DTE AICCOMAS 2025

Student

A Sparse State-Space Model for Electrical Circuits

  • Meissner, Teddy (University of Arizona)
  • Paskaleva, Biliana (Sandia National Laboratories)
  • Bochev, Pavel (Sandia National Laboratories)

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Circuit-level simulations are essential for design, assessment, and analysis of system-level behaviours. Such simulations use transistor-level circuit descriptions built from compact device models using modified nodal analysis. This leads to systems of differential algebraic equations (DAEs) whose size is proportional to the number of devices in the circuit. As a result, highly detailed circuit-level simulations may become infeasible for large circuits, prompting significant interest in the application of model order reduction (MOR) to circuits. However, most existing MOR require knowledge of the full order circuit model and/or snapshots of its internal states. For highly complex or proprietary circuits, engineers often have no access to the internal states and are constrained to input-output data pairs alone. In this talk we introduce a novel, non-intrusive MOR to construct accurate state-space models from input-output data pairs alone. To that end we leverage the previous work on Sparse Identification of Nonlinear Dynamical Systems (SINDy) and nonlinear state-space system identification (SysID). SINDy aims to discover symbolic expressions for time-series data through sparse regression of a predefined library. SysID on the other hand aims to predict the output data by means of dynamic latent states, which can be in the form of DAEs. While SysID enables a state-space representation closely matching the physics of a circuit, it requires knowledge of the complete functional form. On the other hand, SINDy requires internal state data, which is unknown, but does not require knowledge of the exact functional form. In this work, we create a nonlinear state-space model by means of sparse identification, which can be seen as a natural step into blending these two approaches. Our results indicate that this approach (i) can extrapolate beyond the training data with good accuracy, and (ii) results in computationally efficient parsimonious data-driven models that can provide a basis for effective digital twins of complex electrical circuits and systems.