Physics-informed neural networks without a phenomenological model available – applications in regression problems

Abstract

Physics-Informed Neural Networks (PINNs) aim to incorporate the phenomenology of the process into their training through an additional mathematical model based on conservation principles (physical laws). This work presents a method for training feedforward neural networks with physics-informed constraints related to static gain signals between the output and inputs in real cases in which a phenomenological model is not available. The proposed approach was applied to feedforward networks considering gradient-based and gradient-free learning methods (Extreme Learning Machine, ELM). This work shows that, even in training approaches involving a weight initialization strategy coupled with a constructive algorithm for defining the number of hidden units, the neural model, identified without any physical information, does not ensure that static gain signals between the output and inputs are consistent with the physical reality of the phenomenon. The case studies comprised 3 real datasets widely used as benchmarks for regression problems. The results show that in the absence of any equations capable of describing the physics of the analyzed problem, it is feasible and desirable to incorporate hard constraints into the training. This can ensure the correct direction of effect of each input on each output, and therefore the qualitative consistency of the models, besides their quantitative performances.