Data-Driven Parameter Estimation of Lumped-Element Models Via Automatic Differentiation

Lumped-element models (LEMs) provide a compact characterization of numerous real-world physical systems, including electrical, acoustic, and mechanical systems. However, even when the target topology is known, deriving model parameters that approximate a possibly distributed system often requires educated guesses or dedicated optimization routines. This article presents a general framework for the data-driven estimation of lumped parameters using automatic differentiation. Inspired by recent work on physical neural networks, we propose to explicitly embed a differentiable LEM in the forward pass of a learning algorithm and discover its parameters via backpropagation. The same approach could also be applied to blindly parameterize an approximating model that shares no isomorphism with the target system, for which it would be thus challenging to exploit prior knowledge of the underlying physics. We evaluate our framework on various linear and nonlinear systems, including time- and frequency-domain learning objectives, and consider real- and complex-valued differentiation strategies. In all our experiments, we were able to achieve a near-perfect match of the system state measurements and retrieve the true model parameters whenever possible. Besides its practical interest, the present approach provides a fully interpretable input-output mapping by exposing the topological structure of the underlying physical model, and it may therefore constitute an explainable ad-hoc alternative to otherwise black-box methods.