Lie Generator Networks enable linear system identification with guaranteed physical stability and dissipation by construction rather than through loss penalties.
March 31, 2026
Original Paper
Interpretable Physics Extraction from Data for Linear Dynamical Systems using Lie Generator Networks
arXiv · 2603.27442
The Takeaway
By shifting from integration to matrix exponentiation within a structured parameterization, this architecture recovers exact system eigenvalues with two orders of magnitude less error than standard Neural ODEs. It bridges the gap between flexible deep learning and the rigid stability requirements of control theory and circuit analysis.
From the abstract
When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet when system parameters must be inferred from data, recent neural approaches offer flexibility at the cost of physical guarantees: Neural ODEs provide flexible trajectory approximation but may violate physical invariants, while energy preserving architectures d