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ott_esn

A classic ESN with one additional transform that squares half the reservoir states before the readout, introduced by Pathak et al. (2018) for forecasting chaotic systems.

Wiring

Input → Reservoir → SelectiveExponentiation → Concatenate(Input, Augmented) → Readout

SelectiveExponentiation(index=0, exponent=2.0) squares the even-indexed state units and passes the odd-indexed ones through untouched. A tanh reservoir is an odd function of its drive, so without this the readout only sees odd-order terms, and an autonomous forecast can settle onto the mirror image of the attractor. Squaring half the units gives the readout even-order features and breaks that symmetry, while the concatenation keeps the raw input available as in classic_esn. The factory builds the readout as a CGReadoutLayer.

wiring

Computation graph of ott_esn.

Use

import torch
from resdag.models import ott_esn
from resdag.training import ESNTrainer

series = torch.cumsum(0.1 * torch.randn(1, 1201, 3), dim=1)

model = ott_esn(
    reservoir_size=500, feedback_size=3, output_size=3,
    topology=("watts_strogatz", {"k": 6, "p": 0.3}),
    spectral_radius=0.95,
)
ESNTrainer(model).fit(
    warmup_inputs=(series[:, :200],),
    train_inputs=(series[:, 200:1200],),
    targets={"output": series[:, 201:1201]},
)
preds = model.forecast(series[:, :200], horizon=100)   # (1, 100, 3)

Parameters

Parameter Default Notes
reservoir_size, feedback_size, output_size required units, input dim, output dim
topology, feedback_initializer None any initialization spec
spectral_radius 0.9 the factory scales; the bare ESNLayer defaults to None
leak_rate 1.0 1.0 = no leak
activation "tanh" also "relu", "sigmoid", "identity"
bias, trainable True, False random bias on; frozen reservoir
readout_alpha, readout_bias, readout_name 1e-6, True, "output" ridge strength; readout_name keys the targets dict
**reservoir_kwargs — forwarded to ESNLayer (e.g. bias_scaling)

Reference

J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach, Phys. Rev. Lett. 120, 024102 (2018). The factory name follows the common attribution of this architecture to Edward Ott's group; the paper's first author is Pathak.

See also