A physical neural network (PNN) has both the strong potential to solve machine learning tasks and intrinsic physical properties, such as high-speed computation and energy efficiency. Reservoir computing (RC) is an excellent framework for implementing an information processing system with a dynamical system by attaching a trained readout, thus accelerating the wide use of unconventional materials for a PNN. However, RC requires the dynamics to reproducibly respond to input sequence, which limits the type of substance available for building information processors. Here we propose a novel framework called generalized reservoir computing (GRC) by introducing a general form of postprocessing to turn this requirement on its head, which makes conventional RC a special case. Using substances that do not respond the same to identical inputs (e.g., a real spin-torque oscillator), we propose mechanisms aimed at obtaining a reliable output and show that processed inputs in the unconventional substance are retrievable. Finally, we demonstrate that, based on our framework, spatiotemporal chaos, which is thought to be unusable as a computational resource, can be used to emulate complex nonlinear dynamics, including large scale spatiotemporal chaos. Our results extend the applicable range of the conventional RC framework to general dynamical systems. Overall, our framework removes the limitation to building an information processing device and opens a path to constructing a computational system using a wider variety of physical dynamics.