Fluid mechanics
Solve the field, then interrogate the wake.
A Navier–Stokes PINN around a 2D obstacle so the twin can replay velocity, pressure, and drag without re-running a full CFD mesh.
Open NS 2D obstaclePhysical Systems Twins
Four domains. One twin loop.
Welcome.Fluid mechanics, capital markets, oil & gas, and medicine share the same idea: learn the governing physics, then query the twin — field, price, stress, or anatomy — and write it into a report.
Capital markets
Price from physics, not from a fitted smile alone.
Black–Scholes PINN twins for European options: snapshot quotes, inference on V(S, τ), a board of calls and puts, then Gemini assessment with Eve.
Open Black–Scholes twinOil & gas
Geomechanics first, then strength at the well.
Reservoir stress and UCS twins so pore pressure, principal stresses, and unconfined strength stay in the same loop as the report.
Open reservoir geomechanicsMedicine
A twin that can be queried, not only viewed.
Liver and brain anatomy as live digital twins — vessels, tumors, and ducts you can inspect, then send into a surgical report with Eve.
Open liver twinWorkspaces
Pick a domain, then a twin.
Same sidebar destinations, grouped the way the product is actually used.
Fluid mechanics
Flow around bodies
Capital markets
Options, Itô, and bonds
PINN Prep
SPX snapshot quotes, smiles, and the collocation table that feeds Black–Scholes training.
OpenBlack–Scholes twin
Trained PINN inference: price field, smile slice, Greeks, board, and Gemini assessment with Eve.
OpenI1 Heat twin
Forward Kolmogorov heat equation: PINN p(z, t) vs closed-form teachers from PS5 Q3.
OpenB4 Yield curve
Inverse Vasicek PINN on US Treasury par yields: bootstrap zeros, fit (α, ȳ, σ), query P(τ, y).
OpenEU Options
Market data, simulation & pricing, and reporting on the same European book.
OpenOil & gas
Reservoir rock
Medicine
Anatomy you can query
Liver twin
Hepatic vessels and biliary tree as a queryable 3D twin for surgical planning.
OpenLiver IRCAD
Public IRCAD anatomy for the same hepatobiliary loop — vessels, parenchyma, and ducts.
OpenHepatic vasculature
Portal and hepatic venous trees as a dedicated vessel twin.
OpenPancreas
Pancreatic anatomy in the same surgical-planning loop as liver and ducts.
OpenBrain tumor
Tumor relative to vessels and ventricles, then a report the team can interrogate.
OpenVessels & ventricles
Cerebral vasculature and ventricular system as a navigable twin.
OpenShared loop
Data, twin, inference, report — across every domain.
01
Data
CFD collocation, option quotes, well logs, or segmented anatomy — the snapshot the twin is allowed to know.
02
Twin
PINN or anatomy model: Navier–Stokes, heat/Kolmogorov, Black–Scholes, geomechanics, UCS, liver, brain.
03
Inference
Query the field — velocity, V(S, τ), stress, UCS, or a vessel — without re-solving the original system.
04
Report
Board, assessment, and Eve so the same numbers stay in the narrative the team ships.