PINNeval: A Comprehensive Evaluation Standard for Physics-Informed Neural Networks

The Physics-Informed Neural Network (PINN) literature has produced a rapidly expanding catalogue of methods. We divide a PINN training pipeline systematically into four components and observe that many existing benchmarks study these components in isolation. These components are domain-importance adaptation, loss balancing, the neural network architecture, and the optimization scheme. Moreover, the studies set the surrounding and not considered components of the pipeline to a minimal default that is no longer representative of current best practice approaches. Conclusions drawn under such conditions lead to suboptimal results. In this work, we propose a new evaluation protocol that (1) treats the four components as an integrated system; (2) requires as a key aspect a competitive implementation of the components not currently under investigation; (3) specifies the metrics and reporting format, and (4) is accompanied by structured documentation that ensures the traceability of evaluations across studies. Based on this comprehensive protocol, we release with PINNeval an innovative JAX package containing 18 different methods from the current literature as well as nine efficiently implemented benchmark problems. Using PINNeval, we illustrate our evaluation protocol in relation to established benchmark studies and report on results that challenge established assumptions.