Speaker
Description
Physics-informed learning has emerged as a powerful paradigm for system identification, enabling data-driven models to capture complex nonlinear dynamics while respecting underlying physical structure. Building on our recent work on learning nonlinear port-Hamiltonian (pH) systems from input–state–output data, we investigate how model performance scales with available learning resources.
We present a unified framework for identifying nonlinear pH systems using neural networks as structured function approximators. By embedding the port-Hamiltonian framework into the learning architecture, the proposed approach preserves passivity and energy-based properties while leveraging the universal approximation capabilities of modern neural networks. Incorporating prior knowledge about the underlying physical structure constrains the hypothesis space, improves data efficiency, and yields models that are more accurate, physically consistent, and reliable for long-term prediction than purely data-driven approaches.
Then the scalability of such physics-informed models is studied through the lens of neural scaling laws, relating identification loss to data, model size, and computational budget. While scaling behavior is well established in domains such as natural language processing, the quantitative relationship between learning resources and identification accuracy remains poorly understood in dynamical systems settings. We empirically verify neural scaling laws across a range of architectures, including standard input-affine models and physics-informed port-Hamiltonian representations. By training thousands of models and evaluating their performance using standardized metrics, we determine scaling relationships that quantify how improvements in resources translate to gains in accuracy. These scaling laws provide practical guidance for forecasting achievable accuracy, selecting architectures, and designing data acquisition strategies, connecting structure-preserving system identification with neural