Extended Data Fig. 2: Symbolic regression on synthetic vs. real data.
From: Causal chambers as a real-world physical testbed for AI methodology
Estimated expressions and their R2 scores when we apply the symbolic regression method from Fig. 6b to the real data from the light tunnel (right), and synthetic data (left) following Malus’ law (see Supplementary Material IV.2.1). The synthetic data is produced by fitting the law to the data and adding Gaussian noise to simulate sensor noise. For the real data, the estimated expression varies with the random initialization of the method, whereas for the synthetic data, the method recovers the ground-truth expression in each run. This phenomenon does not carry over to the task of recovering Bernoulli’s principle, where the method output is highly variable for both the synthetic and real data (see Supplementary Figure 1).
