Jump-Augmented Reservoir Computing for Trajectory Forecasting and Measurement Correction

Echo state networks (ESNs) replace gradient-based recurrent training with a fixed, randomly generated reservoir and a single linear readout. We introduce hybrid reservoirs, in which we augment the dynamics of the reservoir state to allow for discrete, event-triggered jumps that reset the reservoir state instantaneously. Deciding when and where to jump is a challenging problem that is usually application-specific. In this work, we provide a general formulation of hybrid reservoirs and showcase their potential on trajectory forecasting and measurement correction. For both applications, a well-chosen jump map lets the reservoir be reset into the right region of its state space, improving performance over a standard, jump-free ESN without sacrificing the closed-form, replay-free training that makes reservoir computing attractive in the first place.