We demonstrate that data-driven system identification techniques can provide a basis for effective, non-intrusive model order reduction (MOR) for common circuits that are key building blocks in microelectronics. Our approach is motivated by the practical operation of these circuits and utilizes a canonical Hammerstein architecture. To demonstrate the approach we develop a parsimonious Hammerstein model for a non-linear CMOS differential amplifier. We train this model on a combination of direct current (DC) and transient Spice (Xyce) circuit simulation data using a novel sequential strategy to identify the static nonlinear and linear dynamical parts of the model. Simulation results show that the Hammerstein model is an effective surrogate for the differential amplifier circuit that accurately and efficiently reproduces its behavior over a wide range of operating points and input frequencies.

Several recent works have examined continuous-depth idealizations of deep neural nets, viewing them as continuous-time ordinary differential equation (ODE) models with either fixed or time-varying parameters. Traditional discrete-layer nets can be recovered by applying an appropriate temporal discretization scheme, e.g., the Euler or Runge-Kutta methods. In applications, this perspective has resulted in advantages concerning regularization (Kelly et al., 2020; Kobyzev et al., 2021; Pal et al., 2021), efficient parameterization (Queiruga et al., 2020), convergence speed (Chen et al., 2023), applicability to non-uniform data (Sahin and Kozat, 2019), among others. As a theoretical tool, continuous-depth idealizations have lead to better understanding of the contribution of depth to model expressiveness and generalizability (Marion, 2023; Massaroli et al., 2020), new or improved training strategies via framing as an optimal control problem (Corbett and Kangin, 2022), and novel model variations (Jia and Benson, 2019; Peluchetti and Favaro, 2020). Considered as generic control systems, continuous-depth nets can admit a number of distinct inputoutput configurations depending on how the control system "anatomy" is delegated. Controlled neural ODEs (Kidger et al., 2020) and continuous-time recurrent neural nets (Fermanian et al., 2021) treat the (time-varying) control signal as the input to the model; the initial condition is either fixed or treated as a trainable parameter; the (time-varying) output signal is the model output; and any free parameters of the vector fields (weights) are held constant in time.

Radiation-induced photocurrent in semiconductor devices can be simulated using complex physics-based models, which are accurate, but computationally expensive. This presents a challenge for implementing device characteristics in high-level circuit simulations where it is computationally infeasible to evaluate detailed models for multiple individual circuit elements. In this work we demonstrate a procedure for learning compact delayed photocurrent models that are efficient enough to implement in large-scale circuit simulations, but remain faithful to the underlying physics. Our approach utilizes Dynamic Mode Decomposition (DMD), a system identification technique for learning reduced order discrete-time dynamical systems from time series data based on singular value decomposition. To obtain physics-aware device models, we simulate the excess carrier density induced by radiation pulses by solving numerically the Ambipolar Diffusion Equation, then use the simulated internal state as training data for the DMD algorithm. Our results show that the significantly reduced order delayed photocurrent models obtained via this method accurately approximate the dynamics of the internal excess carrier density -- which can be used to calculate the induced current at the device boundaries -- while remaining compact enough to incorporate into larger circuit simulations.

There has been a recent shift in sequence-to-sequence modeling from recurrent network architectures to convolutional network architectures due to computational advantages in training and operation while still achieving competitive performance. For systems having limited long-term temporal dependencies, the approximation capability of recurrent networks is essentially equivalent to that of temporal convolutional nets (TCNs). We prove that TCNs can approximate a large class of input-output maps having approximately finite memory to arbitrary error tolerance. Furthermore, we derive quantitative approximation rates for deep ReLU TCNs in terms of the width and depth of the network and modulus of continuity of the original input-output map, and apply these results to input-output maps of systems that admit finite-dimensional state-space realizations (i.e., recurrent models). Papers published at the Neural Information Processing Systems Conference.

There has been a recent shift in sequence-to-sequence modeling from recurrent network architectures to convolutional network architectures due to computational advantages in training and operation while still achieving competitive performance. For systems having limited long-term temporal dependencies, the approximation capability of recurrent networks is essentially equivalent to that of temporal convolutional nets (TCNs). We prove that TCNs can approximate a large class of input-output maps having approximately finite memory to arbitrary error tolerance. Furthermore, we derive quantitative approximation rates for deep ReLU TCNs in terms of the width and depth of the network and modulus of continuity of the original input-output map, and apply these results to input-output maps of systems that admit finite-dimensional state-space realizations (i.e., recurrent models).