Logan Voss
Open research framework · Version 0.1.0 · 2026
Find where your measurements say same but the system's futures disagree—then synthesize the missing coordinate.
Invariant Synthesis Engine (ISE) is an open research framework for discovering compact, testable observables in complex dynamical systems. It starts from consequential collisions: trajectories that look alike in the current representation but lead to materially different outcomes. It then composes candidate expressions, subjects them to invariance and transfer tests, and adds only those that repair the ambiguity on held-out data.
This repository is the domain-neutral foundation. The included energy-grid example is a demonstration, not the boundary of the framework. The same loop can be applied to energy, industrial processes, computing infrastructure, transportation, aerospace, climate, robotics, biological systems, and experimental science.
trajectories → current observables → consequential collisions
→ synthesize a discriminator
→ test invariance + transfer + simplicity
→ augment the representation → repeat
Complex systems are only partially observed. Two physically different states can collapse onto the same dashboard, latent vector, or engineering summary:
state A → current representation Φ → "normal" → recovery
state B → current representation Φ → "normal" → cascade
The useful question is not merely “Can a classifier tell these apart?” It is:
What observable is missing from the current description of reality?
ISE turns that question into a falsifiable search objective. Its output is an inspectable coordinate such as a ratio, difference, lag relation, spectral statistic, coupling term, or composition—not just an anomaly score. Engineers can test it, reject it, connect it to physics, deploy it as a read-only monitor, or use the remaining collisions to justify new measurements.
The original prototype proved the pressure loop using hand-authored hypotheses. This version removes that central limitation. Candidate expressions are generated from a bounded grammar and admitted through a counterexample-guided validation pipeline:
- Collision pressure finds nearby trajectories with materially different outcomes.
- Automatic composition searches primitives and
+,-,×, safe division, absolute value, square, and log-magnitude transformations. - Empirical invariance contracts reject formulas that break under user-declared nuisance transformations such as gain changes, offsets, time-origin shifts, sign symmetries, or valid channel relabelings.
- Group-aware holdouts test transfer to unseen assets, sites, regions, devices, or operating regimes.
- Block-weighted repair gives each accepted coordinate enough representational weight to repair a wide dashboard instead of being numerically diluted by it.
- Dimensional safeguards reject invalid additions and penalize gratuitously complex units while allowing physically meaningful products and ratios.
- Observability-gap reporting treats failed synthesis as information. It records which consequential pairs remain ambiguous and clearly distinguishes bounded search failure from proof of impossibility.
The objective is approximately:
candidate value =
held-out collision separation
+ outcome association
+ invariance under declared transformations
+ transfer across groups
+ novelty relative to Φ
+ train/validation agreement
- expression complexity
- unit complexity
- numerical instability
Then Φ ← Φ ⊕ candidate, collisions are mined again, and the description repairs itself.
| Method | Primary question | Typical output |
|---|---|---|
| Anomaly detection | Is this event unusual? | anomaly score |
| Classification | Which known class fits? | label/probability |
| PCA / autoencoders | What compresses the data? | latent coordinates |
| Symbolic regression | What predicts a supplied target globally? | fitted expression |
| System identification | What dynamical model fits? | model parameters/equations |
| Invariant synthesis | What coordinate repairs consequential ambiguity and survives valid transformations? | validated candidate observable + unresolved collision map |
ISE can complement every method in that table. A model embedding can be the starting representation; a simulator can supply counterfactual trajectories; a system-identification residual can become a primitive; a discovered invariant can become a feature for a downstream predictor.
| System | Consequential collision | Potential synthesized object |
|---|---|---|
| Energy grids | recovering and unstable disturbances look alike | damping, interface, or modal coordinate |
| Data centers | benign and grid-interacting load patterns overlap | workload-to-power coupling fingerprint |
| Industrial plants | safe drift resembles runaway precursor | balance, lag, or boundary-flow relation |
| Aerospace | recoverable perturbation resembles control degradation | frame-invariant stability indicator |
| Manufacturing | normal variation resembles failure precursor | process-consistency or wear coordinate |
| Cloud / telecom | transient congestion resembles cascade onset | topology-aware load-flow invariant |
| Batteries | healthy transients resemble latent degradation | scale-stable electrothermal relation |
| Transportation | recoverable congestion resembles network collapse | flow/capacity or propagation coordinate |
| Science | different mechanisms project to the same observables | symmetry, conserved residue, or missing measurement |
The near-term product posture is intentionally read-only: discovery, retrospective validation, prospective monitoring, and sensor-design evidence. The framework does not autonomously control safety-critical infrastructure.
ISE requires Python 3.10 or newer.
git clone https://github.com/LoganVoss/invariant-synthesis-engine.git
cd invariant-synthesis-engine
python3.11 -m venv .venv
source .venv/bin/activate
pip install -e ".[dev]"
ise demo --output artifacts/energy-grid-demoThe deterministic demo deliberately makes ordinary whole-window statistics collide. The engine recovers an amplitude-scale-invariant growth coordinate:
(early_rms[frequency_deviation] / late_rms[frequency_deviation])
The run writes:
synthesis_report.md— a human-readable validation report;synthesis_result.json— expressions, scores, collision histories, configuration, and unresolved pairs;synthesis_model.json— portable canonicalization, primitive, and expression AST state;synthetic_grid_events.npz— the reproducible demonstration dataset.
The synthetic data is designed to test the algorithm. It is not a validated power-system model and should never be presented as field evidence.
from invariant_synthesis import (
EngineConfig,
InvariantModel,
InvariantSynthesisEngine,
TrajectoryDataset,
)
from invariant_synthesis.transformations import global_scale, time_shift
dataset = TrajectoryDataset(
values=trajectories, # shape: samples × time × signals
outcomes=outcomes, # categorical or continuous consequence
signal_names=("flow", "pressure", "temperature"),
units=("kg/s", "bar", "degC"),
groups=asset_ids, # optional; held out as intact groups
sample_ids=event_ids,
time_step=0.02,
)
config = EngineConfig(
center="initial", # operating-point canonicalization
max_rounds=3,
)
engine = InvariantSynthesisEngine(config)
result = engine.fit(
dataset,
transformations=(
global_scale(1.2, signals=(0,)),
time_shift(2),
),
)
for discovery in result.discoveries:
print(discovery.expression)
print(discovery.score.validation_collision)
print(discovery.score.invariance)
result.save("artifacts/my-run")
repaired_coordinates = result.feature_matrix(dataset)
# Apply the frozen representation later without re-running synthesis.
model = InvariantModel.load("artifacts/my-run/synthesis_model.json")
repaired_coordinates = model.transform(new_compatible_dataset)Only declare a transformation if the target coordinate should survive it. Treating a real physical change as a nuisance transformation can erase the signal you are trying to find.
The CLI accepts compressed NumPy .npz files:
| Array | Shape | Required | Meaning |
|---|---|---|---|
values |
N × T × D |
yes | trajectory windows |
outcomes |
N |
yes | consequential labels or numeric outcomes |
signal_names |
D |
yes | unique channel names |
units |
D |
no | opaque unit labels; defaults to dimensionless |
groups |
N |
no | asset/site/regime IDs for leakage-resistant holdout |
sample_ids |
N |
no | event IDs used in unresolved-pair reports |
time_step |
scalar | no | sample interval; defaults to 1.0 |
Missing values are linearly interpolated within each event window. Fully absent trajectory/channels use the across-trajectory median and are recorded in run metadata. For high-stakes work, perform domain-appropriate quality control before synthesis.
ise discover telemetry.npz \
--output artifacts/plant-run \
--center initial \
--rounds 3 \
--global-scale 1.1src/invariant_synthesis/
data.py validated trajectory contract, imputation, canonicalization
primitives.py temporal, spectral, coupling, and pairwise descriptor leaves
expressions.py unit-aware symbolic grammar and safe evaluation
collisions.py blocked consequential-neighbor mining
scoring.py held-out, invariance, transfer, novelty, and complexity pressure
search.py bounded beam search over generated expressions
engine.py iterative representation-repair loop
report.py machine and engineering reports
transformations.py explicit empirical invariance contracts
See Architecture, Methodology, Industry applications, and Extending the grammar.
ISE is designed to make seductive formulas harder to accept:
- synthesis and acceptance use separate collision families;
- group IDs prevent the same asset or site leaking across the split;
- invariance is measured against explicit transformed trajectories;
- expression and unit complexity are penalized;
- numerical saturation is penalized;
- every run records alternatives, pressure history, configuration, and unresolved examples;
- reports say candidate invariant, never discovered law.
For real deployment, add chronological holdouts, prospective replay, bootstrap confidence intervals, comparison against strong baselines, domain-specific simulation, and independent physical review. See Methodology for a staged evidence ladder.
This is a serious research foundation, not a finished autonomous scientist.
- The search is bounded beam search, so grammar exhaustion is not mathematical impossibility.
- Collision mining is blocked but still quadratic in the number of trajectories.
- The built-in unit system treats labels such as
MWas opaque atoms; it is not a full SI dimensional-analysis package. - Fixed-length aligned windows are currently required.
- The initial release focuses on scalar trajectory descriptors; graph-native and differential-equation grammars are roadmap items.
- Statistical validation cannot establish causality or physical meaning.
- Human review remains mandatory for safety-critical applications.
These limits are surfaced because trustworthy scientific discovery depends as much on knowing what was not established as on ranking what looked promising.
- approximate-neighbor collision mining for million-event archives;
- graph/topology primitives and subsystem-boundary synthesis;
- typed SI units and conservation-law templates;
- equivariant outputs, not only invariant ones;
- Pareto-front search over separation, invariance, complexity, and transfer;
- bootstrap stability and nested cross-validation;
- streaming/prospective invariant watchtower;
- sensor-value-of-information recommendations from unresolved collision fibres;
- simulator-in-the-loop interventions and causal falsification;
- pluggable primitive and operator registry.
Contributions are welcome, especially benchmark datasets, physically grounded transformations, validation methods, graph primitives, and adversarial counterexamples. Read CONTRIBUTING.md before opening a pull request.
Logan Voss — GitHub
If you use this software in research, please cite the repository. See CITATION.cff.
MIT licensed. See LICENSE.
The software is provided for research and engineering decision support. It is not certified for autonomous operation of grids, plants, vehicles, medical devices, or other safety-critical systems. Report security issues through SECURITY.md.