Fig. 4: Equation learner framework.
a Our equation learner framework uses a customized neural network with physics-based activation functions defined for each neuron. Stage 1 first performs an initial fit to the dataset, establishing an acceptable error level on the training and validation set (green). Stage 2 then iteratively prunes this network, removing neurons that have the lowest contribution in each layer, which is repeated until the highest level (e.g., 90%) of sparsity before the loss terms increase. Finally, in Stage 3, we write an equation using the neural network’s weights and activation functions and simplify it using sympy75. b The training process (logarithm of the mean squared error of the network vs the training epochs) for generating equations represents the three stages described in Fig. 4a. The dashed horizontal represents the loss-threshold for initiating the pruning of the least contributing neurons the network. The color bar represents the sparsity progression during the process.
