silva_therino Reproduction Dossier

thermodynamically informed solution-space equilibrium operator. 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	stiffness tensor field and prescribed bulk strain -> local strain/stress fields
Source relation	paper-adaptation
References	[73]
Repositories	https://arxiv.org/abs/2411.06529
Editable scale plan	experiments/reproduction/configs/silva_therino.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

epsilon_star=ProjectMacro(U_theta([epsilon_star, C:epsilon_star, 0.5 epsilon_star:C:epsilon_star, epsilon_bar]))

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

• fixed-point iteration in the physical strain field rather than an abstract latent state
• thermodynamic encoding through strain, stress, elastic energy density, and macroscopic loading
• shared neural-operator update, macroscopic-strain projection, and strain/stress/energy supervision

What Can Be Replaced

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

• replace the constitutive encoder, solution-space update, or bulk projector
• supply nonlinear, anisotropic, dissipative, or weak-form material laws
• voxel resolution
• Fourier modes
• thermodynamic channels
• root-solver budget

Constructor and Shape Contract

silva_therino(strain_components: 'int' = 3, *, hidden_channels: 'int' = 24, modes_height: 'int' = 8, modes_width: 'int' = 8, encoder: 'SILVAThermodynamicEncoder | None' = None, update: 'nn.Module | None' = None, enforce_macro_strain: 'bool' = True, 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: epsilon_star=ProjectMacro(U_theta([epsilon_star, C:epsilon_star, 0.5 epsilon_star:C:epsilon_star, epsilon_bar]))
• 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:

• fixed-point iteration in the physical strain field rather than an abstract latent state
• thermodynamic encoding through strain, stress, elastic energy density, and macroscopic loading
• shared neural-operator update, macroscopic-strain projection, and strain/stress/energy supervision

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_therino_elastic_dataset gives periodic diagonal-elastic cells with exact strain, stress, energy, and macroscopic loading.

Acceptance checks:

• record strain localization error
• record stress and elastic-energy error
• record homogenized stiffness error
• record out-of-distribution contrast error
• 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:

• Reproduce the source periodic microstructure generator, constituent laws, finite-element labels, load cases, split, and normalization before fitting the operator.
• 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:

• Reproduce the source periodic microstructure generator, constituent laws, finite-element labels, load cases, split, and normalization before fitting the operator.
• Configure the physical-state transition with the reported three-dimensional Fourier update, macroscopic-strain projection, and Anderson solve.
• Train strain, stress, and energy objectives and report localization, homogenized response, contrast transfer, iterations, and memory against the declared baselines.
• source periodic microstructure generator, finite-element labels, stiffness contrast, loading cases, and normalization
• three-dimensional Fourier operator width/modes, Anderson settings, optimizer, schedule, and random seeds
• strain, stress, energy, homogenized response, out-of-distribution contrast, and iteration metrics

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:

• periodic two-phase linear-elastic microstructures
• nonlinear constitutive localization fields
• compact exact diagonal-elasticity cells

Authoritative routes:

• https://arxiv.org/abs/2411.06529
• https://doi.org/10.1016/j.cma.2025.117939

Access obligations:

• The source experiments use procedurally generated periodic microstructures and numerical mechanics labels rather than one packaged benchmark archive.
• Record geometry generation, constituent stiffness tensors, periodic boundary conditions, load cases, finite-element discretization, and every split seed.

Storage planning:

• Dense mechanics bytes = samples * voxels * (material + strain + stress channels) * bytes per element.
• Keep microstructures, stiffness tensors, finite-element strain/stress labels, normalization, and checkpoints in separate shards; three-dimensional labels usually dominate storage.

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:

• strain localization error
• stress and elastic-energy error
• homogenized stiffness error
• out-of-distribution contrast error
• root iterations and residual

This family is verified through its listed mechanism tests and executed notebook. It is not included in a same-task comparison when another family does not share its input, state, output, and loss contract. The absence of a comparison row is therefore a scope decision, not missing implementation evidence.

Executed notebook paths:

• notebooks/package_api/34_silva_therino_mechanics.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

• Reproduce the source periodic microstructure generator, constituent laws, finite-element labels, load cases, split, and normalization before fitting the operator.
• Configure the physical-state transition with the reported three-dimensional Fourier update, macroscopic-strain projection, and Anderson solve.
• Train strain, stress, and energy objectives and report localization, homogenized response, contrast transfer, iterations, and memory against the declared baselines.

Benchmark-specific requirements:

• source periodic microstructure generator, finite-element labels, stiffness contrast, loading cases, and normalization
• three-dimensional Fourier operator width/modes, Anderson settings, optimizer, schedule, and random seeds
• strain, stress, energy, homogenized response, out-of-distribution contrast, and iteration metrics

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