HaomingLuo/AgentFEM-Material-Loading-Memory

AgentFEM Material Loading Memory

An open, reproducible research dataset for path-dependent material modeling, neural constitutive surrogates and finite-element deployment tests. The repository contains six staged, explicitly separated releases.

Start here

Goal	Recommended entry
Understand the current dataset	This page and the sealed-test data card
Train or benchmark a constitutive model	DENIM start guide
Reproduce the multiaxial baseline study	Multiaxial v2 guide
Reproduce the original loading-memory release	Original v1 guide
Use the latest DENIM checkpoint	AgentFEM-DENIM

Current trajectory accounting:

Role	Trajectories	Interpretation
Training	1,808	Optimization data for the current v2.2 model
Validation	503	Checkpoint selection and anti-forgetting guardrails
Development test	1,349	Frozen historical benchmarks; later aggregate results informed subsequent model design
Prospective sealed test	128	Published after model freeze; never used for training or selection
Total	3,788	Complete histories, not exchangeable independent experiments

What is a loading history, and why does it matter?

A loading history is the ordered sequence of deformation applied to a material. For an elastic spring, only the present deformation matters. For an elastoplastic metal, the route matters as well: loading, unloading, reversing, rotating the loading direction or adding a mean strain changes the material's internal state. Two specimens can therefore arrive at the same current strain with different stresses because they arrived there by different routes.

This dataset varies the history deliberately rather than merely sampling more points on one curve:

History variation	Question being tested
Proportional and reversed cycles	Can the model reproduce yielding, unloading and the Bauschinger effect?
Non-proportional and rotating multiaxial paths	Can it track changing stress directions and coupled material memory?
Nested minor loops and non-periodic sequences	Can it remember partial unload/reload events instead of resetting its state?
Amplitude and mean shifts	Can it extrapolate when the load becomes larger or biased to one side?
100--200-cycle histories	Does a small state error accumulate into long-term drift?
Matched coarse/fine discretizations	Is the prediction tied to the physical path or to a particular step size?
Material-parameter variation	Can one conditioned model represent a family of materials rather than one fixed curve?

The scientific object is therefore not an isolated stress value. It is the mapping from material parameters + ordered loading history + current internal state to the next stress and state. Randomly shuffling time steps or mixing related resolution groups across data roles would destroy this meaning.

Recommended evaluation metrics

Report absolute stress RMSE in MPa together with a scale-free metric. MPa is needed for engineering interpretation; a relative metric makes results easier to compare across cohorts and stress levels.

• Relative L2 error (%) = ||stress_pred - stress_ref||2 / ||stress_ref||2 × 100. This is the preferred scale-free trajectory/state metric for signed cyclic stresses.
• Yield-normalized RMSE (%) = RMSE / reference_yield_stress × 100. This answers how large the average error is relative to the 280 MPa reference yield stress used by the sealed protocol.
• R2 is useful as a supplementary global fit indicator, but should not replace an engineering error in MPa.
• MAPE is not recommended because cyclic stress repeatedly crosses zero; division by values near zero can make an accurate prediction look arbitrarily poor.

For the sealed reference data, the stress RMS scales are 359.540 MPa for global path OOD, 91.411 MPa for 150/200-cycle histories, 371.687 MPa for amplitude and mean shifts, and 206.814 MPa over all 128 trajectories. These denominators are published so every model can be compared under the same convention. Model scores remain in the model repository to keep this page focused on the data and evaluation contract.

Releases

• T2 v1: 1,008 proportional cyclic J2 trajectories for loading-memory baselines and forward/reversed ordering controls.
• T2 multiaxial v2: 1,024 independently generated J2 and Chaboche trajectories in the complete five-dimensional deviatoric strain space, with ID, path-OOD and parameter-OOD splits.
• T2 DENIM closure v1: 128 multiaxial trajectories from a deliberately richer three-memory, tabulated-hardening reference material. The published two-memory DENIM model must learn the missing internal-variable closure.
• T2 DENIM boundary v1: 500 additional trajectories for training-density, path, amplitude, long-history and integration-resolution boundaries.
• T2 DENIM capability v4: 1,000 trajectories for 100-cycle horizons, full six-component loading, AgentFEM-derived structural paths and paired discretization/noisy-observation tests.
• T2 DENIM sealed test v1: 128 prospectively generated trajectories for globally unseen paths, 150/200-cycle horizons and combined amplitude/mean shift. The DENIM v2.2 weights and evaluation protocol were frozen first.

The original 2,660-role protocol remains frozen; capability v4 adds its own roles and the sealed release adds no optimization data. The six releases form a staged evidence chain and must not be pooled or randomly reshuffled without respecting material, path-family, resolution-group and release boundaries.

Historical Path-OOD labels are protocol-relative: they mean unseen for the model and training split defined at that release. Some historical test-family names entered later training releases, so those scores are not global OOD claims for v2.2. sealed_test_v1 is the current prospective global path-OOD protocol.

Historical material-conditioned DENIM v2 protocol

All 2,660 trajectories now have a frozen role in the conditional study: 1,484 train, 407 validation and 769 test. The release adds no duplicate data. Shared known-material pretraining plus incomplete-material replay reduces long-history RMSE from 10.906 to 4.263 MPa. Reproduction code, exact accounting and complete metrics are in conditional_v2/.

Historical fixed-material DENIM closure

DENIM stands for Discrete-Energy Neural Internal-variable Model. The reference material contains three kinematic memory channels and a non- exponential tabulated isotropic-hardening curve. DENIM retains only two memory channels and receives none of the reference hardening equations or parameters.

Held-out non-proportional path results:

Model	Test RMSE	Test R2
Incomplete J2, no learned hardening	59.541 MPa	0.730208
GRU	76.988 MPa	0.548933
DENIM	1.136 MPa	0.999902

The 918-parameter DENIM also passed coarse/fine increment checks and three notched-bar deployment gates. Cyclic and monotonic reaction relative-L2 errors were 0.636% and 0.500%; the severe cyclic stress test required one global trust-region fallback. This remains a fixed synthetic material study with internal-state supervision, not an experimental calibration or a certified production material.

The standalone weights and model card are published at HaomingLuo/AgentFEM-DENIM.

DENIM capability-boundary extension

The 500-trajectory extension contains 250 training, 50 validation, 80 held-out path, 60 amplitude-extrapolation, 40 long-history and 20 matched-resolution histories. No failed case was silently removed.

Test	Incomplete J2	GRU	Frozen DENIM	Expanded DENIM
Published held-out paths	59.541	98.260	1.136	0.714
New path OOD	58.177	96.959	1.163	0.743
Amplitude OOD	69.315	95.896	3.091	2.294
Long-history stress test	54.394	90.757	11.261	10.906

Values are stress RMSE in MPa. The long-history result is reported as a current capability boundary, not hidden by the stronger ordinary path results. Expanded-DENIM RMSE on matched 61/121/481/961-state histories was 0.673/0.722/0.761/0.767 MPa.

• Viewer-friendly index: data/t2_denim_boundary_v1/index.csv
• Lossless trajectories: data/t2_denim_boundary_v1/cohort.h5
• Data card: data/t2_denim_boundary_v1/README.md
• Quality report: artifacts/t2_denim_boundary_v1/QUALITY_REPORT.md
• Full metrics: artifacts/t2_denim_boundary_v1/model_metrics.json
• All-data usage: docs/T2_ALL_DATA_STAGE_SUMMARY.md

DENIM capability extension v4

The v4 increment adds 1,000 complete trajectories: 300 long-cycle, 300 full six-component non-proportional, 200 AgentFEM-derived local structural paths and 200 matched discretization/observation trajectories. The 100-cycle histories contain 2,001 accepted material states. Fifty continuous paths are integrated at 61, 121, 241 and 481 states and carry explicit group IDs; noisy and sparse observations are fields paired with clean truth, not separately counted cases.

The structure-derived cohort uses local strain bases from twelve AgentFEM linear-elastic unit-load solves on four perforated/notched plates, followed by nonlinear reference-material replay. It does not claim coupled elastoplastic redistribution. See data/t2_denim_capability_v4/README.md for the exact protocol and artifacts/t2_denim_capability_v4/capability_summary.json for machine-readable boundary statistics.

Prospective sealed test v1

The 128-trajectory sealed test is a final, non-training extension: 64 globally unseen path-shape histories, 32 histories with 150 or 200 cycles, and 32 combined amplitude/mean-shift histories. All eight path-family identifiers are disjoint from training. The reference integrator enforces finite values, monotone accumulated plastic strain, a relative yield-surface residual below 1e-8, total equivalent strain no greater than 0.0155, and accumulated equivalent plastic strain no greater than 0.10.

The manifest binds the data to DENIM v2.2 weights SHA-256 d7b848f41aa46616c76c5f0db536d8ecfbc508a5375faa3cbbcc555fb062633b. These samples are ineligible for training, validation, checkpoint selection or model redesign. The repository-level protocol audit reports zero exact cross-role collisions for full model inputs and for input/target pairs. This dataset release intentionally contains no sealed-test model score; evaluation is published separately in the model repository.

• Data card: data/t2_denim_sealed_test_v1/README.md
• Lossless trajectories: data/t2_denim_sealed_test_v1/cohort.h5
• Viewer indexes: data/t2_denim_sealed_test_v1/index.csv and index.jsonl
• Generation contract: configs/t2_denim_sealed_test_v1.json
• Leakage audit: artifacts/t2_denim_protocol_audit_v1.json

AgentFEM runtime validation

The expanded DENIM checkpoint is also available as a checksum-authenticated safetensors bundle in the AgentFEM-DENIM model repository. The safe bundle reproduces the legacy implementation on the fixed 121-step path to a maximum stress difference of 2.68e-7 Pa and identical final PEEQ.

Serial and two-rank AgentFEM implicit plastic-bar runs both completed 4/4 increments, with a reported maximum-stress difference of 5.96e-8 Pa between the two executions. The current plastic automatic-differentiation tangent has a documented 0.05–0.80% discrepancy against fixed-old-state finite differences over the audited plastic states. The demonstrated global cases converge; an exact consistent plastic tangent remains outside the present claim boundary.

• Machine evidence: artifacts/t2_denim_agentfem_v1/runtime_validation.json
• Validation note: artifacts/t2_denim_agentfem_v1/RUNTIME_VALIDATION.md
• Data/model handoff: docs/T2_DATA_MODEL_HANDOFF.md

Multiaxial v2 at a glance

• eight path families, including non-proportional, rotating and random five-direction loading;
• 241 ordered states per trajectory;
• stress, strain, plastic strain, PEEQ, two-family total backstress, plastic increments and physical diagnostics;
• zero quality-gate failures across all 1,024 trajectories;
• six model families evaluated under three frozen protocols;
• element-level deployment in a controlled notched-bar finite-element gate.

Stress RMSE on held-out trajectories:

Model	ID	Path OOD	Parameter OOD
Pointwise MLP	83.51 MPa	105.81 MPa	82.34 MPa
GRU	17.26 MPa	76.03 MPa	19.26 MPa
LSTM	22.67 MPa	102.54 MPa	22.89 MPa
Causal TCN	21.82 MPa	60.44 MPa	21.99 MPa
Physics-state GRU	23.06 MPa	66.00 MPa	24.19 MPa
Physics-integrator NN	0.0128 MPa	0.0237 MPa	0.0275 MPa

The physics-integrator NN predicts a bounded plastic-multiplier correction and then applies differentiable J2/Chaboche consistency corrections while storing plastic strain, PEEQ and two backstress tensors. It passed the mild and severe structural gates with reaction relative-L2 errors of 1.65e-7 and 2.39e-7. The severe case recorded one trust-region fallback at complete unloading.

This is a white-box physics-fusion ceiling: the embedded return-mapping equations match the constitutive families that generated the synthetic data. It demonstrates the benefit of architecture-level physics for this controlled benchmark, but does not establish transfer to unknown materials or misspecified physical models.

Reproduction and evidence

• Dataset details: data/t2_multiaxial_ood_v2/README.md
• Model card: models/t2_multiaxial_ood_v2/README.md
• Quality report: artifacts/t2_multiaxial_ood_v2/QUALITY_REPORT.md
• Full metrics: artifacts/t2_multiaxial_ood_v2/model_metrics.json
• Structural gates: artifacts/t2_multiaxial_ood_v2/structural_validation/
• Manuscript roadmap: docs/T2_MULTIAXIAL_RESEARCH_MEMO.md
• Literature map: docs/T2_MULTIAXIAL_LITERATURE.md
• Commands: T2_V2_REPRODUCE.md
• DENIM data and evidence: DENIM_START_HERE.md
• DENIM reproduction: DENIM_REPRODUCE.md

The original multiaxial release used AgentFEM commit 058faecc05aeda143d014fd229401003a9258bbb (0.3.7.dev0). Later release manifests record their own software revisions and hashes. All quantities use SI units. Voigt order is xx, yy, zz, xy, yz, xz, with tensor shear.

Scope

The releases are controlled synthetic, small-strain benchmarks for J2/Chaboche families, material-parameter variation and one deliberately hidden three-memory reference material. They are not a general metals database and do not constitute experimental calibration, fatigue-life prediction, damage, finite-strain plasticity or a production-certified learned material. Complete internal states are privileged simulation labels, not quantities normally available from standard material tests. Data are CC BY 4.0; code files are covered by the included code license.

Evidence protocol v3

See article_evidence_v3/ for frozen ablation and leave-one-family-out split definitions.