluate the family equation: h_(l+1)=h_l+dt sigma(W h_l+F_inv(R_theta F(h_l))+c)
• Declare every tensor axis, boundary, mask, graph, or physical unit.
• Check the transition output has exactly the same shape as the equilibrium state.

Acceptance checks:

• finite transition values
• shape-preserving state update
• all conditioning variables affect the intended branch

Evidence target: contract-verified.

2. Primitive mechanism reconstruction

Objective: Build the retained source mechanism from replaceable modules.

Procedure:

• layer-independent Fourier kernel, pointwise channel map, bias, and residual increment
• input lift and shallow projection for displacement or damage fields
• shared-depth nonlocal integration and optional zero-increment root solve

Acceptance checks:

• primitive modules expose trainable parameters and gradients
• mechanism-specific invariance or constraint check passes
• direct transition evaluation is deterministic under a fixed seed

Evidence target: compact-verified.

3. Public abstraction equivalence

Objective: Verify that the assembled family evaluates the same transition as its primitives.

Procedure:

• Copy the primitive module parameters into the public family constructor.
• Evaluate one transition and one complete equilibrium with identical inputs.
• Compare outputs, residuals, and parameter gradients with declared tolerances.

Acceptance checks:

• transition outputs agree
• equilibrium residual is finite and decreases
• primitive and assembled gradients agree on the compact case

Evidence target: compact-verified.

4. Compact real or analytic task

Objective: Exercise training, evaluation, diagnostics, and serialization end to end.

Procedure:

• make_ifno_material_dataset gives heterogeneous coefficient/loading fields and analytic displacement targets.

Acceptance checks:

• record relative displacement/damage L2 error
• record resolution transfer error
• record increment norm
• record memory
• checkpoint reload reproduces the recorded prediction
• result record contains data and configuration fingerprints

Evidence target: compact-verified.

5. Official-data subset

Objective: Validate the complete source data path before spending the full budget.

Procedure:

• Choose exactly one source material task and reproduce its simulator or DIC preprocessing, units, split, and normalization.
• Freeze preprocessing, split logic, metric code, and checkpoint format.
• Run a deterministic subset large enough to expose batching and memory failures.

Acceptance checks:

• dataset receipt and checksum are stored
• resume and evaluation paths reproduce the same subset metric
• memory and runtime are measured rather than estimated

Evidence target: subset-verified.

6. Source-scale reproduction or declared extension

Objective: Run the cited protocol, or change it explicitly as a SILVA extension.

Procedure:

• Choose exactly one source material task and reproduce its simulator or DIC preprocessing, units, split, and normalization.
• Map coordinates, material descriptors, loads, and boundary values to input channels and use the shared SILVAIFNO increment at the reported depth and modes.
• Evaluate displacement or damage error, depth stability, and resolution transfer before adding new constitutive regimes.
• source simulation or DIC fields, train/test split, grid, normalization, modes, and depth continuation
• task-specific hyperelastic, anisotropic, brittle-fracture, or experimental loading protocol
• relative field error, resolution transfer, depth stability, and source baselines

Acceptance checks:

• all required artifacts are archived
• reported metrics use the cited evaluation protocol
• every architectural or training deviation is listed
• claims match the achieved evidence status

Evidence target: planned.

Data, Access, and Storage

Candidate datasets:

• Darcy flow
• hyperelastic and anisotropic material simulations
• brittle-fracture fields
• digital image correlation measurements
• compact heterogeneous bars

Authoritative routes:

• https://arxiv.org/abs/2203.08205

Access obligations:

• The cited article describes simulation and experimental DIC tasks but does not identify one public benchmark archive.
• Use an openly released task when available, regenerate the stated constitutive simulations, or provide licensed DIC tensors; never substitute a different task silently.

Storage planning:

• Dense field bytes = samples * (input channels + output channels) * height * width * bytes per element.
• Add simulator outputs, normalization statistics, optimizer state, and checkpoints; use sharded tensors for multi-resolution fields.

Preprocessing record:

• record dataset version, split, normalization, shape convention, and seed
• preserve masks, graph indices, boundaries, or physical units required by the domain

Metrics and Current Evidence

Required metrics:

• relative displacement/damage L2 error
• resolution transfer error
• increment norm
• memory

The field compact suite ran this family on the same task and data as the other compatible families in that suite.

Measure	Recorded value
Initial loss	0.325763
Final loss	0.145279
Fractional loss reduction	0.554
Residual or final increment norm	8.72337
Iterations or tied increments	5
Parameter count	1021
Final gradient norm	0.378233

These values are compact-verified evidence. They establish finite optimization, gradient flow, and diagnostic reporting; they are not a publication ranking.

Executed notebook paths:

• notebooks/package_api/30_silva_ifno_materials.ipynb

Mechanism tests:

• tests/test_emerging_equilibria.py

Compact Defaults

Option	Value
tier	'smoke'
config	SolverConfig(solver='anderson', max_iter=12, tol=1e-05, alpha=1.0, history=3, ridge=0.0001, beta=1.0, stop_mode='relative', relative_eps=1e-08, anderson_batch_dims=1, track_residuals=True, reengage=True, backward_mode='implicit', backward_solver='gmres', backward_max_iter=20, backward_tol=1e-05, backward_stop_mode='relative', backward_relative_eps=1e-08, phantom_steps=1, phantom_tau=1.0, neumann_terms=5, shine_refine_steps=0, indexing=(), return_best=True)

Full Defaults

Option	Value
tier	'full'
config	SolverConfig(solver='anderson', max_iter=60, tol=1e-05, alpha=1.0, history=6, ridge=0.0001, beta=1.0, stop_mode='relative', relative_eps=1e-08, anderson_batch_dims=1, track_residuals=True, reengage=True, backward_mode='implicit', backward_solver='gmres', backward_max_iter=80, backward_tol=1e-05, backward_stop_mode='relative', backward_relative_eps=1e-08, phantom_steps=1, phantom_tau=1.0, neumann_terms=5, shine_refine_steps=0, indexing=(), return_best=True)

Defaults establish a starting budget; the cited source protocol takes precedence whenever reproduction is the claim.

Source-Scale Checklist

• Choose exactly one source material task and reproduce its simulator or DIC preprocessing, units, split, and normalization.
• Map coordinates, material descriptors, loads, and boundary values to input channels and use the shared SILVAIFNO increment at the reported depth and modes.
• Evaluate displacement or damage error, depth stability, and resolution transfer before adding new constitutive regimes.

Benchmark-specific requirements:

• source simulation or DIC fields, train/test split, grid, normalization, modes, and depth continuation
• task-specific hyperelastic, anisotropic, brittle-fracture, or experimental loading protocol
• relative field error, resolution transfer, depth stability, and source baselines

Required archived artifacts:

• machine-readable model and solver configuration
• dataset receipt with source revision, split, license, and checksum
• preprocessing and normalization record
• seeded training and evaluation log
• checkpoint and optimizer-resume state for trained experiments
• task metrics and equilibrium diagnostics in a machine-readable result
• runtime, peak-memory, device, precision, and dependency record
• declared deviations from the cited protocol

Reporting Rule

Report the achieved evidence status, not the intended one. A compact or subset run may validate the implementation and data path, but only a completed cited protocol supports a source-scale reproduction statement. Modified operators are valuable SILVA extensions when every deviation is named and measured.

Where to Go Next

Question	Page
Where are all family dossiers?	Family Dossier Index
How is a custom family assembled?	Advanced Extension Handbook
How are experiment stages represented in the API?	Research-Depth API
Which lab inspects every dossier?	Family Dossier Lab