LOOP · NSCS
Mode: Mechanistic + Residual
Neural Self-Consistent System (NSCS)
Closed-loop model discovery framework that ingests time-series trajectories, proposes symbolic candidates,
rejects unstable forms, and applies neural residual correction to improve stability and predictive fidelity.
Input
Time-series trajectories
Simulator outputs (e.g., BSE organ trajectories) or experimental curves.
Output
Selected governing form
Best candidate equation + residual term (if needed) + audit trail.
- 1) Ingest: read trajectories (states over time), normalize channels, define target variables and candidate feature library.
- 2) Symbolic candidate generation: generate ODE candidates via constrained symbolic regression / structured search (candidate families, parameter sweeps).
- 3) Score + reject: evaluate candidates on fit + stability (e.g., exploding/oscillatory divergence, nonphysical trends) and discard unstable solutions.
- 4) Residual correction: train a neural residual model Δ(t, x) to learn the mismatch between mechanistic candidate predictions and observed trajectories.
- 5) Compose: final model = mechanistic form + residual correction (only if it improves stability/generalization) with versioned metrics.
- 6) Feedback: inject improved equation/parameters back into BSE to iteratively refine the simulator under the same evaluation protocol.
Why residuals: preserves interpretability of the mechanistic backbone while absorbing unmodeled dynamics
(measurement artifacts, omitted nonlinearities, hidden coupling terms) in a controlled, testable way.