Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/8/eaat5218/DC1

Section S1. DEER kernel derivation

Section S2. Performance illustrations for networks of different depth

Section S3. Effects of transfer functions, choke points, and bias vectors

Section S4. Behavior of Tikhonov regularization for exchange-coupled systems

Section S5. Behavior of neural networks with the increasing level of noise

Fig. S1. DEERNet performance illustration, distance distribution recovery: two-layer feedforward network, fully connected, with 256 neurons per layer.

Fig. S2. DEERNet performance illustration, distance distribution recovery: three-layer feedforward network, fully connected, with 256 neurons per layer.

Fig. S3. DEERNet performance illustration, distance distribution recovery: four-layer feedforward network, fully connected, with 256 neurons per layer.

Fig. S4. DEERNet performance illustration, form factor recovery: two-layer feedforward network, fully connected, with 256 neurons per layer.

Fig. S5. DEERNet performance illustration, form factor recovery: three-layer feedforward network, fully connected, with 256 neurons per layer.

Fig. S6. DEERNet performance illustration, form factor recovery: four-layer feedforward network, fully connected, with 256 neurons per layer.

Fig. S7. Tikhonov analysis of synthetic data produced as described in the main text and featuring a unimodal distance distribution in the presence of a fixed exchange coupling (cf. Fig. 17).

Fig. S8. A randomly generated DEER data set with the noise SD set at 2.5% of the modulation depth and the resulting distance distribution reconstruction by DEERNet.

Fig. S9. A randomly generated DEER data set with the noise SD set at 10% of the modulation depth and the resulting distance distribution reconstruction by DEERNet.

Fig. S10. A randomly generated DEER data set with the noise SD set at 30% of the modulation depth and the resulting distance distribution reconstruction by DEERNet.

Table S1. Distance distribution recovery performance statistics for feedforward networks with hyperbolic tangent sigmoid (tansig) and logistic sigmoid (logsig) transfer function at the last layer.

Table S2. Performance statistics for a family of feedforward networks set up as a sequence of fully connected layers with a choke point in the position indicated.