Adaptive Sensing of Continuous Physical Systems for Machine Learning

Physical dynamical systems can be viewed as natural information processors: their systems preserve, transform, and disperse input information. This perspective motivates learning not only from data generated by such systems, but also how to measure them in a way that extracts the most useful information for a given task. We propose a general computing framework for adaptive information extraction from dynamical systems, in which a trainable attention module learns both where to probe the system state and how to combine these measurements to optimize prediction performance. As a concrete instantiation, we implement this idea using a spatiotemporal field governed by a partial differential equation as the underlying dynamics, though the framework applies equally to any system whose state can be sampled. Our results show that adaptive spatial sensing significantly improves prediction accuracy on canonical chaotic benchmarks. This work provides a perspective on attention-enhanced reservoir computing as a special case of a broader paradigm: neural networks as trainable measurement devices for extracting information from physical dynamical systems.