PHINN synthesises realistic rare-event time series — conditioned on the topological fingerprint of a crisis — so your forecasting, risk and autonomy systems are ready for the tail before the tail arrives.
The events that matter most — a geomagnetic superstorm, a cascading grid trip, a caster breakout, a sudden shift in adversary behaviour — are the ones with almost no data. Statistical and diffusion generators smooth them away. Matching moments isn't enough; you need to match the shape of a crisis.
Rare events leave a fingerprint in topology — characteristic transitions in Betti numbers that are more stable, more interpretable and more discriminative than statistical moments.
PHINN reads that fingerprint from the few real events you have, then generates thousands of new, structurally faithful scenarios to train, stress-test and price against.
A conditional flow-matching generator, steered by dynamic Betti curves and held to the topology of real events by a differentiable persistence-landscape loss.
Each window of the series is lifted into a point cloud — jointly across sensors and modalities.
Grow neighbourhoods and watch features appear and vanish: components, loops, voids.
β₀, β₁, β₂ over time — a compact, interpretable signature of how a crisis unfolds.
New scenarios are generated to hit target Betti curves, with H₁/H₂ consistency enforced in training.
Evaluated on financial-crisis, epidemiological and multi-modal time-series benchmarks against statistical and diffusion-based baselines.
Topological error versus all statistical and diffusion baselines tested.
Reproduces when a rare event begins and breaks — not just how big it gets.
Matches jump-diffusion models on tail coverage while exceeding them on shape fidelity.
All reported results carry 95% confidence intervals. Source: Yusuf, Takahashi & Bhaduri, arXiv:2606.15452 (2026).
We started in defense and space. The same mathematics applies anywhere a rare, high-consequence event hides in sensor data.
Adversaries don't repeat the playbook you trained on. PHINN generates the anomalies, surges and shocks that sit outside the historical record — for test, evaluation and red-teaming.
The space weather record holds only a handful of truly extreme storms. PHINN generates thousands of physically shaped variants — for operators, insurers and regulators who must plan for the next one.
A breakout or furnace upset is rare, violent and expensive — and the plant historian holds only a few. PHINN turns those few into a training set large enough to catch the next one early.
Grids are engineered for the expected. Blackouts come from the unexpected — compound, cascading, fast. PHINN generates the cascades your planning models have never had to survive.
We earn trust with measurable results, not slideware. Every engagement starts with a test you design the scoring for.
Pick a rare event that matters to you. We agree the success criteria up front — pre-registered, so nobody can move the goalposts.
PHINN runs on your historical data and feeds your existing models, risk tools or test ranges. Results reported against the agreed criteria.
Licensed deployment, on-prem or air-gapped where required, with joint research and publication where it serves both sides.
The method is published for scrutiny. The production system, sector models and tooling are our IP.
In preparation: applied studies on extreme space weather and orbital catalogue custody, and pre-registered forecasting tests with defense partners.
Briefings for defense, space, steel and power organisations, insurers and research partners.