Explore a changing signal.
Control the noise and disturbance. Compare two estimators on identical observations.
New evaluation surface: choose repeatable datasets, export CSV and run the local black-box MAE comparison.
RUN THE MAE CHALLENGE →A map of a changing system.
A complex system cannot always be understood from one measurement. Lexium represents it with a compact collection of variables: its state. At time t, that collection is the state vector.
Measurements are observations. They may be noisy, incomplete or indirect. An estimator uses those observations to estimate hidden state. A transition model describes how that state can change. Uncertainty records how strongly the evidence supports the estimate.
Hospital uses the same idea. A Heart Twin state might contain rate, load, contractility, demand and recovery; a Lung Twin might contain ventilation, flow, exchange, load and recovery. The 3D/VR layer visualises state — it does not create truth or clinical authority.
OPEN BIOHOSPITAL →Signal, noise & evidence.
Compare five causal estimation methods on identical observations. Explore the trade-off between noise rejection, delay, abrupt changes and missing data.
Add the authentic local Lexium 6.10.2 trace to this run.
Paused / 0 of 160 samples
Run the experiment to reveal the observations and estimates.
Horizontal: sample number. Vertical: synthetic signal units. Missing observations leave a gap; both estimators hold their last value.
| Model | MAE | RMSE | Max error |
|---|---|---|---|
| A: Fixed gain | -- | -- | -- |
| B: Scalar Kalman | -- | -- | -- |
MAE: average absolute distance from truth. RMSE gives larger errors more weight. Max error is the worst observed distance. Lower is better within this run; this is not a probability or a universal ranking.
Methods, controls & limitations
Every method receives the same observations, never the true signal. Fixed gain starts at 35 and updates x = x + gain * (measurement - x). The latest-measurement baseline holds the last observed sample. Moving average and median use up to five most recent available measurements; the median averages the middle pair during even-length startup.
The scalar Kalman filter uses a random-walk model, initial estimate 35, initial variance 25, process variance Q = 1 per tick and observation variance R = noise amplitude squared / 3 (minimum 1e-9). During missing observations its variance grows; all methods hold their estimate. These parameters are disclosed teaching defaults, not tuned to win.
The signal is 45 + 8 * sin(tick / 18), with the selected disturbance. Noise is uniform and seeded. Reset reproduces the run; changing settings resets it. Scores include startup and dropout samples. Repeat across seeds and scenarios; these results do not establish general superiority.
Make the state path visible.
The observation and estimator values come from the same seeded browser experiment above. Geometric confidence and transition pressure are derived display dimensions, not additional measurements.
The geometry is a projection of selected dimensions. It does not add a new engine state or change estimator output.
Contained experiment: inspect a bounded feedback fork without giving it authority over the live estimator.
OPEN SHADOW LAB →OBSERVE
A noisy measurement of a hidden state.
ESTIMATE
Move the estimate toward each new observation.
COMPARE
Compare the estimate with the known simulated truth.
BROWSER SIMULATION
This demonstration runs in your browser. It is not connected to the local Lexic runtime and does not establish real-world performance.